ETT-R&D Publications E. Terrell
IT Professional, Author / Researcher December 2001
Internet Draft
Category: Proposed Standard
Document: draft-terrell-logic-analy-bin-ip-spec-ipv7-ipv8-10.txt
Expires June 13, 2002
Logical Analysis of the Binary Representation and the IP
Specifications for the IPv7 and IPv8 Addressing Systems
Status of this Memo
This document is an Internet-Draft and is in full conformance
with all provisions of Section 10 of RFC2026. Internet-Drafts
are working documents of the Internet Engineering Task Force
(IETF), its areas, and its working groups. Note that other
groups may also distribute working documents as Internet-
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documents at any time. It is inappropriate to use Internet-
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"work in progress". The list of current Internet-Drafts can be
accessed at http://www.ietf.org/ietf/1id-abstracts.txt. The list
of Internet-Draft Shadow Directories can be accessed at
http://www.ietf.org/shadow.html.
Conventions
The '^' sign is the Mathematical Symbol used to represent the
Exponential Operation. Where '2^2 = 4', is the same equation
represented by '2 * 2 = 4', which is the Multiplicative
equivalent. Moreover, it is significant to mention that, the
Version Numbers, IPv7 and IPv8, are not the actual Version numbers
assigned to these IP Specifications by IANA. However, an application
has been submitted for the assignment and use of IP Specification
Numbers that would be used to represent the IPv7 and IPv8 versions.
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TABLE OF CONTENTS
Abstract
Overview
Chapter I: The Analysis of the Errors Plaguing IPv4 and the
Binary System
Chapter II: An Overview of IPv7
Chapter III: An Overview of IPv8 the Enhancement of IPv7
Chapter IV: The Header Structure and the Decimal Representation
of IPv8
Chapter V: Subnetting, Supernetting, and Routing in IPv7 & IPv8
Chapter VI: Conclusion: Outlining the Benefits of IPv7 and IPv8
Security: The Relationship between IPv7 & IPv4, and the Security;
Suggested and Recommended Alternatives for IPv8
Appendix I: Graphical Schematic of the IP Slide Ruler
Appendix II: The Beginnings of the Discovery; Mathematical
Anomaly
Appendix III: The Reality of IPv6 vs. IPv8
Appendix IV: A Succinct Proof of the Fall of the Binary System
Overall, which questions the validity of
Machine Language
References
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Abstract
The Information Age Revolution established by the Internet, as viewed
through its World Wide Popularity, ushered not only a need for additional
IP Addresses, which serve the ever growing needs and demands of every
individual in the World today. Will also be viewed, through the resolution
of the IP addressing problem, as the impetus fueling the Revolution in the
whole of the Mathematical and Engineering Sciences as well. In other words,
the resolution of the problem regarding the need for additional IP
Addresses, and the correction of the Errors inherent in the current system.
Resulted not only in the discovery of two New IP Specifications, IPv7 and
IPv8, which are logical derivatives of IPv4. But, through the Discovery and
Correction of an Error in the underlying Mathematical Logic of the Binary
System. It sustains a more pronounced Revolution, having such a profound
impact, that it produces Results which not only 'Commands the Fall and the
Elimination of the IPv6 IP Specification'(IPng), as the suitable replacement
for the IPv4 Specification. But, it Mandates a Change for the Entire
Foundation of the Method for Enumeration in the Binary System as well.
Needless to say, the daunting implication(s) is that, any change in the
Binary System will produce a corresponding change in Machine Language,
cascading the effects, which will impact Industries all over the world.
Nevertheless, it will become clear, why such temporary fixes as the
Supernetting of IPv4, which yields approximately '4.145 x 10^9' IP
Addresses for the entire addressing system, could not work. And while IPv6
yields a greater number of available IP Addresses, approximately
3.4 x 10^38, it remains slightly less than IPv8's 128 Bit Address
availability of '3.40282 x 10^38'. Furthermore, when noting the benefits
offered by IPv6, which are taunted as being advantageous. No presentation
emphasizing its high lights, can suppress the severity of the drawbacks it
maintains. In fact, IPv6 is not only cumbersome and difficult to use,
implement, and employ. But, it lacks a Mathematically Derived Logical
Structure, which results in a 'Default Addressing Structure' being
superfluously defined. And it retains its association, Mathematical HEX
Translation, with the Binary System this paper proposes to change, because
its Method of Enumeration is wrong (e.g.; 'F = 1111 = 15', See Table 8).
Not to mention, the employment of a Backwards Compatibility with the Error
Plague IPv4 IP Addressing System.
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However, because IPv7 and IPv8 are logical derivatives of the IPv4
Specification. The promises offered by the implementation of these IP
Specifications, are inherent features, which provides: Ease of use and
Implementation; An increase in the number of available IP Addresses; The
controls that optimize IP Address distribution and provides a more gradual
and stable growth; And its effectiveness in the reduction of the 'Cost per
Change Index'. [Which is a measurement used by Companies and Organizations
to determine and compare the 'Benefits' (Gains or Losses) vs. 'Cost'
(Dollars Invested), with the effects of the 'Impact' and, or 'Needs' that
are associated with 'Change'.] Furthermore, while these are just a few of
the innumerable benefits, which grant these IP specifications an
unprecedented superiority over IPv6. They nevertheless, retain a shadow
presence in the possibilities of the benefits, produced by the wake,
resulting in the change of more than a 150 years, which is the History of
the Binary System of Enumeration.
Furthermore, it was reported that the number of IP Addresses in IPv7 was
equal to the IP Address count existing in IPv4. It will be shown
nonetheless, even this calculation proved to be in error, which is a
direct result of the errors inherent in every explanation of the current
IP Addressing System. And while the existing benefits, as seen through the
employment of IPv7 and IPv8 remains a valid conclusion, regardless. These
benefits, which underlie every presentation, are indeed the hallmark
underpinning its logical structure. Moreover, it shall also be concluded
that IPv7 maintains a greater number of IP Addresses than IPv4, a total of
4.278 x 10^9*, which is approximately '133 Million' Addresses greater.
'255 x 256^3 = 4,278,190,080 IP Addresses'
Needless to say, even this calculation represents a loss, because IPv7's
actual IP Address total is equal to '4,294,967,296 IP Addresses', which is
represented by equations '2^32', and '256^4'. However, the reason for this
difference, which shall be discovered in latter Chapters, is that, '256'
is equal to All Binary 1's, which can not be used to designate any valid
IP Address. Notwithstanding, its use, by definition, in the remaining
Octets, if it is not use in the Network Portion of an IP Address, which is
defined by the 'Subnet Identifier'. And while '0', at least in this case,
does not matter because it is an Integer, which is not an element of the
Binary Set. Even so, this still amounts to an un-preventable, and
staggering loss of '16,777,216 IP Addresses'.
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[However, even this IP Address Count Total would not be valid,
that is, not unless the use of '127', as the LoopBack Address,
were not clearly defined. Where by, if the "LoopBack IP
Address" were Defined by only ONE IP Protocol say; 127.1.1.1,
which translates into the Binary Representation given by:
'10000000.00000000.00000000.00000000 = 127.1.1.1 '
(See Table 8 for the Justification of the Binary Representation)
Needless to say, this change would not affect the functional use
nor purpose of the LoopBack IP Address, because its use serves
only the 'NIC' in the Computer in which the Test is performed.
But, the use of any viable IP Address Number in the LoopBack IP
Address, in addition to '127', would not be beneficial for
Reducing IP Address loss. Where by, the preferred choice would
entail a selection that would minimize the loss of IP Address
Numbers. What this implies, is that, the Positive Integer '1'
could be replaced by the Integer '0', as in: '127.0.0.0', which
is equal to '10000000.0.0.0', in the Binary Representation. And
since, the use of the Integer '0' does not effect nor alter the
IP Address total, it is the better choice between the two
options. In either case, the Mathematical operations involving
'0' are clearly defined by the Field Postulates, and should not
change nor affect the outcome resulting from 'Bitwise Anding',
because the Integer '0' is not an Element of the Binary Set.
Which means, its use in any Binary Operation should equate to
the Null Set. Thus, yielding the results given by its former
definition in the Binary System.
Furthermore, since the functions of the "LoopBack Address" serve
only one Computer, and the IP Address associated with its
Network Card, it can be used repeatedly. Therefore, only one IP
Address is necessary for use as the LoopBack IP Address. This is
because the implications of the foregoing, is that; "Only the
Prefix, '127', in the '32 Bit Block Network IP Address', is
necessary for use, when defining the Purpose and Function of the
'LoopBack IP'". In which case, all other uses of '127', when
defined by the 'Subnet Identifier', could be used to represent a
valid Network IP Address.
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In other words, this is significantly less than the 149 million
IP Address Loss in IPv4, which is the result of Errors, failure
to implement a logical structure, and to obey the laws governing
its use. Nevertheless, the beneficial effect this has on the IP
Address count in IPv7, and ultimately IPv8, is a more efficient
use of the Total Number of available IP Addresses. Which
translates to a Total loss of approximately 16.8 Million IP
Addresses, and an increase of approximately 133 million IP
Addresses over the current system. These results are an
unquestionable boon for the IPv7 and IPv8 IP Specifications, and
their IP Address totals, which calculates to a total approximating
'4,278,190,079' IP Addresses, or 4.278 x 10^9*.]
Nevertheless, the calculated IP Address total for IPv7*, when translated to
the IPv8 IP Addressing System, yields approximately 1.091 x 10^12 IP
Addresses available per 'Zone IP', having a total of '255 IP Area Codes'.
Needless to say, this count amounts to a staggering total approximating
2.78 x 10^14 available IP Addresses, in a 64 Bit IP Addressing System,
which uses only 48 Bits to equal this IP Address total. Moreover, while it
was previously concluded that IPv7 and IPv8 were only an exploitation and
expansion of IPv4. It shall be realized that, while IPv7 and IPv8 can be
used in place of IPv4 without any loss of the inherent benefits, existing
applications, other Protocol relations, or a need for testing in any
intra-domain environment. These IP Specification(s) clearly represent a
New and distinct IP System of Addressing.
In other words, in addition to having a dramatic Structural change, its
departure from the current IP Addressing System is a Logical foundation,
which eliminates the errors that beleaguered IPv4. In fact, these IP
Specifications established the first True Global Telecommunication
Standard. Which is the only IP Specification(s) that encompasses the
entire Global Telecommunication Industry, and retains the ease of use and
implementation of the familiar IPv4. Nevertheless, the profound benefit of
IPv7 and IPv8, is that, they provide the entire Global Telecommunications
Industry, as well as every consumer, with enough room for a predicted
growth that would encompass the colonization of the Universe. However,
this is without the 'Multi-Billion Dollar' cost associated with the
training, implementation, or upgrading required by every other 'New IP
Addressing Specification'.
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Nevertheless, the Overview is an attempt to provide the reader with a
succinct introductory foundation of those aspects of the Internet Protocol
encompassing IPv4, which entail both the Class and Classless Systems. This
portion of the presentation will leave intact those parts of the IP
Specification which are directly related to IPv4. While the change that
has been previously discussed as Errors, which has plague this system of
IP Addressing, will be presented in the topics of this paper that deal
with IPv7 and IPv8. The purpose of this method will serve as the necessary
foundation for differentiation, which provides the proof, as would be
needed, to distinguish the IPv7 and IPv8 IP Specifications as a new
Internet Protocol.
In other words, I shall present only those aspects of IPv4 that deal with
its methods for IP Addressing, which are similar and directly related in
functionality to IPv7 and IPv8. This however, should not be viewed as an
over simplification, because the remaining aspects concerning the IPv4
Specification will not change in their respective use, or functional
purpose. Needless to say, the rigor encompassing the correction of the
Errors in 'IPv4' and the 'Binary Method of Enumeration', are serious
enough to render any thoughts to the contrary moot. Notwithstanding, the
impact they jointly maintained, which significantly altered the results of
the initial presentation for the foundation of the IPv7 and IPv8 IP
Specifications. Nevertheless, it should be understood, that the overall
objectives this paper maintains, specifically includes;
1. 'Correction of the Mathematical Errors existing in the
Current IP Specification, and the Errors in the Logic
of the Method for Enumeration in the Binary System'.
2. 'The Development of an IP Specification(s) essential to the
Growth and the Longevity of the Global Internetworking
Community'. Which maintains an overall Superiority to the
IPv6 IP Specification and its Inherent Errors, that results
from the lack of a Mathematically Derivable Logical Foundation,
and its assimilation with the Errors noted in the Current
Foundation of the Binary System'.
3. 'Derivation of the Maximum Possible Number of IP Addresses
from the Mathematical System defined for use in the IP
Specification(s), which results from the completion of
number 2, noted above'. (i.e. the IPv7 and IPv8 IP
Specifications'.
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Furthermore, while the subject matter presented herein represents an
Applied Field of Study. In which the educational demands imposed for an
understanding of its use, function, and application, does not exceed the
requirement for completion of Grade 12. However, to accomplish the
objectives this paper mandates, requires an Analysis of the Theoretical
Foundation of the underlying subject matters from which IPv4, and the
Binary System were derived. Hence, this paper should only be considered as
an excerpt of the underlying subject matter. In which case, it should be
understood, as an opinion I maintain, that an extensive treatment and
comprehensive analysis in a more gradual, or incremental approach, is the
preferred methodology for presentation to the general audience. The
thought here, regardless of the subject matter, is that, the justification
is fostered when any significant change alters the traditional and
established foundation of the Subject being presented. In other words, to
avoid unnecessary arguments and the possibility of confusion. The
prerequisite this paper maintains, commands and assumes, is that, the
readers maintain a level of competency equivalent to either an Engineer,
Mathematician, Computer Scientist, or Logician.
And for this, I apologize.
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Overview
There are several issues of concern when dealing with the topic of IP
Addressing. However, the two main aspects of addressing in the IP
Specifications that warrant mention are, Addressing and Fragmentation.
Nevertheless, since the methods employed in fragmentation and the IP
Specifications dealing with the interaction with other Protocols or its
Modules, will not change as such, they will not be a subject entertained
in this Overview. Where as, the matters which are presented, deal only
with the subject of Addressing and Address Availability in the IP
Specifications for IPv4, which encompass the 'Class and the Classless
Systems'. Hence, all other related subject matters are beyond the scope
of this presentation.
Nevertheless, the current IP Specification methodology for IP addressing
in the present Addressing Scheme, is the 'CLASSLESS System'. However,
while the IP Specifications employing the 'CLASS System' of Addressing are
no longer used. There are similarities remaining in each of these systems,
especially since they are both derived from the IPv4 IP Specifications.
That is, the shared practices, descriptions, and methodologies of each
system is governed by and identified as being:
1. 'The IPv4 Class Address Range';
2. 'The 32 Bit IP Address Format';
3. 'The Method for Subnetting';
4. 'The Principle of the Octet', and
4a. 'The Binary and Decimal representations of the IP
Address'.
'The Binary and Decimal representations in the IP Address'
The Binary and Decimal representations are two different mathematical
systems of enumeration. In which the Binary Representation is a
Mathematical System dealing with the operations of Logical Expressions
having only two states, which can be translated to represent Integers and
Fractions. While the Decimal Representation, is a Mathematical System
involving the operations of Integers, and can only represent the Whole
Numbers (Positive Integers) used in Counting. Needless to say, in spite of
the existing differences. These mathematical systems are shared and used
by both, the Class and Classless Systems.
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The difference however, underlies the structure of their respective
Mathematical Systems. In other words, only two Binary Representations
exist, that being a '1' or a '0'. However, the combined use of One's and
Zero's in a series, can be used to represent any Integer. That is, for
some representative combination of 1's and 0's in a series, there can
exist one and only Integer, in which this Series is Equals. Even then, a
Mathematical Equation involving the Integers must exist, which would
'Translate' this Binary Representation into its Decimal (Integer)
Equivalent. In which case, the result would be an enumeration
Representing 'One-to-One' Correspondence that is an Expression of
Equality. In which two different systems represent the same
quantity. Nonetheless, each would retain an independence from the other, in
any quantitative result of their employ, governed by the Mathematical Laws
specific to their operation.
Nevertheless, the mathematical operation used to perform this Translation
between the Binary and Decimal representations is Multiplication. In which
the equation is an Exponential Operation involving Integers. Where by, for
every Translation of any Decimal Integer) number is given by Table 1a.
TABLE 1a.
4. 3. 2. 1.
X X X X <----------|
| | | | |
| | | | v
1. | | | |<---> 2^0 = B x 2^0
| | |
2. | | |<---------> 2^1 = B x 2^1
| |
3. | |<---------------> 2^2 = B x 2^2
|
4. |<---------------------> 2^3 = B x 2^3
5. etc.
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Where it is given that, the value of B represents the Binary representation
of either a 1 or a 0. Which will equal the value of X (the top of the
Table). Needless to say, it should be clear that any Decimal (Integer
Value) can be represented using this method. Where by, A Binary value of 1,
in the B column of equation 1, is a Binary value of 1 for its corresponding
X, and the result of the equation is the Decimal (Integer value) value
equal to 1. Hence, the Decimal representation is equal to the Sum of the
results from the Equations for which the value of X equals 1, and this
process proceeds from the Left to the Right.
Nonetheless, while the process of Translating a Decimal (Integer value)
number to its Binary equivalent seems a little more involved. It is
nonetheless, the reverse of the process as noted above. Which is shown
in Table 2a.
TABLE 2a.
5. 4. 3. 2. 1.
X X X X X <-------------> |
| | | | | |
| | | | | v
1. | | | | |<---> 2^0: D - (B x 2^0) = Y
| | | |
2. | | | |<---------> 2^1: D - (B x 2^1) = Y
| | |
3. | | |<---------------> 2^2: D - (B x 2^2) = Y
| |
4. | |<---------------------> 2^3: D - (B x 2^3) = Y
|
5. |<---------------------------> 2^8: D - (B x 2^8) = Y
In other words, the Reverse process proceeds from the Right to the Left.
Which means, according to the corresponding equations: 'The Binary
Representation of any Decimal Number D, is equal to the Decimal number
(D) minus the Series, starting with the Highest Value of the Exponential
Equation representing the Binary Number, which yields a Positive Integer
'Y'. Until the value of their Difference, Y, at some point, is Equal to
Zero.
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Nevertheless, it is clearly a conclusion, as noted in the Tables above,
that the Binary Representation of an extremely large Integer number,
would indeed be a very long series of 1's and 0's. Especially since, 1
and 0 are the only numbers used in enumeration in this mathematical
systems. In which the equality of a One-to-One correspondence can exist
only through the use of a mathematical Translation, which clearly shows
the existing differences in their representations.
Nevertheless, the Tables above provided without any specifics or
consideration regarding any defining parameters, an explanation of the
method regarding Mathematical Translation for the representation of
either a Binary or Decimal number, into one or the other.
To be more specific however, in the IPv4 Addressing System, there are
Boundary's imposed upon the size of the Binary Series and the Range of
The Decimal (Integer Values)Representations, which help to define the
32 Bit Address Range of the Internet Protocol. Where by, there can only
be 8 Bits (Binary 1's and or 0's) in a Binary Series, which provides,
in Translation, a Decimal Range of 1 - 255, inclusive.
Furthermore, it can also be concluded that a direct correlation between
the 8 digit and 3 digit displacements that are the foundations of these
respective systems, can not be achieved without some form of Translation
or multiplication Factor. Which would render their respective
displacements Equivalent. However, it should be clearly noted. There is
soundness in any argument for logical foundation that would support such
a justification. That is, a One-to-One Correspondence between these two
Mathematical Systems could not be achieved without it. In other words,
while it is clear that this Digital Representation is an existing
difference between them. It should also be understood, that even without
Translation they each can only represent one Integer Value.
Needless to say, the possibility of Error in the Calculations involving
either of these systems is unavoidable. Especially when either of these
Mathematical Systems is used to represent the value, which are the
Results of the other. That is, errors become impossible to avoid, with
or without performing the necessary Translation to achieve the
One-to-One Correspondence. Which maps accurately the Total count of one
system to that of other. Saying the very least however, it seems to me,
the choice would be to allow either the Machine to manipulate the Binary
Numbers, or calculate using only the Decimal numbers, then translate the
result to a Binary Representation.
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'The 32 Bit Address Format and the Principle of the Octet'
The 32 Bit Address Format in use today, comprises 4 sections, each
Having a Binary Series of 8 Bits which can be any combination of 1's
and 0's. Hence the name, Octet, represents the 8 Bit Binary
representation, of which there are 4 that make up the 32 Bit Address
Format. Nevertheless, its Decimal Translation, yields a Dotted Notation
having an Integer Range of 0 - 255 inclusive.
'The IPv4 Address Class System'
The IP Class System, while somewhat blurred through the use of the
Subnet Mask in the Supernetting methodology of the Classless System,
it has not yet, lost the significance of its use.
Nevertheless, it is given by the defacto Standard that the IP Class of
A given Network Address is determined by the Decimal value of the First
Octet, which relative to the IP Address Class Range in which it is
associated. This method is used in conjunction with the Default Subnet
Mask to determine the total number of IP Addresses available for the
calculation of the total number of Networks and Hosts, and their
distribution counts for every IP Address Range. Where by, the Default
Subnet Mask maintains a Decimal value of 255 for every Octet in which
it is assigned. This Decimal value translates to a Binary Representation
Of all 1's, or 8 Binary 1's (11111111) in every Octet in which it is
used.
However, the mathematical method employed to resolve the Network IP
Address in which the Default Subnet Mask is associated, is called
BITWISE ANDING. Nonetheless, Bitwise Anding is a mathematical operation
Involving the Binary System, and is given by Table 3.
TABLE 3
1. 1 and 1 = 1
2. 1 and 0 = 0
3. 0 and 0 = 0
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Where by, the process of BITWISE ANDING is a Machine calculation that
Can be performed by anyone. Its functional purpose is the resolution of
an IP Address, which can be either a Network or an associated Host.
Nevertheless, the IP Class structure while providing a count of the
Total Networks and Hosts for each IP Class, as shown in Table 4. It
additionally, provided the IPv4 Addressing System with a structure,
methodology, and a small set of rules to govern the distribution,
deployment, and management of IP Addresses within any given Internetwork
or Network domain.
Nonetheless, Table 5 provides the description of its Binary
interpretation, which is related to the number of available Binary
Digits that can be used, when translated, to determine the Decimal
Notation an IP Address, and the total number of addresses available.
Table 4.
Structure Decimal of the IPv4 Representation IP Class System
1. Class A, 1 - 126, Default Subnet Mask 255.x.x.x:
126 Networks and 16,387,064 Hosts: 0
2. Class B, 128- 191, Default Subnet Mask 255.255.x.x:
16,256 Networks and 64,516 Hosts: 10
3. Class C, 192 - 223, Default Subnet Mask 255.255.255.x:
2,064,512 Networks and 254 Hosts: 110
4. Class D: 224 - 239; Used for Multicasting, No Host: 1110
16 x 254^3 = 262,192,024 IP Addresses available
5. Class E: 240 - 254; Denoting Experimental, No Host: 11110
15 x 254^3 = 245,805,960 IP Addresses available
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Table 5
Structure of the Binary Representation of IPv4
1. Class A: 1 - 126, with 8 Bit Network Count and 24 Bit Host
count or 16,777,216 Hosts; Where 0 (Zero ) and 127 reserved
unknown Network and Loopback, respectively.
2. Class B: 128 - 191, with 14 Bit Network Count and
16 Bit Host count or 65,536 Hosts
3. Class C: 192 - 223, with 24 Bit Network Count and
8 Bit Host count or 256 Hosts
4. Class D: 224 - 239; Used for Multicasting,
32 Bit IP Address Count
5. Class E: 240 - 254; Denoting Experimental,
32 Bit IP Address Count
Note: There is no Division of Classes D or E. In fact, the
definitions provide descriptions of their functional use.
The Rules that enabled and govern the structure of the IPv4 Addressing
System, are indeed laws. Where by, either the Internetwork or Networking
Domain could become disabled, if a violation of any one or more of these
laws occurred. Nevertheless, the laws as outlined in Table 6, represents
a Set of Restrictions regarding the Binary and Decimal values assigned
to a given IP Address. However, any further, or more detailed analysis
of Table 6 would be superfluous, because the presentation itself, is a
definition.
Nevertheless, notwithstanding the benefits that the Hierarchical
(0rganizational) Structure of the IPv4 Class Addressing Scheme provided
the Networking Community as a whole. The treatment rendered, regarding
its explanation, while somewhat shallow, shall suffice the overall
purpose, which outlines the objectives of presentation.
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TABLE 6
1. The Network Address portion of an IP address cannot be Set
to either all Binary Ones or All Binary Zeros
2. The Subnet portion of an IP address cannot be Set to either
All Binary Ones or All Binary Zeros
3. The Host portion of an IP address cannot be Set to All
Binary Ones or All Binary Zeros
4. The IP address 127.x.x.x can never be assigned as a Network
Address
'The Differences between the Class and the Classless Systems'
The fall of the IPv4 Class System of Addressing, as such, is viewed the
result of the lack of IP Addresses available for distribution, which
services the very need of the every growing Global Internetworking
Community.
Nevertheless, the IPv4 Class System has been described as an Organized
Hierarchical Class Structure. But, this not a definitive depiction,
Noting that there are parts yet remaining within the IPv4 Class System,
that are indeed wanting of a more conclusive and exacting definition of
their functional purpose. This is a reality, which becomes even more
apparent upon analysis of the use of Default Subnet Mask for the Class
B. That is, when compared with the results of Appendix II and the
definition of the use and purpose of the Default Subnet Mask. Where by,
it is clear from the definition of the Default Subnet Mask. That its
purpose defines the location of the Octet, which is assigned some
Decimal Value from the IP Address Class Range.
While its second use is the identification or resolution of a Network or
Host IP Address. However, clearly this is not sufficient. This is
because, the processes underlying its functional purpose are assumed,
and based upon descriptive use, and not the soundness of Logical
reasoning derived from definitions.
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What this implies, is that only the first Octet of any given Default IP
Address, maintains the right to be governed by some value relative to
the IP Address Range, which defines the IP Class to which any given IP
Address belongs. This, to say the very least, confounds the purpose and
use of the Default Subnet Mask in general, if not overall. This is
especially true for the results of Supernetting in IPv4, and maintains
an even greater significance regarding truth as to the possible root
cause for the IP Address shortage in the Class System. Nevertheless,
while the former might seem questionable. The latter however, entertains
more plausible reality, especially since the Supernetting of IPv4
resulted in a significant increase in the number of available IP
Addresses in IPv4.
In other words, given the Class B as our example. Which has a Default
Subnet Mask of 255.255.000.000. The foundation for this argument becomes
apparent from an analysis of the results the given by equation 1a. Where
it is shown that we could conceivably derive two different Decimal
values, which would be an equally accurate determination of the number
of Networks present in Class B. That is, provided there does not exist a
more precise definition, and or, functional use of the Default Subnet
Mask. And this is true, at least, regarding the present interpretation
and use of the Default Subnet Mask.
1a. 64 x 254 = 16,256 "OR" 64 x 64 = 4,096
(That is, given that: Class B 128 - 191,
Default Subnet Mask 255.255.000.000)
What this implies is that, at present there does not exist within the IP
Specifications of IPv4 definitions we can use, which would provide any
degree of certainty regarding the correct methodology to be employed in
IP Addressing. And while, this reported anomaly does not directly effect
or prevent IP Addressing. It clearly demonstrates regardless of the
method employed, that these are different numerical values representing
the same object. Which are both, significantly less than the reported
number of available Network Addresses as determined to be the calculated
result of the Binary value given by 2^14 (16,384). Furthermore, it
should be understood without the indulgence of another example, this
conclusion is applicable to the Class C as well. (This problem is
eliminated in IPv7.)
NOTE: This issue is even more pronounced when one
considers the Bit Count of the Number of Host
for each of the Default IP Address Class Ranges,
and its corresponding Decimal value.
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Nevertheless, the concept of Masking and its inverse, 'Un-Masking',
deserves some attention. That is, the Subnet Mask, which is the
Catalysis for this presentation, is used by both of these Systems, the
Class and Classless. However, it is the concept of the Subnet Mask, as
it shall be discovered, which maintains a far greater significance when
distinguishing the difference between these two Systems.
Notwithstanding, the notion, idea, or evolution of the Class System,
Which would have been a resulting consequence, predicated by some
inseparable component regardless. Where by, the misnomer, 'Classless',
is not the existing difference, which mandates the defining distinction
that separates these Systems. Needless to say, the doubt, which the
underpinning of this conclusion surmounts, is the functional definition
and the associated boundaries of the IP Class Addressing System. Which
is indeed, the IP Addressing Divisional Methodology employed by each of
these Systems.
Nonetheless, without any support outlining or defining a Structure, one
such component whose defined function, which would have caused the
predestine evolution each, is indeed that of the Subnet Mask. Where by,
the associated problems concerning IP Address availability were resolved
through the creation of another Sub-Division of the Subnet Mask. Which
indeed, is the 'DEBARKATION LINE', defining the difference between these
Systems. However, this was a two-phase progression, involving two
divisions of the Subnet Mask, the VLSM and the SUPERNETTING of the Class
C, CIDR. Nevertheless, Supernetting maintains the distinction as being
the USHER for the Classless. That is, the underlying difference
distinguishing these Systems. It does moreover, impose a barrier, which
limits the overview's presentation to the relevance pertaining thereto.
Nonetheless, it is worthy of mention, noting that Supernetting can be
viewed as a refinement of VLSM, Variable Length Subnet Mask. However,
the promises of Supernetting, when viewed from its exploitation of the
Class C, as relinquishing the dependence upon the Class Structured
System, can be realized only if this application is applied to the
remaining Classes. At least, this is the current and accepted outline
of the Populist's view of the objectives presented. Notwithstanding,
the most discomforting drawback encompassing this objective, is the
elimination of the process and use of the Default Subnet Mask(Which is
blurred anyway.). Which ultimately means, the redefining of the
functional use of all Binary 1's and 0's within the any given Octet,
and the loss of the Logical Structure in IP Addressing as well.
Nevertheless, there is indeed a warrant for an analysis of the process
of Supernetting, which transcends the obligations of this overview, and
imposes a dialectic upon this presentation in general. Needless to say,
the foundational support of this argument is the underlying objectives
found upon the Internet Draft upon which this presentation resides.
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Nonetheless, prior to the analysis and investigation of Supernetting, a
brief introduction of some of the foundational principles of Subnetting,
from which Supernetting is derived, is indeed required.
The Binary Representation of 1's and 0's, and the specific rules for
their combination or usage, is the chosen form of communication used in
Machine Language. The principles of BITWISE ANDING was presented in the
Section entitled, "The IPv4 Address Class System", which is the
Mathematical method used by the Computer when the Subnet Mask or the
Default Subnet Mask is used to resolve either a Network or Host IP
Address. That is, if you were given a Decimal Network IP Address of
172.16.182.19, the Machine or Computer could not read nor translate
these Integers into any usable format. That is to say, there is a
Translator for the Input and Output for the Computer, because its
language is of the Binary Format. In other words, the Computer would
read the Input of the IP Address, 172.16.182.19, as given in figure 1.
Figure 1
Bit Map of the 32 Bit IP Address
10101100 00010000 10110110 00010011
However, through the use of the Default Subnet Mask, 255.255.255.000,
and its Binary translation, as given in figure 2. The Computer or Router
could, through the use of Bitwise Anding resolve the Network Address for
the given IP Address, as shown in figure 3. Whose Decimal translation
through the Binary Mathematics of Bitwise Anding would yields the
Network IP Address as, 172.16.182.000.
Figure 2
Bit Map of the 32 Bit IP Address
11111111 11111111 11111111 00000000
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Figure 3
Bit Map of the 32 Bit IP Address
10101100 00010000 10110110 00000000
Nevertheless, there are several advantages that can be ascertained
Through the use of the Subnet Mask, and even more, if the mathematics
of Bitwise Anding remain same. In other words, the problems associated
with the difference between the Binary and Decimal methods of
enumeration do not exist within the Machine's Mathematical Calculations
for the Translation into the Binary format. That is, the Binary Format
allows for the manipulation of individual BITS. Where by, the resulting
Decimal Translation could be either a Fraction or an Integer. In which
case, it is assumed that any resulting Fractional Component produces a
Range of possible Subnet numbers in which several Network IP Addresses
might belong. (Supernetting)
Nonetheless, the Breaking-Up, or the division of any Network into
Smaller Sub-Networks, is called Subnetting. Which is accomplished
through the use of the Subnet Mask. Where the Subnet Mask can be used or
mapped onto any Octet, except the first Octet, which is used to identify
the Address Class Range to which a particular IP Address might belong.
Needless to say, there is a De Facto process by which a Subnet Number is
chosen, and these numbers are given in Table 7.
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TABLE 7
Values of Least Binary Decimal Number
Significant Bit: Representation: Equivalent: of Subnets: Host/per
^ ^ ^ ^ ^
| | | | |
v v v v v
0 00000000 0* 0 0
2^7 10000000 128 1 128
2^6 11000000 192 3 64
2^5 11100000 224 7 32
2^4 11110000 240 15 16
2^3 11111000 248 31 8
2^2 11111100 252 63 4
2^1 11111110 254 127 2
2^0 11111111 255* N/A
Note: The 'Asterisk' represents Values that can not
be used by the OCTET, which is define by the
'Subnet Mask', this is a Law/Rule.
Nonetheless, the first example of the use of the Subnet was that of the
Default Subnet Mask, which was used with the Binary Mathematical
Operation of Bitwise Anding to resolve the Network IP Address. However,
from the list summarized by Table 7, the Subnetting concept can be
further expanded, and use in an example to demonstrate the division of a
Network Address into several smaller Network Addresses. That is, if
given the Parent Network IP Address of '172.16.0.0', for which smaller
Subdivisions are sought. This being the conclusion based upon an
examination of the over all Network performance and needs. Then the
appropriate Subnet Mask can be derived from the 7 choices given by Table
7 based upon the conclusions.
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Wherefore, if '252' is chosen, the IP address of this Decimal Number
corresponds to the Subnet Mask given by an IP Address of '225.255.252.0'.
In which a total number of 63 available Subnets can be generated from
'252'. Which is the result generated by its (252) division by the factor
determined as being the value of the Least Significant Bit of its Binary
Representation (4). However, the inclusive count would maintain a composite
value equal 64, which includes 252 in the total. Nevertheless, the
resulting Subnet IP Addresses generated would be determined by sequential
additions of the Least Significant Bit (4) to the Parent IP Network
Address. Which also determine number of hosts per Subnet, and is summarized
in Table 7.
Notwithstanding, that the example above was a demonstration of the concepts
and the principles underlying Subnetting. However, its principles and
concepts needless to say, is the foundation from which the principles
underlying the concept of Supernetting is derived. Moreover, since it is
the First Octet that is reserved for the Identification of the IP Address
Class to which any IP Address belongs. The example chosen could have been
selected from any one of the 3 primary IP Address Classes. Hence,
Supernetting is the Subnetting of an IP Address having the Default Skeletal
Structure as defined for the Class A.
The concepts for the principles and beliefs in the Classless System, in
closing, is a derivation from the concepts of 'CLASSLESS INTERDOMAIN
ROUTING' (CIDR). In which, the basic strategy involves the 'Combining
of Multiple IP Addresses into One AGGREGATION' by using IP Bit Address
of the Subnet Mask from one of the Address Class Divisions, essentially
forming One Network. Hence, the creation of an Addressing System in which
every Division would have the same 'Default IP Address Structure'. And
whose resulting overall IP Address number would exceed that of the initial
IP Address Class, and could be Routable using a 'One Route Path' for its
thoroughfare. In other words, the only real difference between the CLASS
and CLASSLESS Systems is that of the Routing Methodology they employ.
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Chapter I: The Analysis of the Errors Plaguing IPv4 and the
Binary System
The Overview's presentation highlighted some of the most significant
principles involved in the IP Specification of IPv4 Addressing. It also
provided a glimpse of some of the problems associated with the error(s)
existing in the IPv4 Addressing System. However, while almost every
inherent flaw that exist within this System can be shown to be an ambiguity
resulting from the lack of an adequate Logical structure or precise
definitions. There also exist another foundational error, which thwarts all
the traditional proofs that would encompass an elementary analysis and
presentation. In fact, I can conclude with a measurable degree of
certainty, especially since the resolution of this problem entertains
elements from the branch of Mathematics known as Number Theory, and the
principles derived from my works dealing with the proof of Fermat's Last
Theorem, from which the 'Logic of Quantification' was derived. That this
error, which is the problem associated with the difference existing between
'255' and '256', is not only the source of this confusion, but it severely
hampered the results of every mathematical calculation in the IPv4
Addressing System.
Furthermore, it should be understood, this is a problem that includes
IPv7 and IPv8. In other words, the overwhelming significance that underlies
these IP Specifications as the Logical Succession to IPv4, is the use of an
identical method of enumeration for IP addressing. Nevertheless, the
initial proof of Fermat's Last Theorem concern the concept of the "Common
Coefficient" and the association thereto, which contrasted the difference
between Exponential Functions. This difference, which form the bases for
proving Fermat correct in his assumption: " There are no solutions in Whole
Numbers to the Equation; 'X^N + Y^N = Z^N', where N is greater than 2",
also maintains and establishes the "Common Coefficient" as the binding
force for its validity. Where by, it was a fact established within the
proof, that in all cases there must exist a "Common Coefficient",
which was determined to be a sequential growth pattern starting with and
incremented by an additive factor of '1'. Which also, mapped directly with
the "Counting Numbers"; 1, 2, 3, ... etc.
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However, the underlying logic here, concerned only the Base and the results
from the calculation of the Exponential Power to which it was raised. Which
also established that these conditions were not valid for all values of the
Base, and were true only for Exponential Powers Equal to 2. In other words,
Fermat was correct in his assumption 'If and only If' there exist an
"Common Coefficient" between the Base and the results from the Exponential
Power to which it was raised, which itself a is whole number (Positive
Integer). These results were indeed profound, because they promoted the
need to rethink the very foundation underlying the entire mathematical
field, and enhanced the use of the Exponent with the precise definition of
being a Logical Operator. Who's underlying function and operation was also
a 'Short-Hand' method to reduce the size of an equation, which contained
repetitious operations involving identical multiplicands or expressions.
What this ultimately meant, was that, its functional use now maintained a
more broader benefit, which could now be applied to Pure and Applied
Mathematics, and their underlying Logic as well. Furthermore, while this
conclusion was derived from the first proof of Fermat's Last Theorem, it
served no direct purpose in the proof.
However, this was not the first use of the Exponent in logical Analysis.
In fact, George Boole, in his "Theory of the Laws of Thought', use the
Exponent to establish the significance of '1' and '0' as a foundational
premise, which the "Truth Table" and "Boolean Algebra" were later derived.
Nevertheless, the Exponent assumed a pivot role in a second proof. Where
by, the Exponent, for the first time, was defined as having obtain a
permanent place in a Pure Logical Environment. This was indeed an
advancement in Logical Analysis. Which not only allowed for the Exponential
Expansion of the Operations involving Set Theory and the Field Postulates,
developed the Theory for an Algebra that is Finite and obeys the Closure
Laws, but laid the foundations to derive the "Distributive Law for
Exponential Functions" as well. In other words, George Boole's work
established the foundation from which the Binary Mathematics used in IP
Addressing was derived. Which in every respect, it is indeed equivalent, if
not identical to any Mathematical Theory, which must obey and be governed
by not only the Laws and Rules pertaining thereto, but, those Laws and
Rules governing the underlying Logic as well.
Nevertheless, the above represented the grounding foundation for the
analysis to determine the difference between "255" and "256", and the
reason for assigning the Binary Number 2^8 as being equal to 255. Which
raises several questions concerning the How's and Why's, regarding an
explanation, which would rationalize the reason for building the foundation
of the Binary Mathematics upon an Error. Where by, equation æ1Æ provides
the platform from which this analysis shall begin.
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1. 2^8 = 255 = 11111111
The above represents the current and acceptable value for the Binary
Representation of the 'Decimal' number 255. However, this is truly an error
in the calculation for the determination of value of 2^8. Where by, the
actual value of 2^8 is given in equation 2.
2. 2^8 = 256 = 11111111
While the actual Binary Representation for 255 is given by equation 3.
3. 2^7 + 2^6 + 2^5 + 2^4 + 2^3 + 2^2 + 2^1 + 2^0 =
128 + 64 + 32 + 16 + 8 + 4 + 2 + 1 =
255 = 11111110
Nevertheless, it is clear from any study of Elementary Mathematics that the
Exponent can be assigned to any value maintained by the variable 'X'. In
fact, it is from this association with the variable, that a Theory of the
Operation and the Laws governing the Exponent were derived. And while its
value may be associated with any Number Group within the Field Postulates.
It is the result from the Equation of the combined value of Base and the
Exponent, which determines the Number Group it belongs.
However, the functionality of the Exponent, which established its use in
logical Analysis, and forms the foundation for this argument, is that, the
Exponent can never generate a Null value, or be equated Zero. Needless to
say, the significance of this conclusion, emphasizes the importance of the
'Short-Hand method' for representing any Mathematical or Logical
expression, in which repetition becomes the issue. Which again, is
dependent upon the value resulting from an argument involving the Base and
the Exponent in the Equation in which it is used.
The fact that the Exponent can not generate a value of Zero in any equation
in which it is used, is a fact derived from the laws governing the
operations involving the Exponent, and it is a conclusion given by equation
4. Where by, it was established in the Elementary foundations of Algebra,
that:
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{(A, X) | 'A' and 'X' are both elements of 'R'};
when only 'X' equals 0:
4. A^0 = 1,
and if there exist a case, where by:
{(A, X) | 'A' and 'X' are both elements of 'R'},
when only 'A' equals 0:
5. 0^X = 0,
and in all cases, we have:
{(A, X) | 'A' and 'X' are both elements of 'R'},
when both equal 0:
6. 0^0 = 0,
and again, in all cases, we have:
{(A, X) | 'A' and 'X' are both elements of 'R',
when 'X' = 1:
7. A^1 = A
These are the fundamental Principles of the Exponent, which invokes the
provision that allows the Exponent to be utilized in both pure and applied
Mathematics or Logical Analysis. However, 'George Boole' did not seem to
grasp these principles, but he clearly understood the logical implications
when the value of the Base equaled either '1' or '0', in an equation having
an Exponent equal to 2.
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Nevertheless, it should be pointed out that, while equations '4', '5',
and '7' are established laws governing the operation of the Exponent,
Equation '6' is not, but, it can be shown as a resulting derivative. In
other words, the Principles of the Exponent established a 'Conditional
2 State' relationship between the Base and its Exponent, that does not
alter the value of the expression when either of their values is a '1'
or a '0'. These states or conditions, which are associated with '1' and
'0', yields a Constant result that is independent of the changing value of
either the Base or the Exponent, depending upon which of the equations
above noted are used. However, there is only one state in which the Base
and the Exponent are equal, and the result of this Equation, is an identity
equaling that given by these components, which is 'A True Value of 0'.
Nevertheless, what the foregoing suggest, relative to the respective
values of the results from all of the Equations noted above, and its Base
and Exponent. Is that, the Exponent itself, is another form of Counting,
which determines the number of multiplicands used in the equation yielding
a Product. This conclusion becomes even more evident, when the process of
this New form of Enumeration is clearly understood. Where by, it is from
'The Method of Quantification', that the concept of the Common Coefficient
obtained not only a greater significance, but an overwhelming value in the
proof of Fermat's Last Theorem. In other words, consider the Law, as
deduced in Elementary Algebra, which provides the logical justification for
equation 4, noted above.
8. "If A, C are elements of R, and A is not equal to 0, where b,
p are elements of N, where b > p, then;
8a. A^b/A^p = A^(b -p) and (A/C)^b = A^b/C^b
Which means:
8b. For every A that is an element of R, and A is not
equal to 0 and b, p are elements of N, and b > p, then:
A^b/A^p = A^(b -p), this means, that if b = p, then;
A^b/A^p = A^(b -p) = A^0, and Since, b = p, and p = b
Therefore,
8c. A^b/A^b = 1, Hence, A^b/A^b = A^(b - b) = A^0, then
8d. A^0 = 1
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Where by, it should be understood that, 1 x A^0 = A^0,
and '1' is the Coefficient of A^0, which is also equal
to '1 x 1 = 1 x A^b / A^b = 1 x A^(b - b) = 1 x A^0',
for the {1, A, b} | 1, A, and b are elements in 'R'.
In other words, if this were an actual mathematical operation, in lieu
of a method of Counting, then any equation having an Exponent whose value
is zero, would generate a value of zero for the equation in question. This
is because, the Exponent is nothing more than a 'Short-Hand' method for
representing the number of multiplicands that repeat within a given
equation, which answers the question; 'How many Multiplicands equaling the
value of the Base are there?' And in equation 4, noted above, since there
are no (zero) multiplicands, then the result is equal to the value of the
Coefficient, or '1'. Which is noted by number '8' above, as being equal to
'1 x 1 = 1', where '1 = A^b/A^b = A^b - b = A^0'.
Thus far, I have spoke of the Exponent as being another method of
Counting'. However this, in and of itself, is meaningless, because there
are several ways, and forms of enumeration. To be specific however, when I
speak of Counting, I am referring to the Set of 'Positive Integers'. While
yet, I have already mentioned that, the Exponent can represent the value of
the any variable, which is an element in 'R'. But, the purposes expressed
here, concerns the Binary Representation, and the inherent method of
enumeration is the 'Positive Integers'. The point to be made here, is that,
there must exist a One-to-One Correspondence between the value Exponent,
equal to the variable 'X', and the Number Points on the line, the Positive
Integers, represented in figure 4 below.
FIGURE 4
--+--+--+--+--+--+--+--+--+--
0 1 2 3 4 5 6 7 8
However, before I can begin this analysis, I must first establish where
the starting point for the Binary method of enumeration would exist. That
is, I must first establish the location, with respect to the Number line,
of the FIRST POSITIVE INTEGER. This is the location of the Point in which
any succession, by an additive factor of '1' would begin.
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Nevertheless, while the Base, Exponent, and their Result, are elements of
'R'. The 2 states, '1' and '0', which combine to represent the result from
this equation, are not elements of 'R'. And while, George Boole Employed
their use in his work, because these, at the time, were the only values
that did not change the result of an equation, regardless of the value
assigned to the Exponent. This fact, needless to say, is evinced by the
'History of Mathematics', because it is recorded that 'Set Theory' was
developed about the same time period as the work of George Boole. In other
words, the 'Operators' used in Mathematics are not the same as those used
in the Logical Analysis of Statements. And it is this fact alone, which
allowed the Exponential Expansion of 'Set Theory', that not only resulted
in the "Distributive Law of Exponential Functions", but the evolution of
"Finite Mathematics" as well.
What this means, is that, the 'States', '1' and '0', can not have the same
meaning as would result if they were defined as being elements of 'R'. This
is seen true because, NO Statement can have or maintain a 'Zero' meaning or
value. And if the contrary were the case, then the statement would not
exist, because its value would be defined as 'NULL'. In which case, there
would be absolutely no distinction between a 'Null' or 'Empty Set', and one
in which its members were not related in some comparison. Which would yield
a 'Null' result, if such a comparison were made between 2 or more
'Statements', and they were all distinctly different. In other words, '0'
is a Symbolic Binary Notation used in Binary Mathematics, which has
absolutely No relationship with, nor is it equal to, the Null value that is
Empty, or the non-existent representation provided by 'Zero', when '0' is
an element of 'R'.
The conclusion of the foregoing becomes even more evident, when an
understanding of the function of the Base and equation 6, as noted above,
is achieved. Where by, it should be understood, that the Base in the
Exponential Equation of Binary Mathematics, represents the total number of
'States' contained in the 'Set' of all elements representing the members of
the Binary Notation. In this case, there are only 2 elements or members of
this 'Set', which forms the Logic of its foundation.
10. {(1, 0) | (1, 0)} are Symbols, which are the
elements used in Binary Notation.
Nevertheless, it should be emphasized that, equation 6 represents a
condition in which the 'Set', whose members are elements of the 'Binary
Notation', as noted in 10 above, is 'Empty'. That is, it contains No
members, and represented by 11 below.
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11. "If there exist such a case where (1, 0) = ( , ), then
{(1,0) | (1, 0) = {0}, is the 'Null Set' and
contains No members." Expressed Mathematically, we have:
11a. 0^0 = 0
What this means is that, the Symbol '0' in Binary Notation, is Equal to
Zero, when '0' is an element of 'R'. The reasoning here, is that, there
must exist, in Binary Notation, a Point of Progression By some
representative of '1', which would generate a Series in Counting. The
resulting Series must maintain a One-to-One correspondence with the
'Positive Integers', and can only utilize the "1's'" and "0's" as a 'Method
of Counting' to achieve this result. In other words, the "1's" and "0's" as
such, do not maintain a distinct value, as such, in Binary Notation. They
in essence, establish the Foundation, which is the 'Number Pair' in Binary
Enumeration, used for Counting. Which ultimately means, they do not, and
can, maintain nor establish by themselves, a direct relationship with the
'Positive Integers'. In which case, it would be their combine usage, which
provides a 'Method of Counting' that represents some Numerical Value being
an 'Element of R'.
Therefore the meaning of the results of equation 4, as noted above: "Is
the 'Set' of All the Elements contained in the 'Set', which represent
the elements of the Set containing the members representing the 'Binary
Notation', can have ONE and only ONE member". Which means in addition,
that when there exist such a case as denoted by equation 4, then the
situation is that, only one possible result can be derived. This implies
moreover, the existence of a 'Count', which is number whose value is
inherent in the count of the total number of 'States' that exist, which
is also a 'State'. In other words, the total number of possible 'States',
which is represented by '1', is equal to 2, and the total number of 'Non
-Zero' 'States', that is represented by '0', is equal to 1.
Nevertheless, the Logical reasoning of the latter is established and
validated through the used of 'Truth Table Analysis'. Where by, given any
Statement, which can be either True or False for the same condition, we
have:
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12a. If in any Statement, when such conditions are set forth,
that the Statement represents a value that is True, then
there are 2 equal possibilities. Where by the Statement
itself, is either 'True AND False', or it is 'True OR
False', these are the only possible conditions that exist.
This is to say, for any True Statement, the total number possible of
'States' that can exist, which represent the value of this Statement, is 2.
12b. 'True AND False is True, or 'True OR False is True'
Which is expressed Logically as, 1 = 2; 2 possibilities
represented as:'
1 = 1 'AND' 0 = 1, or, 0 = 1 'OR' 1 = 1.
Where its Exponential (Mathematical) Representation is given by equation 7,
noted above. Hence,
12c. X^1 = X, or the Binary expression
becomes; 2^1 = '2'
13a. If in any Statement, when such conditions are set forth,
that the Statement represents a value that is True, and has
only 1 possible solution. Then equally valid, only a True OR
a False condition exist, such that, the total number of
'States' for which this Statement represents, is 1.
13b. 'True OR False is True' Which is expressed Logically as, 0 = 1;
1 possibility represented as:'
0 = 0 OR 0 = 1
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Hence, '13b' is represented Mathematically as being the same as:
14a. A^0 = 1, Positive Integer = 1
and
14b. 1^0 = 1, or 2^0 = 1, Binary Representation = 00
Nevertheless, the validity of 14b, which was derived as a from the
foregoing argument, maintains that, there exist only '1' possible 'State
that can be derived from the Binary representation of '0'. This is true,
especially since, the Binary Representation of a Zero condition, is the
same as that represented in the 'Positive Integers'. In other words, the
Binary Notation for a '0 State', which is not equal to Zero, or an 'Empty
Set', can equal only one of 2 possible States. In which case, only '1'
solution or State can exist!
Therefore, the correct mapping of the One-to-One Correspondence existing
between the Binary Method of Counting or Exponential Enumeration, and that
of the 'Positive Integers'. Is derived from the foregoing logical analysis
and based upon equations 15, 16, 17, which provides clarity to the logical
analysis and justification for conclusions displayed in Table 8 below.
Where it should be understood, that in all cases, the 'Null Set', the
'Positive Integer 0', and the 'Empty Set' in the Binary Notation, are all
Equal representations, which establish an identity with the same entity.
15. 00000000 - 00000000 = {0} = 0, Integer
16. 00000000 + 00000000 = 00000001
OR
16a. 00 = 1, Positive Integer
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17. 00000001 - 00000000 = 00000000
AND
17a. 01 - 00 = 00 = 1, Positive Integer
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TABLE 8
"The Reality of the Binary System of Enumeration"
"And the Series Generated when Counting, using
only " 1's " and " 0's, which are the
Abstract Entities belonging to the
Binary Set"
æExponential EnumerationÆ æBinary RepresentationÆ æPositive IntegerÆ
^ ^ ^
/ | \ / | \ / | \
v v v
1. 0^0 = 0 0 0
2. 2^0 = 1* 00000000 = 00 1
3. 2^1 = 2* 00000001 = 01 2
4. ....... 00000010 = 10 3
5. 2^2 = 4* 00000011 = 11 4
6. ........ 00000100 = 100 5
7. ........ 00000101 = 101 6
.. ........ 00000110 = 110 7
9. 2^3 = 8* 00000111 = 111 8
.. ....... 00001000 = 1000 9
.. ....... 00001001 = 1001 10
.. ....... 00001010 = 1010 11
.. ....... 00001011 = 1011 12
.. ....... 00001100 = 1100 13
.. .......... .................. ...
17. 2^4 = 16* 00001111 = 1111 16
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.. .......... .................. ...
33. 2^5 = 32* 00011111 = 11111 32
.. .......... .................. ...
65. 2^6 = 64* 00111111 = 111111 64
.. .......... .................. ...
129. 2^7 = 128* 01111111 = 1111111 128
.. .......... .................. ...
257. 2^8 = 256* 11111111 = 11111111 256
Note: The equations marked with an asterisk are of primary
concern in the IP Specifications relating to IPv7 and IPv8.
And it can be concluded from "Logic of the Method of
Quantification", that every Binary Number derived, which
represented as all '1's', is the Fundamental Principle of
the Binary System. In other words; " 2 x 2 = 2 + 2 ".
In fact, it is from the conclusion deduced above, and that which the
Concept of Exponential Enumeration maintains, which will ultimately cause
a change not only in the method of enumeration in Binary Mathematics, but
the whole of the Theoretical and Applied Biological and Physical Sciences
as well. Which clearly provides, an explanation for the creation of the
Synthetic Process called 'BITWISE ANDING'. In fact, it could be argued,
this Method is derived from the Process of Truth Table Analysis, which
sustains the unquestionable similarity. That deals with Pure Logic, and
not the numerical values of the IP Address Range. Where by, its use
provided a functional means, which compensated for the Enumeration Errors
inherent in the Binary System. In addition to the fact that, in Truth Table
Analysis there is less overhead, because there is far less calculation
involved than in the process of Binary Subtraction. Nevertheless, it should
be understood that, the foundation of this Process is based upon the
'Concept of Differentiation, which is clearly Derived from the concepts as
established in '13a', noted above.
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Internet Draft December 13, 2001
In other words, it can be concluded that, the IP Address Range equals a
total of 256 IP Addresses, which represents the inclusive count established
by the Range '1 - 256', because the Integer '0' is not defined as an
Element of the Binary Set. Furthermore, it should be understood that, Zero
maintains the same functional purpose, regardless of whether or not its
consideration is Binary or Integer. However, since there is No Actual
Binary Representation for Zero, indicating the Empty Set, as such. Then
consideration must be given, as to provide some distinction between the two
representations. In this case, I would advise the use of '00' as indicating
All Binary Zeros (which equals the Positive Integer '1'), and the use of
'0' (The Integer Zero) to represent the Integer value. Beyond this however,
it should be clearly understood, all other uses of "0", maintain its
distinction by definition from the assigned Mathematical System which
employs its use.
Nevertheless, these changes and resolutions of the errors plaguing IPv4,
established the foundation for the logical derivation of IPv7 and IPv8,
which is incorporated in the succeeding Chapters. Moreover, it is from
these discoveries and the results they yield, which provides the necessary
and final distinction that will server to establish IPv7 and IPv8, as a New
IP Specification.
Chapter II: An Overview of IPv7
The logical replacement for IPv4 is IPv7, because the method of Enumeration
used in its IP Addressing Schematic is identical, and it provides a greater
adherence to the rules of a logical system having an underlying
mathematical foundation. Furthermore, while there exist stark differences,
which are the Structural modifications to its IP Addressing Schematic. It
can nonetheless, be used in place of IPv4, without any change in the
foundational applications or associations presently in use, except where
the error corrections mandate. In other words, all of the grounding
principles, associations, and applications that are an integral part of
IPv4, are the same in IPv7.
Nevertheless, the results from Chapter I and the analysis of Tables 4, 5,
and 6, which includes the concepts of Supernetting. Produced the results,
which provide the logical justification and derivation of the results of
Table 9.
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Internet Draft December 13, 2001
Table 9.
" The Reality resulting from Supernetting, the
combination of TABLES 4 and 5 yields a Total
of '4.145 x 10^9' available IP Addresses"
Class A, 1 - 126, Default Subnet Mask 255.x.x.x:
126 Networks and 254^3 Hosts: 0
Total Number of IP Addresses Available:
126 x 16,387,064 = 2,064,770,064
Class B, 128- 191, Default Subnet Mask 255.x.x.x:
2^6 Networks and 254^3 Hosts: 10
Total Number of IP Addresses Available:
64 x 16,387,064 = 1,048,772,096
Class C, 192 - 223, Default Subnet Mask 255.x.x.x:
2^5 Networks and 254^3 Hosts: 110
Total Number of IP Addresses Available:
32 x 16,387,064 = 524,386,048
Class D, 224 - 239, Default Subnet Mask 255.x.x.x:
2^4 Networks and 254^3 Hosts: 1110
Total Number of IP Addresses Available:
16 x 16,387,064 = 262,193,024
Class E, 240 - 254, Default Subnet Mask 255.x.x.x:
15 Networks and 254^3 Hosts: 1111
Total Number of IP Addresses Available:
15 x 16,387,064 = 245,805,960
Note: While Hosts are shown to exist for Class D and E,
their existence is not define in IPv4. However,
this provides a clarity, which is necessary for
the introduction of IPv7 and IPv8. Furthermore,
this method eliminates the need to assign entire
IP Address Classes for use as MultiCast or
Experimental IP Addresses. Where the Total Number
of Available IP Addresses in IPv4 is given as;
'253 x 254^3 = 4.145 x 10^9'.
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Internet Draft December 13, 2001
The foregoing clearly shows, without having the Default Subnet Mask Define
as limiting the values of the Octet to the Address Range of the Class in
which it is mapped. Then, only the Value of the First Octet in any IP
Address can determine the IP Address Class of which, the resulting IP
Address might belong. This means that, the Total number of IP Addresses
available is equal to the Binary Bit Count of the Address Range multiplied
by the Host Bit Count, 2^24. That is, every Class can maintain the Default
IP Address as given for the Class A, which justifies the Expansion as given
in Table 10.
Table 10.
"The Logically derived Structure of the 'Synthetic' Decimal
Representation of the IPv7 Class System"
CLASS A
1. Class A-1, 1 - 128, Subnet Identifier 256.Y.X.X:
Class A-2, 1 - 128, Subnet Identifier 256.256.Y.X:
Class A-3, 1 - 128, Subnet Identifier 256.256.256.Y:
Class A-4, 1 - 128, Subnet Identifier 256.256.256.256:
2^7 Networks and 256^3 Hosts: 0
Total Number of IP Addresses Available:
128 x 16,777,216 = 2,147,483,648
CLASS B
2. Class B-1, 129 - 192, Subnet Identifier 256.Y.X.X:
Class B-2, 129 - 192, Subnet Identifier 256.256.Y.X:
Class B-3, 129 - 192, Subnet Identifier 256.256.256.Y:
Class B-4, 129 - 192, Subnet Identifier 256.256.256.256:
2^6 Networks and 256^3 Hosts: 10
Total Number of IP Addresses Available:
64 x 16,777,216 = 1,073,741,824
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CLASS C
3. Class C-1, 193 - 224, Subnet Identifier 256.Y.X.X:
Class C-2, 193 - 224, Subnet Identifier 256.256.Y.X:
Class C-3, 193 - 224, Subnet Identifier 256.256.256.Y:
Class C-4, 193 - 224, Subnet Identifier 256.256.256.256:
2^5 Networks and 256^3 Hosts: 110
Total Number of IP Addresses Available:
32 x 16,777,216 = 536,870,912
CLASS D
4. Class D-1, 225 - 240, Subnet Identifier 256.Y.X.X:
Class D-2, 225 - 240, Subnet Identifier 256.256.Y.X:
Class D-3, 225 - 240, Subnet Identifier 256.256.256.Y:
Class D-4, 225 - 240, Subnet Identifier 256.256.256.256:
2^4 Networks and 256^3 Hosts: 1110
Total Number of IP Addresses Available:
16 x 16,777,216 = 268,435,456
CLASS E
5. Class E-1, 241 - 255, Subnet Identifier 256.Y.X.X:
Class E-2, 241 - 255, Subnet Identifier 256.256.Y.X:
Class E-3, 241 - 255, Subnet Identifier 256.256.256.Y:
Class E-4, 241 - 255, Subnet Identifier 256.256.256.256:
15 Networks and 256^3 Hosts: 1111
Total Number of IP Addresses Available:
15 x 16,777,216 = 251,658,240
Note: The Equation for Determining the IP Address Range for any
IP Class is; (REN - RBN) + 1 = Total of Available IP
Addresses for the given Class. (Where R = Range, E = End,
B = Beginning, N = Number).
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Internet Draft December 13, 2001
However, the resulting expansion, that is IPv7, as summarized in Table '10'
raises an issue, while not a major problem. It does indeed, represent a
Mathematical Conflict within the IPv7 Class Addressing Scheme, as depicted
in Table 10. Where by, the Mathematics Analysis reveals that the Second
Octet of the Primary Section of Each Class maintains a Set of Values within
each of their respective IP Address Ranges. Which can not be employed or
used as part of the count resulting in the total number of available IP
Addresses. This is because they are not available as a valid IP Address,
and if they were, then there would exist a mathematical conflict with the
calculation of the total number of available IP Addresses for Every Section
Succeeding the Primary Section of each IP Address Class.
In other words, there would arise an error in reporting the results of the
calculated totals. This can easily be visualized when compared with the
results of the second Octet of the Secondary Section for each of the IPv7
Class Address Ranges. That is, there exist a barrier imposed by the use of
the Subnet Identifier in every Octet Succeeding the Primary Section of each
IPv7 Class Address Schemes, which bars the use of any of the numbers given
by the IP Address Range for that given IP Address Class. This is seen true,
because the 1 - 256 = 256 is the inclusive total. However, the current
definitions excludes the use of all Binary 1's and Integer 0's from use in
the Network portion of the IP Address. Which also includes the Host Count,
whose total is equal to '256 - 1 = 255'. Nevertheless, because '0' is an
Integer, it is not a Binary Representation, nor is it included in the IP
Address Count. Which does indeed contain all of the numbers available to be
used as IP Addresses. Needless to say, this does not cripple the IPv7 Class
Addressing System.
Where by, the calculation of the mathematical difference between every
Division / Section for each IP Address Range within every Address Class can
realized, logically, which would justify the existence for the results
given by Table 10. This is especially true, since the correction of the
error in the Binary System, as well as the IP Addressing Scheme are found
upon the Logic of the Method of Quantification. However, this does require
a further analysis, which provides a distinction, governing definitions and
Laws describing the function and use of the 'Default Subnet Mask', the
'Subnet Mask', and the 'Subnet Identifier'.
Nevertheless, the results from these definition and Laws, it shall be
concluded, are conformance with the logical conclusions as derived from the
analysis provided in Chapter I. Which will be viewed as a modification of
some of the definitions employed in the current system. Where by, 'Table
6a' changes the conditions outlined in 'Table 6', regarding the 'All Binary
0's, to the Integer '0', because the 'Binary 0', it was concluded as having
a Positive Integer value of '1'. In other words, the Binary Set has No
Numerical Value(s), and there is No Binary Representation for the Null Set.
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Internet Draft December 13, 2001
TABLE 6a
1. The Network Address portion of an IP address, as Represented by the
'Subnet Identifier', cannot be Set to either 'All Binary Ones' (256)
or 'All Integer Zeros'(Which also Bars there use in the Zone IP and
the IP Area Code portion of an IP Address: See Chapter IV)
2. The Subnet portion of an IP address, as represented by the
'Subnet Mask', cannot be Set to either 'All Binary Ones' or
'All Integer Zeros'
3. The Host portion of an IP address, characterized as not Being defined
by either the 'Subnet Identifier' or the 'Subnet Mask' cannot be Set
to 'All Binary Ones' or 'All Integer Zeros'
4. The IP address 127.0.0.0* can never be assigned as a Network
Address, because is the 'LoopBack' test IP Address. Which is
the only IP Address, other than 'Emergency BroadCast IP Address',
allowed to use 'All Integer Zeros' in the Host portion
*Note: All Binary 0's equals the Positive Integer '1'. And
following the suggestion from the Abstract, (4) noted
above becomes, 127.0.0.0, which is the only value
assigned to the LoopBack Address, because All Integer
Zeros has no effect upon the IP Address Total and it is
not a Member of the Binary Set.
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Definitions
1. The Subnet Identifier defines the Default Subnet Mask and the
Octet, which can only be assigned the values specified by in
the IP Class Address Range within boundaries of IP Address
Class in which it is used.
2. The Default Subnet Mask has a Binary value of 11111111 and a
Decimal value of 256, it is used calculate the IP Network
Address and to map the location of the Network portion of the
IP Address defined by the Subnet Identifier.
3. The Subnet Mask is used to divide any Parent Network IP Address
into several smaller and Logical Sub-Networks. When used in
conjunction with the Default Subnet Mask, it identifies the
resulting Sub-Network IP Address it was used to create.
Nonetheless, the analysis of mathematical procedures for the elimination of
this discrepancy is achieved by definitions resulting from the Laws of the
Octet, which are summarized in Table 11.
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Internet Draft December 13, 2001
TABLE 11
{" The Laws of the Octet "}
'If the "Subnet Identifier specifies the value for the Variable Y",
then the "Subnet Identifier" is said to Define the value of
every Octet, for All Address Classes, in which the 'Y'
variable is assign': Hence;
1. By definition, there exist 4 distinct Sections or Divisions
for every IP Address Class. However, the number of Sections
or Divisions that any IP Address Class can maintain is
Mathematically derived, which is related to, and dependent
upon, the IP Bit Address Number and the Total Number of IP
Addresses defined for the IP Address Classes.
2. The Sections or Divisions of the IP Address Class are defined
as: Primary, Secondary, Ternary, etc...And are labeled
according to their respective Class Location (e.g.: Class A
would be Class A-1, Class A-2, Class A-3, and continued as
would be necessary to distinguish every Division(s) of the
Class, and the respective Divisions of the remaining IP
Address Classes; i.e. Address Classes B - E).
3. The Subnet Identifier assigns to the First Octet within each
Section or Division of every IP Address Class, when it is not
use as the Default Subnet Mask, only the value of the numbers
available in the IP Address Range assigned to the IP Address
Class.
4. Every OCTET, in every Address Class, which is not defined by
the Subnet Identifier, can be assigned any value defined
by the range given by; '1 - 256' (which excludes the use of All
Integer '0's'). That is, provided that there is no succeeding
Section or Division within the same Address Class, whose
reference would be the same OCTET Number, which is Defined by
the Subnet Identifier. (In other words, if there is such an
OCTET in the succeeding Section or Division, then neither, can
be defined by the Subnet Identifier and use All of the
Numbers in the Integer Range specified above.)
5. For every OCTET within each Section or Division of every IP
Address Class, that is defined by the Subnet Identifier, and
it is preceded by a Section or Division within the same
Address Class, whose reference is the preceding Octet Number.
Then, the Octet of the preceding Section or Division must be
defined by the Subnet Identifier. (Because with the exception
of the First Octet, the Octet of the preceding Section, or
Division, must be defined by 'Y', and can NOT be assigned the
value denoted by the Integer Range, which DEFINES the IP
Address Range assigned to that IP Address Class.)
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Internet Draft December 13, 2001
Needless to say, this situation can be further explored, provided that, it
is understood that the Total Number of available IP Addresses for Class A,
is equal to, 2,147,483,648 = 128 x 256^3. That is, if given Class A, as our
example, then from the Mathematical analysis of Sections A-1 and A-2, we
have:
1. Class A-1, 1 - 128, Subnet Identifier 256.Y.X.X:
128 Networks and 256^3 Hosts: 0
2. Class A-2, 1- 128, Subnet Identifier 256.256.Y.X:
128^2 Networks and 256^2 Hosts: 10
Note: The Host value is within the Range
of the equation '1 - 256 = 256', the
result of '256 - 1 = 255' , which is
a Variable equal to the inclusive
total yielding '255'. (See Table 6a)
Nevertheless, the examination of these classes yields the conclusion:
'That the total number of available IP Addresses for each Division or
Section, within any given Address Class, must equal the total number of
IP Addresses available for the given Address Class'.
Therefore, if Class A-1's second Octet were to maintain any of the Values
in the IP Address Range, '1 - 128', then it would be reporting IP Address
of Class A-2 because the second Octet of this Class is defined by the
'Subnet Identifier'. However, the easiest mathematical method for the
determination of the total number of available IP Addresses for any
Division within any Address Class, would be to calculate the total number
of IP Addresses available from its DEFAULT IP Address Structure, as given
above, and defined by the Laws of the Octet.
Hence, the total number of IP Addresses available to any Section or
Division of any Address Class is the product of the IP Address Range value,
as determined by the Subnet Identifier, and the assigned IP Address of the
remaining Octets, which is a function of the Laws of the Octet. In other
words, the total number of IP Addresses available for any given Address
Class, must be equal to the sum of the total number of addresses in each
section or division comprising that Class. In which case, our example would
yield:
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Internet Draft December 13, 2001
3. Class A-1, 1 - 128, Subnet Identifier 256.Y.X.X:
(128 x 128 x 256 x 256) = 1,073,741,824 Network IP's
{Where Y = the value of the Range of the Octet,
which precedes the Octet defined by the Subnet
Identifier = '256 - 128 = the Range 129 - 256'.)
And
4. 128 x (255)^2 = 8,323,200 Hosts: 0
(This complies with the Rules in
Table 6a.)
Where the determination of the Number of available Host IP Addresses æFor
AllÆ Classes, is given by the equation 5.
5. T x 255^N = Host IP Address Count
This is valid, because 127 can be used in Class A, given that 'T' is equal
to 'IP Address Range Inclusive Total', and 'N' equals the number Remaining
Octets, which are not defined by the Subnet Identifier. Which means that
the number of available Host IP Addresses in the 'Last Octet' of the Last
Section or Division of each IP Address Class is equal to the Inclusive
Total of the Number of IP Addresses available in the IP Address Range.
Hence, the total number of available IP Addresses, in this example, for
the Class A would be that given as:
6. 128 * 256^3 = 2,147,483,648
In other words, equation 6 represents the total number of available IP
Addresses in the Class A, and equation 4 represents the total number of
Hosts available to each network IP Address assigned to Class A-1.
Furthermore, it should be understood from the Laws of the Octet, that the
total number of available Network IP Addresses assigned to Class A-1 is
given by equation 7:
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Internet Draft December 13, 2001
7. 128 x (256 - 128) x 256 x 256 = 1,073,741,824
This method is summarized in Table 12. Where the results of equation 7
equals the total number of IP Addresses available for assignment as a
Parent Network in a Global Internetworking Environment, and the results of
equation 4 yield the number of Hosts that can be repeatedly assigned and
used as private Domain Network IP Addresses. In which case, one would need
to access the Parent Network to have access to any of these internal
private Networks and Hosts identified by these IP Addresses. Thus, there
would be no conflict from their continued use, which is the process now
employed.
NOTE: So not to violate the Laws of the Octet. It should
be clearly understood that the last section of every
Class can only be represented by the Default Address
given by: 256.256.256.yyy. (Where y = is the
difference given by the equation: "Y = 256 û Q
{Where Q = IP Address Range for the given Address
Class}". Where the total number of available Hosts,
when Class A is the given example, then the last
section, Class A-3 is given by:
8. Q = 256 - Y = 256 - 128 = Host Count Factor = 128
Hence, the Host Count Factor, HCF, is equal to the Total Number of IP
Addresses in the IP Address Range of each Address Class. Nevertheless,
these results are displayed in Table 12.
9. Q = 256 - Y = 256 - (256 - 'Y') = Host Count Factor
(Where 'Y' = 256 - 'IP Class Address Range Total')
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Internet Draft December 13, 2001
Table 12.
"Reality of the Mathematically Derived Addressing Schematic / Structure
of the Decimal Representation for the IPv7 Class System." (Where the
Value for the variable 'Y' is given by the Laws of the Octet, which
yields 4.278 x 10^9 Addresses: And '128 + 64 + 32 + 16 + 15 = 255,
which Yields 255 x 256^3 IP Addresses'.)
1. Total IP Addresses for Class A = 128 x 256^3 = 2,147,483,648
Total available IP Addresses for Class A = 128 x 256^3
Total available IP Host Addresses Equals 128 x 255^N
(Where N = Number of Octet, and 'Y' equals the Address
Range '129 - 256', 1 - 128 is not included in the
Address Range Represented by the equation
'Y = 256 - 128'.)
Class A-1, 1 - 128, Subnet Identifier 256.y.x.x:
1,073,741,824 Networks and 8,323,200 Hosts: 0
Class A-2, 1 - 128, Subnet Identifier 256.256.y.x:
536,870,912 Networks and 32,640 Hosts
Class A-3, 1 - 128, Subnet Identifier 256.256.256.y:
268,435,456 Networks and 128 Hosts
Class A-4, 1 - 128, Subnet Identifier 256.256.256.256:
268,435,456 Network / MultiCast IP Addresses / AnyCast
2. Total IP Addresses for Class B = 64 x 256^3 = 1,073,741,824
Total available IP Addresses for Class B = 64 x 256^3
Total available IP Host Addresses Equals 64 x 255^N
(Where N = Number of Octet, and 'Y' equals the Address
Range '256 - Q'; 129 - 192 is not included in the
Address Range Represented by the equation
'Y = 256 - 64'.)
Class B-1, 129 - 192, Subnet Identifier 256.y.x.x:
805,306,368 Networks and 4,161,600 Hosts: 10
Class B-2, 129 - 192, Subnet Identifier 256.256.y.x:
201,326,592 Networks and 16,320 Hosts
Class B-3, 129 - 192, Subnet Identifier 256.256.256.y:
50,331,648 Networks and 64 Hosts
Class B-4, 129 - 192, Subnet Identifier 256.256.256.256:
16,777,216 Network / MultiCast IP Addresses / AnyCast
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Internet Draft December 13, 2001
3. Total IP Addresses for Class C = 32 x 256^3 = 536,870,912
Total available IP Addresses for Class C = 32 x 256^3
Total available IP Host Addresses Equals 32 x 255^N
(Where N = Number of Octet, and 'Y' equals the Address
Range '256 - Q'; 193 - 224 is not included in the
Address Range Represented by the equation
'Y = 256 - 32.)
Class C-1, 193 - 224, Subnet Identifier 256.y.x.x:
469,762,048 Networks and 2,080,800 Hosts: 110
Class C-2, 193 - 224, Subnet Identifier 256.256.y.x:
58,720,256 Networks and 8,160 Hosts
Class C-3, 193 - 224, Subnet Identifier 256.256.256.y:
7,340,032 Networks and 32 Hosts
Class C-4, 193 - 224, Subnet Identifier 256.256.256.256:
1,048,576 Network / MultiCast IP Addresses / AnyCast
4. Total IP Addresses for Class D = 16 x 256^3 = 268,435,456
Total available IP Addresses for Class D = 16 x 256^3
Total available IP Host Addresses Equals 16 x 255^N
(Where N = Number of Octet, and 'Y' equals the Address
Range '256 - Q'; 225 - 240 is not included in the
Address Range Represented by the equation
'Y = 256 - 16'.)
Class D-1, 225 - 240, Subnet Identifier 256.y.x.x:
251,658,240 Networks and 1,040,400 Hosts: 1110
Class D-2, 225 - 240, Subnet Identifier 256.256.y.x:
15,728,640 Networks and 4,080 Hosts
Class D-3, 225 - 240, Subnet Identifier 256.256.256.y:
983,040 Networks and 16 Hosts
Class D-4, 225 - 240, Subnet Identifier 256.256.256.256:
65,536 Network / MultiCast IP Addresses / AnyCast
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Internet Draft December 13, 2001
5. Total IP Addresses for Class E = 15 x 256^3 = 251,658,240
Total available IP Addresses for Class E = 15 x 256^3
Total available IP Host Addresses Equals 15 x 255^N
(Where N = Number of Octet, and 'Y' equals the Address
Range '256 - Q'; 241 - 255 is not included in the
Address Range Represented by the equation
'Y = 256 - 15'.)
Class E-1, 241 - 255, Subnet Identifier 256.y.x.x:
236,912,640 Networks and 975,375 Hosts: 1111
Class E-2, 241 - 255, Subnet Identifier 256.256.y.x:
13,881,600 Networks and 3,825 Hosts
Class E-3, 241 - 255, Subnet Identifier 256.256.256.y:
813,375 Networks and 15 Hosts
Class E-4, 241 - 255, Subnet Identifier 256.256.256.256:
50,625 Network / MultiCast IP Addresses / AnyCast
The Rules given in Table 6a and Table 10 (Laws of the Octet) Limits the
Range for the Value of the Variable 'Y' and 'X'. That is, when 'X' = 'Y' or
'X' = '256', which represents only the IP Address Count, then the Range of
Values that 'X' or 'Y' can be assigned is governed by the Laws and Rules
noted above. Which encompasses the Range given by '1 - 256', inclusive.
These principles can be expressed mathematically, given that it is
understood that the Total number of available IP Addresses per unit of
Division of the Address Classes of IPv7, can not be greater than the Total
number of available IP Addresses as would result from any calculation used
to determine this total without such a division. In other words, the Total
Number of Available IP Addresses for every Address Class, can not be
greater than any sum, representing a division of this total, which implies
an equality between the whole and its constituents. This concept is given
by equation 10.
E Terrell [Page 49]
Internet Draft December 13, 2001
10. {A | A = Z in 256.X.X.X, and 256.X.X.X is the format which
results from this process. Where, in all situations the
expression 256.X.X.X represents the equation 256 * X * X * X,
which equals some value that indicates the Total Number of IP
Address for a given Address Class, then the total number of
Addresses for any given Division of this Class is to the Sum
of there Totals: [A + B + C + D + E].
Hence, the total number of available IP addresses in IPv7, which comprise
several divisions, is equal to the Sum of the total number of IP Addresses
that exist in each Division. That is, if and only if, there exist no
condition such that, there is a violation of the Laws of the Octet.
Nevertheless, the demand for logical continuity commands that the Host
Count for All Sections or Divisions follow the same provisions as outlined
for every Section or Division of each Class. In other words, the logical
format from which the creation of the Host portion in every division, for
each Class, is derived from the laws of the Octet. This process allows
creation of Host for the first 2 divisions, which is not a function of the
total number of available IP Addresses, as given by their respective IP
Address Totals. However, preserving the logical continuity, which is
derived directly from the 'Laws of the Octet'. The analysis maintains, that
the total number of Host, as derived for the last division of each Class,
is equal to the Total Number of IP Network Addresses as would be assigned
to the Class itself. And while this process might appear inconsistent with
the methods for deriving the total number of available Hosts in the first 2
divisions. However, it should be understood from the analysis, that this is
a 64 Bit System, which only uses 48 Bits. What this implies, is that, the
method used in the last section is the same method used throughout the
Class, as would be the case if there was another section, which followed,
that which is now the last section.
Nevertheless, from the analysis it should be clearly understood that the
features of Supernetting did not eliminate the IP Address Classes. In fact,
the analysis showed not only an increased in the total number of available
IP Addresses it provided, but a Class System, which remained intact as
well. Needless to say, the claim of an aesthetic appeal to make the Class C
Addresses inviting to businesses, provided more than a mere change in the
schematic of the IPv4 Address structure. However, these benefits, while
significant for distribution IP Addresses did nothing regarding the errors.
E Terrell [Page 50]
Internet Draft December 13, 2001
In other words, IPv4 offered approximately 3.12 * 10^9 IP Addresses, and
Supernetting increased the number of available IP Addresses to Approximate
3.64 * 10^9, with the claim of the elimination of the Class System of
Addressing. However, the implementation of a Logical Structure and the
errors corrected, IPv7 provided another increase in the count of the total
number of IP Addresses available. In fact, the provisions encompassing the
IPv7 Addressing System, provides a more efficient use of the available IP
Addresses, which is not only more stable, but less redundant than the
highly taunted IPv6. Furthermore, while there exist a Binary Representation
depicting the results from the Supernetting of IPv4. It should be clear,
that there is no such representation for IPv7, which is a benefit that
prevents confusion between the Binary and Decimal methods of enumeration.
Nonetheless, is summarized in Table 13 and 14 respectively. Where Table 14
is indeed correct, but a comparison of Table 14 with that of Table 12,
clearly shows the impossibility of its existence, which does not maintain a
translation.
Table 13.
"The Reality resulting from Supernetting,
the Binary Representation"
Class A, 1 - 126, Default Subnet Mask 255.x.x.x:
126 Networks and 2^24 Hosts: 0
Class B, 128- 191, Default Subnet Mask 255.x.x.x:
2^6 Networks and 2^24 Hosts: 10
Class C, 192 - 223, Default Subnet Mask 255.x.x.x:
2^5 Networks and 2^24 Hosts: 110
Class D, 224 - 239, Default Subnet Mask 255.x.x.x:
2^4 Networks and 2^24 Hosts: 1110
Class E, 240 - 254, Default Subnet Mask 255.x.x.x:
15 Networks and 2^24 Hosts: 1111
E Terrell [Page 51]
Internet Draft December 13, 2001
Table 14
Structure of the Resulting Synthesis of a Binary Representation
for IPv7 Class System*
CLASS A
1. Class A-1, 1 - 128, Subnet Identifier 256.000.000.000:
2^7 Networks and 2^24 Hosts: 0
Class A-2, 1 - 128, Subnet Identifier 256.256.000.000:
2^15 Networks and 2^16 Hosts: 0
Class A-3, 1 - 128, Subnet Identifier 256.256.256.000:
2^23 Networks and 2^8 Hosts: 0
Class A-4, 1 - 128, Subnet Identifier 256.256.256.256:
2^31 Network / MultiCast IP Addresses / AnyCast
CLASS B
2. Class B-1, 129 - 192, Subnet Identifier 256.000.000.000:
2^6 Networks and 2^24 Hosts: 10
Class B-2, 129 - 192, Subnet Identifier 256.256.000.000:
2^14 Networks and 2^16 Hosts: 10
Class B-3, 129 - 192, Subnet Identifier 256.256.256.000:
2^22 Networks and 2^8 Hosts: 10
Class B-4, 129 - 192, Subnet Identifier 256.256.256.256:
2^30 Network / MultiCast IP Addresses / AnyCast
CLASS C
3. Class C-1, 193 - 224, Subnet Identifier 256.000.000.000:
2^5 Networks and 2^24 Hosts: 110
Class C-2, 193 - 224, Subnet Identifier 256.256.000.000:
2^13 Networks and 2^16 Hosts: 110
Class C-3, 193 - 224, Subnet Identifier 256.256.256.000:
2^21 Networks and 2^8 Hosts: 110
Class C-4, 193 - 224, Subnet Identifier 256.256.256.256:
2^29 Network / MultiCast IP Addresses / AnyCast
E Terrell [Page 52]
Internet Draft December 13, 2001
CLASS D
4. Class D-1, 225 - 240, Subnet Identifier 256.000.000.000:
2^4 Networks and 2^24 Hosts: 1110
Class D-2, 225 - 240, Subnet Identifier 256.256.000.000:
2^12 Networks and 2^16 Hosts: 1110
Class D-3, 225 - 240, Subnet Identifier 256.256.256.000:
2^20 Networks and 2^8 Hosts: 1110
Class D-4, 225 - 240, Subnet Identifier 256.256.256.256:
2^28 Network / MultiCast IP Addresses / AnyCast
CLASS E
5. Class E-1, 241 - 255, Subnet Identifier 256.000.000.000:
15 Networks and 2^24 Hosts: 11110
Class E-2, 241 - 255, Subnet Identifier 256.256.000.000:
2^11 Networks and 2^16 Hosts: 11110
Class E-3, 241 - 255, Subnet Identifier 256.256.256.000:
2^19 Networks and 2^8 Hosts: 11110
Class E-4, 241 - 255, Subnet Identifier 256.256.256.256:
2^27 Network / MultiCast IP Addresses / AnyCast
*Note: Because of the Mathematics involved, it should be clear from
Table 14, that there does not exist an accurate depiction of
the Addressing Schematic in the Binary Representation for
either the IPv7 or the IPv8 IP Specifications.
E Terrell [Page 53]
Internet Draft December 13, 2001
Nevertheless, by exploiting the Default Subnet Mask, that is, understanding
its real purpose as used in BITWISE ANDING. Which is IP Network Address
Resolution by determining the value of the defining Octet. Then anyone
could easily visualize that, the former IPv4 Class Addressing Scheme, as
summarized in Tables 4 and 5, warrants the expansion to that given by Table
12. Where the Default Subnet Mask, now the Subnet Identifier, assumes the
duties of its actual definition. That is, it remains the Default Subnet
Mask, which when used in Bitwise Anding serves to resolve the Network IP
Address. This working definition provides further justification for the
acceptance of IPv7. Especially since, IPv7 while distinct, it retains the
same method of enumeration, which allows it be viewed as the expansion of
the IPv4 Address Class. While its structure clearly represents, the logical
derivative from the change in the Default Structure defining each division
of the IPv4 Class, which resulted from the use of Supernetting.
Nevertheless, Supernetting produced a change in all of the Default IP
Address Structures of the IPv4 Classes, to the Default Structure as
depicted for the Class A. Needless to say, this is the definitive proof,
that while IPv7 is a New IP Specification, its evolution is a logical
derivative founded upon changes made in IPv4, which corrects its Errors
and compensates for the shortages in the number of available IP Addresses.
In other words, beyond the correction of the Errors, these changes have
absolutely no effects upon the foundation, which retains the same methods
of enumeration. Needless to say, the inherent premises associated with any
logical conclusion, would indeed necessitate the evolution of IPv7.
Especially since, it not only offers a tremendous cost reduction when
considering any other IP Specification, but, it also provides a solution
for the shortages in the number of available IP Addresses.
Nevertheless, while IPv7 is indeed a New IP Specification, it yet retains
an identity of being nothing more than a 'TRANSPARENT OVERLAY' for the IPv4
Addressing System. In which, the resounding effects of its implementation
would increase the overall efficiency of IP Addressing, while leaving the
underlying foundations characterizing IPv4, intact.
E Terrell [Page 54]
Internet Draft December 13, 2001
Chapter III: An Overview of IPv8 the Enhancement of IPv7
The over all structure and organization regarding the overview of IPv8
differs only in a minor change in the format of the IP Addressing
Schematic, which is a slight distinction from that underlying IPv7. In
other words, it is viewed as an enhancement of IPv7, which provides
separate copies of the entire IP Addressing Scheme for distribution, as
summarized in Table 12. Thus, by developing a system which allows separate
copies of the entire addressing scheme to be distributed, I created an IP
Specification whose functional use, efficiency, and applications provides
an almost unlimited number of available IP Addresses to the
Telecommunication Industries of the entire World.
In other words, the enhancement offered by IPv8 is characterized by the use
and implementation of PREFIXES to the 32 Bit Block IP Address, such as;
'Zone IP' and 'IP Area Codes'. Which is a boon for the expansion of the
Telecommunication Industry, because it is a Logical Derivative of IPv7.
These measures guarantees the Life of the Internet, with the promise of
being the only medium necessary for all of the World's Telecommunications
Traffic. However, these benefits are not without a cost, or an additional
burden upon the IT Industry itself.
Where by, some of the benefits incorporated in the implementation of IPv8,
without a doubt, will increase the demand upon the Use and Function of the
Global Internetworking System's Backbone. Even so, it still provides enough
gains to offset any discrepancies concerning any performance issues. In
fact, it offers a significant increase in Router performance, which yields
a significant boost over the use of 'CIDR' (as shall be discussed in later
chapters). And while, further impacting the Backbone Traffic, is the
possibility of reducing or eliminating the need for the use of Long
Distance Charges in Telephone Calls, because they could be Routed with
greater efficiency via the Global Internetworking System. However, even
these problems can be eliminated through the deployment of IPv8, because
automated control systems can be implemented, which could quite easily
govern Backbone Traffic and protect the system in the event of some,
foreseen or unforeseen, catastrophic occurrence.
Nevertheless, the advantages offered by this IP Specification, even
transcends the barriers of language, because it is possible to route within
an IP Area Code, or to a Zone IP, to Servers whose function is language
Translation. Needless to say, there is no end to the benefits: Interactive
Television, Live Video Telephone Systems, Video Teleconferencing, Live
Medical Diagnosing, etc., etc., etc. All while spawning the Intellectual
Revolution of the Information Age, that this Global Telecommunication
System and the Social Interactive Community it has established, allows
everyone having a telephone today, the opportunity to participate. In other
words, with the implementation of IPv8, every electrical signal or analog
communication, which can be Digitized, can use the Internet as its
thoroughfare.
E Terrell [Page 55]
Internet Draft December 13, 2001
Chapter IV: 'The Header Structure and the Decimal Representation
Of IPv8'
The IP Addressing Scheme of IPv7 can serve the Global Internetworking
Community now. Its implementation offers the most significant Improvements
ever conceived, well beyond any planed replacement system, or those
presently in use. However, while there is a learning curve, it would
actually impose no challenge for the seasoned professional. In fact, there
are 'SEVEN' reasons that support its implementation and the reality of it
being the logical replacement for IPv4.
1. It maintains the Identical methods of enumeration for IP
Addressing, as in IPv4, with a guarded respect for error
correction(s).
2. Its Header does not change from that used in IPv4,
which means the version number can remain the same.
3. It is only a 'Transparent Overlay' of the present
Addressing System, which provides an increase of
more than 133 million additional IP Addresses.
4. It is a Logical Derivative of the IPv4 Addressing
System, which eliminates all of the 'PREDEPLOYMENT'
testing required of a New System, all while providing
a flawless transition for its expansion, IPv8. Which
makes the implementation of IPv7 and IPv8 cost effective.
5. It Increases the Efficiency in the use of IP Addresses,
because there are Absolutely No IP Addresses wasted on
Host assignments in any of the Divisions or Sections of
the respective IP Address Classes. But! Any Mathematical
Analysis however, would clearly show that the Difference
between the noted IP Address Loss in the 'Abstract' above
(16,777,216), and total Number of Host IP Addresses
(16,581,375), represents a further reduction of the Total
Number of reported IP Address Losses in the IPv7 IP
Specification, to approximately 195,841 Addresses. In
other words, the number of available Hosts IP Addresses
determined by 'Laws of the Octet', is always a 'Constant',
and provides an unquestionable Efficiency in the use of
the Total Number of Available IP Addresses for the IPv7
IP Specification*.
E Terrell [Page 56]
Internet Draft December 13, 2001
6. There is no Mandate Requiring Any Change to The Current
Structure of the Private Networking Domains, nor to their
Existing IP Addressing System or Format, which would extend
beyond providing the Users with an additional convenience.
In other words, asides from the Requirement for Changing
the numbering and Naming of 'Default IP Subnet Mask' used
in the DNS Server, and DHCP Servers, implementing these
changes, which results from the change in the Binary
System, would be all that is needed. Especially since,
other than the Operating System itself, these changes
would provide all the consideration as would be needed
by the Applications the individual systems might contain.
7. The existence of the Use of the Integer '0', except for the
use in EMERGENECY BROADCAST COMMUNICATION. Which means, the
Integer '0' would be excluded from any use involving any
Normal IP Addressing Format. Thus, barring it from the use
in any Octet of the IP Address, except in an Emergency.
However, this is a special case, and an important function
of the Integer '0', which is beyond the limits imposed that
Bars its (ALL Integer 0's) use in the 'Zone IP', 'IP Area
Code', and the Octet(s) Defined by the 'Subnet Identifier'.
In other words, this requirement prohibits All Network
Administrators, Except those Responsible for Administrating
the EMERGENECY BROADCAST COMMUNICATION Network, from the use
or assignment of All Integer '0' to any Octet within an IP
Address. And this does not effect nor alter the number of
available of IP Addresses for use in the IPv7 and IPv8 IP
Addressing Specification, nor its use in defining the
'Default Subnet Mask'.**
*Note: This conclusion is valid for the IPv8 IP Specification
as well, because IPv8's Default, or Base, IP Addressing
Schematic is identical to IPv7, which differs only in
its use of the Zone IP and IP Area Code Prefixes. And it
is through the use of Prefixing the IPv7 IP Specification,
that accounts for the Staggering number of available IP
Addresses in the IPv8 IP Specification. Nevertheless, this
is a Hidden benefit, which can not be Translated into the IP
Address Count for the Total Number of Available IP Addresses
in the IPv7 and IPv8 IP Specifications, because there is no
an actual increase. That is, the calculated loss of 195,841
IP Addresses results from the Host Count, which is determined
by the Definitions outlined in Table 6a.
E Terrell [Page 57]
Internet Draft December 13, 2001
**Note: This, in essence would reverse the Definitions of All
Binary '1's', '256', as Broadcast, to mean "this Network
only". In which case, any Octet containing All Integer
'0's', where the Zone IP, IP Area Code, and 'Subnet
Identifier' are permanently excluded, would be reserved
for "[Emergency] Broadcasts only; and LoopBack Address".
In other words, IPv7 is a system that can be used now, which provides the
ease of use and implementation of IPv4. While at the same time, IPv7
provides an almost seamless transition for its enhancement, IPv8.
Furthermore, these protocols could represent the END of the DHCP Server,
because other than considerations for IP Address mapping to a 'Name', or
the facilitation it provides in making IP Address assignment an automatic
process, there would be No need for assigning a temporary IP Address.
Which does ultimately suggest, Re-Defining the functions for a DHCP
Server. Where by, the New specification would provide the complete
Specifications and Capabilities for Sub-Net Creation, that would allow
Variable Sizing. It must also be capable of Suggesting, or Specifying
the Number of IP Addresses Allocated for creating the Sub-Net, which
would use the 'Gateway Router's Permanente IP Address' as the 'Point of
Demarcation' to Assign an IP Address from the 'Sub-Net Pool' to every
Device which is attached to the Sub-Net. In addition to Sizing and
Maintaining the Reserve (Surplus) IP Address Pool, and also maintaining a
Permanente Server IP Address Assignment. The New definition for the 'DHCP
Server' would also incorporate all of the functions, which would be
necessary to allow any person to Design and implement a Network of any
Size. Moreover, this specification must also included 'IP PBX' suffixing
Capabilities. That is, the specification for Enabling the Trailing Numbers
('1 - 999') ':X.X.X', which are attached to the End of an IP Address, that
would provide the Services for 'VVoIP' (Video & Voice Over IP), using only
the Router to Direct the Communications to the Right Sub-Components in a
'Session Initialization Protocol' Environment. And to complete the set-up
for Network Operations, the 'DHCP Server' must also establish, and verify,
the final LAN, WAN, or MAN (etc...) Connections.
Nevertheless, while IPv7 is called the "Global Internetworking Community
Standard", IPv8 is called the "Global Telecommunication Standard". The
difference however, distinguishing these systems, are two fold. Where by,
the former is a shared IP Addressing System, which utilizes the Network
medium for limited communication. However, the latter represents a Global
Standardization for all Telecommunications Systems in use today.
E Terrell [Page 58]
Internet Draft December 13, 2001
The advantages of IPv8 however, surmount far beyond any 32 Bit IP
Addressing System now employed, or any IP Addressing System ever conceived.
Nevertheless, while retaining the ease of use and implementation of IPv4 /
IPv7, IPv8 provides an additional number of available IP Addresses that's
staggering, to say the very least. In other words, the comparable analogy
would be, IPv7 can provide an individual IP Address to 'nearly' every
person in the world today. While IPv8 presently, using only 48 Bits of this
64 Bit IP Addressing System, can sustain the inhabitants of more than '46
Thousand Planets'. And if the total Address Range of this 64 Bit System is
used, then IPv8 can provide an individual IP Address to the inhabitants of
more than '3 Billion Planets', with each planet having a population equal
to the population total of the world today. Which is to say, if IPv8 were
expanded to the same Address Space as IPv6, which is a 128 Bit IP Address.
Then the total number of available IP Addresses would be greater than
3.402 x 10^38. Which is greater than the available IP Address offering of
IPv6. In other words, what this means in the terms of the foregoing
scenario, is that: 'The people of planet Earth can, when using the 128 Bit
IP Addressing format of IPv8, colonize more than 5.36 x 10^28 Planets, with
each Planet having a population total equal to the existing count, and
still have reserve IP Addresses'.
[5.36 x 10^28 = 53,600,000,000,000,000,000,000,000,000 Planets! And guess
what?...A Light Year Distance is only 5,873,960,000,000 miles!]
Furthermore, while the foundations underlying IPv8 (it's Base), is the same
as that given in IPv7, which indicate its cost effectiveness, because it
does not require any pre-deployment testing. There is indeed another
distinction between these systems, which provides an accountability
regarding the method to increase, what is clearly, a staggering number of
available IP Addresses. The difference, while similar to IPv6, is the
change in the structure of the IP Header associated with IPv8, and their
depiction is given in Figure 5.
E Terrell [Page 59]
Internet Draft December 13, 2001
Figure 5
IP Header for IPv4 and IPv7
0 1 2 3
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
| VER | IHL | TYPE OF SERVICE | TOTAL LENGHT |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IDENTIFICATION |FLA| FRAGMENT OFFSET |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| TIME TO LIVE | PROTOCOL | CHECK SUM HEADER |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| SOURCE ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| DESTINATION ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| OPTIONS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| DATA |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
IP Header for IPv8
0 2 4 6
0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2 4 6 8 0 2
| VER | IHL | TOS & NEXT HEADER | TL & DIRECTION BIT |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IDENTIFICATION & SECURITY BIT |FLA| FRAGMENT OFFSET |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| TTL & HOP LIMIT | PROTOCOL | CHECK SUM HEADER |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| S RESERVED | S RESERVED | S IP ZONE CODE |S IP AREA CODE |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| SOURCE ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| D RESERVED | D RESERVED | D IP ZONE CODE |D IP AREA CODE |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| DESTINATION ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| OPTIONS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| DATA |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
E Terrell [Page 60]
Internet Draft December 13, 2001
Note: TTL and Hop Limit are program functions related to the
Router's Table. And the Security Bit is a 2 Bit
representation of some combination of 1, and 0. Where a '1'
in the first bit tells the Router to route as a Direct
Connection, and a '1' in the second Bit tells the Router
that the transmission is Encrypted. While Type Of Service
remains unchanged and Next Header is a 1 Bit indicator,
being either a '1' or a '0'. And the Total Length
remain the same, but the Direction Bit of either a '1' or
'0' tells the Router if the Packet is an InterCom or
OuterCom communication, which would assist the FireWall
in Blocking Illegal Attempts to Access Private Domains.
IP Header for IPv6
0 40 80 128
0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1
| VER | PRIO. | FLOW LABEL |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| PAYLOAD LENGTH | NEXT HEADER | HOP LIMIT |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
| |
| |
| |
| SOURCE ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
| |
| DESTINATION ADDRESS |
| |
| |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
|+ + + + + + + + + + + + + DATA + + + + + + + + + + + + + + + |
|-------------------------------------------------------------|
E Terrell [Page 61]
Internet Draft December 13, 2001
Nevertheless, it is quite obvious, that a detailed analysis of the
Headers yields, the Headers for every IP Specification maintain arbitrary
definitions depicting their operation. In fact, only the IP Address boxes
maintain any real significance, because everything else in the Header is a
matter of choice. Needless to say, the addition of the Security Bit in the
Identification Section of IPv8's Header, would serve to control IP
Stripping, Encryption, Secure Connections, and provide a more Direct
Routing of the Communications Packet. In other words, by allowing the
Headers to maintain an almost arbitrary choice in the definitions that
implement the Control Functions, which determine how a Router might handle
a Communications Packet. Through the use of Smart (Computer Controlled)
Routers, the definitions outlining the Control Functions can become 'Multi
-Purpose', which would ultimately provides greater control of the
Communication Packets and render the advantage necessary to enhance
performance.
Nevertheless, the actual Benefit described above, is that which allows IPv8
to have the increase and functional purpose, which underlies the staggering
number of IP Addresses it provides, and the associated techniques it
employs. Where by, the over all structure of the IPv8 Header of figure 5
is similar to that of IPv6, except that it 'Divides' the Source and
Destination Sections of IPv6's Header Structure. However, its defining
purpose is the similar as that given for IPv7. The distinct on however, is
the addition of two additional sections, one for the Source and the other
for the Destination. These additions make provisions for a greater
individual use and deployment of this IP Addressing Scheme.
In addition, above the Source Address Section there is another 32 Bit
Section, which is divided into 4 distinct and separately defined Octets. In
which, there are 2 Octets reserved for growth and expansion, and another is
defined as the Source Address Zone, while the last is defined as the Source
IP Address Area Code. The Destination Address Section also has an
additional 32 Bit section, which maintains comparable assignments,
excepting that, they are defined for the Destination Address Section.
Nevertheless, the numbering system employed for use in these sections is
defined as being 8 BIT Sections that employ the same methods of enumeration
governing IP Addressing. However, the difference maintained in the overall
IP Address Structure allows each individual IP Address Section to be
Routable, which is same as that governing the 32 Bit IP Address. The
significance of an 8 Bit Routable IP Address, is indeed that which gives
IPv8 its superiority over any other System of Addressing. Furthermore,
while the advantages of Routing an 8 Bit IP Address are enormous, this is
not a System that could be employed for use in the entire IP Address
format. And while, the latter can not be concluded or deduced from the
Header diagrams of figure 5. It should be pointed out, that the
hierarchical structure defining either the methods of Routing or
Networking, itself, could not be maintained if all of the 32 Bit IP Address
of IPv8, were routable as 8 Bit Sections.
E Terrell [Page 62]
Internet Draft December 13, 2001
Nevertheless, figure 6 outlines the Mathematically Derived 'Default IP
Address Structure' that is used in IPv8, which employs IPv7's Addressing
Schematic as its Default, or Base Addressing Format. Which is also Prefixed
by the Zone IP and the IP Area Code IP Addresses, and designated by the
Subnet Identifier.
FIGURE 6
1. Source Addressing Structure: S1-Reserved = (X.X.X):
2. Source Addressing Structure: S2-Reserved = (X.X.X):
3. Source Addressing Structure: 256:256:256.256.256.000
4. Destination Addressing Structure: D1-Reserved = (X.X.X):
5. Destination Addressing Structure: D2-Reserved = (X.X.X):
6. Destination Addressing Structure: 256:256:256.256.000.000
Nevertheless, figure 6 depicts the 'Default IP Address Structure' for the
Primary, Secondary, Ternary, and Quaternary IP Address Divisions / Sections
for each of the 5 IP Address Classes, and the respective IP Address
Prefixes (i.e. Zone IP and the IP Area Code) for the Source and Destination
Addresses contained in the IP Header for IPv8. Furthermore, each depiction
of the 'Zone IP' and 'IP Area Code' sections of the IP Address are
separated by a Colon (:), which not only indicates their distinction, order
of precedence, but the way in which they would be Routable as well. Now
observe the Structure, as given in Table 15, that this IP Addressing Scheme
yields, and compare its results with that of Table 12. Which is the Base /
Default Addressing Foundation of IPv7, from which it was derived.
E Terrell [Page 63]
Internet Draft December 13, 2001
Table 15.
"Reality of the Structure of the Decimal Representation for the IPv8
Class System."(Where the Value for the variable 'Y' is given by
the Laws of the Octet, which yields 2.78 x 10^14 IP Addresses.)*
1. Total IP Addresses for 'Class A' having '255' 'Zone IP' Addresses
= 255 x 255 x 128 x 256^3
= 255 x 255 x 2,147,483,648
= 1.39640 x 10^14
Total Number of 'IP Area Code' Addresses per 'Zone IP' Address
= 255 x 128 x 256^3
= 255 x 2,147,483,648
= 5.47608 x 10^11
Distribution per 'Zone IP' Address yielding the 'IP Area Code' Addresses
Class A-1, 1 - 128, Subnet Identifier 256:256:256.y.x.x:
2.73804 x 10^11 Networks and 8,257,536 Hosts: 0
Class A-2, 1 - 128, Subnet Identifier 256:256:256.256.y.x:
1.36902 x 10^11 Networks and 32,256 Hosts
Class A-3, 1 - 128, Subnet Identifier 256:256:256.256.256.y:
6.84510 x 10^10 Networks and 128 Hosts
Class A-4, 1 - 128, Subnet Identifier 256:256:256.256.256.256:
6.84510 x 10^10 Network / MultiCast IP Addresses / AnyCast
E Terrell [Page 64]
Internet Draft December 13, 2001
2. Total IP Addresses for 'Class B' having '255' 'Zone IP' Addresses
= 255 x 255 x 64 x 256^3
= 255 x 255 x 1,073,741,824
= 6.98201 x 10^13
Total Number of 'IP Area Code' Addresses per 'Zone IP' Address
= 255 x 64 x 256^3
= 255 x 1,073,741,824
= 2.73804 x 10^11
Distribution per 'Zone IP' Address yielding the 'IP Area Code' Addresses
Class B-1, 129 - 192, Subnet Identifier 256:256:256.y.x.x:
2.20046 x 10^11 Networks and 4,194,304 Hosts: 10
Class B-2, 129 - 192, Subnet Identifier 256:256:256.256.y.x:
5.13383 x 10^10 Networks and 16,384 Hosts
Class B-3, 129 - 192, Subnet Identifier 256:256:256.256.256.y:
1.28346 x 10^10 Networks and 64 Hosts
Class B-4, 129 - 192, Subnet Identifier 256:256:256.256.256.256:
4.27819 x 10^9 Network / MultiCast IP Addresses / AnyCast
E Terrell [Page 65]
Internet Draft December 13, 2001
3. Total IP Addresses for 'Class C' having '255' 'Zone IP' Addresses
= 255 x 255 x 32 x 256^3
= 255 x 255 x 536,870,912
= 3.49100 x 10^13
Total Number of 'IP Area Code' Addresses per 'Zone IP' Address
= 255 x 32 x 256^3
= 255 x 536,870,912
= 1.36902 x 10^11
Distribution per 'Zone IP' Address yielding the 'IP Area Code' Addresses
Class C-1, 193 - 224, Subnet Identifier 256:256:256.y.x.x:
1.19789 x 10^11 Networks and 2,097,152 Hosts: 110
Class C-2, 193 - 224, Subnet Identifier 256:256:256.256.y.x:
1.49737 x 10^10 Networks and 8,192 Hosts
Class C-3, 193 - 224, Subnet Identifier 256:256:256.256.256.y:
1.872 x 10^9 Networks and 32 Hosts
Class C-4, 193 - 224, Subnet Identifier 256:256:256.256.256.256:
2.6738 x 10^8 Network / MultiCast IP Addresses / AnyCast
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Internet Draft December 13, 2001
4. Total IP Addresses for 'Class D' having '255' 'Zone IP' Addresses
= 255 x 255 x 16 x 256^3
= 255 x 255 x 268,435,456
= 1.74550 x 10^13
Total Number of 'IP Area Code' Addresses per 'Zone IP' Address
= 255 x 16 x 256^3
= 255 x 268,435,456
= 6.84510 x 10^10
Distribution per 'Zone IP' Address yielding the 'IP Area Code' Addresses
Class D-1, 225 - 240, Subnet Identifier 256:256:256.y.x.x:
6.41729 x 10^10 Networks and 1,048,576 Hosts: 1110
Class D-2, 225 - 240, Subnet Identifier 256:256:256.256.y.x:
4.01080 x 10^9 Networks and 4,096 Hosts
Class D-3, 225 - 240, Subnet Identifier 256:256:256.256.256.y:
2.50675 x 10^8 Networks and 16 Hosts
Class D-4, 225 - 240, Subnet Identifier 256:256:256.256.256.256:
1.6712 x 10^7 Network / MultiCast IP Addresses / AnyCast
E Terrell [Page 67]
Internet Draft December 13, 2001
5. Total IP Addresses for 'Class E' having '255' 'Zone IP' Addresses
= 255 x 255 x 15 x 256^3
= 255 x 255 x 251,658,240
= 1.63641 x 10^13
Total Number of 'IP Area Code' Addresses per 'Zone IP' Address
= 255 x 15 x 256^3
= 255 x 251,658,240
= 6.41729 x 10^10
Distribution per 'Zone IP' Address yielding the 'IP Area Code' Addresses
Class E-1, 241 - 255, Subnet Identifier 256:256:256.y.x.x:
6.04127 x 10^10 Networks and 967,740 Hosts: 1111
Class E-2, 241 - 255, Subnet Identifier 256:256:256.256.y.x:
3.5398 x 10^9 Networks and 3,810 Hosts
Class E-3, 241 - 255, Subnet Identifier 256:256:256.256.256.y:
2.0741 x 10^8 Networks and 15 Hosts
Class E-4, 241 - 255, Subnet Identifier 256:256:256.256.256.256:
1.2903 x 10^7 Network / MultiCast IP Addresses / AnyCast
*Note: In other words, IPv8 represents 255^2 (65,025) copies
of the IPv7 IP Addressing Schematic, in which there is
only one copy assigned per IP Area Code Address. While
there are only 255 IP Area Codes per Zone IP Address,
and a total of 255 Zone IP Addresses that use only 48
Bits of this 64 Bit Addressing System. It amounts to a
total availability of 2.78 x 10^14 IP Addresses, which
forms the Base, or Default Addressing Schematic for the
IPv8 IP Specification, that can be expanded to 128 or
more Bits utilizing the foundation of IPv7 as its Base.
E Terrell [Page 68]
Internet Draft December 13, 2001
Nevertheless, it should be very clear that there exist 255 Zones IP's, that
contains 255 IP Area Codes. In which each IP Area Code, is a IP Block
Address, which contains an independent copy of the entire IPv7 IP
Specification. This translates into approximately 4.278 x 10^9 available IP
Addresses per 'IP Area Code' IP Address. Needless to say, the value of the
of the IPv8 Addressing Scheme, is that, if it were employed today, its use
would probably equal approximately 1/36 of the total number of IP Addresses
available in 48 Bits. Where by, given our present population total, which
is distributed over 7 continents, calculates to an approximate 6 Billion
people. Then there would only be a need for the use of 7, from the 255
total number of Zone IP's that exist in IPv8. What this means, is that,
each continent would have 255 IP Area Code Addresses for distribution, and
248 Zone IP Addresses would remain unused. In fact, this IP Specification
provides for the total and complete integration of every aspect of the
entire Telecommunication Industry, into the very fabric of all that which
is life today. And there would yet remain, room for expansion.
Chapter V: Subnetting, Supernetting, and Routing in IPv7 & IPv8
The logical Division of a Network IP Address, the 'Whole', into several
smaller 'Sub-Network Units', the 'Parts', which underline the methods of
Subnetting and its derivative, Supernetting, will differ somewhat, if not
significantly from the techniques presently employed in IPv4. In fact, the
routing techniques described in the closing sections of this chapter, which
outlines the 'Network Hierarchical Architecture' of IPv8. Requires, if not
mandate, more precise definitions and laws, which establish the logical
foundation for the procedures governing the Subnetting and Supernetting
techniques use in the IPv8 IP Specification. However, this is not to say,
nor imply, that these techniques are not applicable to IPv7, because they
do indeed apply. In other words, the Laws and Definitions is a direct
consequence of the conclusions derived from the preceding Chapters, which
are built upon the logical derivation of a New Method for Enumeration in
the Binary System.
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Definitions
1. By Definition, every IP BIT Address is divided into sections
called OCTETS. And, in every IP Bit Address there must exist
at least One OCTET Defined by the Subnet Identifier. Where
each Octet maintains a total of 8 Binary representations of
either 1's, 0's, or any combination thereof, that can
collectively be Translated into one, and only one Decimal
(Positive Integer) Representation.
2. Every Octet not defined by the Subnet Identifier, may be Defined
by the Subnet Mask. Where the value of the Subnet Mask is defined
as equaling the Binary Difference that yields the Binary values
represented by the Decimal Numbers; 2^7, 2^6, 2^5, 2^4, 2^3, 2^2,
2^1, and 2^0. Where the Minuend equals the 'Subnet Identifier'
(256 or 11111111).
3. Every Network IP Address may contain at least one Subnet Mask.
Where the Total Number of Subnet Mask that it can have, depends
upon the Number of available Octets, and the Binary Bit Address.
4. Every Network IP Address having an Octet defined by a Subnet Mask,
can be subdivided into Multiple Sub-Networks. Where the process of
creating logical divisions of an IP Address is called 'Subnetting',
and the Subnetting any IP Address, which contains only one Octet, is
called 'Supernetting'.
5. For every IP Address, having one or more Octets defined by the
Subnet Identifier, and at least one which is not, defines an IP
Network Address, which can be Supernetted. Where, if any Logical
Division of an IP Network Address, creates multiple IP Addresses
derived from the original. Then the derived IP Addresses are
called Sub-Networks of the initial IP Address, which is said to
be Subnetted. This is provided that the OCTET defined by the Subnet
Mask, is not defined by the Subnet Identifier.
6. For every Octet defined by the Subnet Mask for any Sub-Network IP
Address. The Octet referenced as being the IP Network Address
from which it was derived, can not be assigned any value in the
IP Address Range, which the Subnet Identifier defines.
7. The Laws of the OCTET are applied to every Octet defined by the
Subnet Mask. That is, it can not be used in IP Address that would
result in a conflict with any IP Address, whose Octet is defined
by the Subnet Identifier.
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Internet Draft December 13, 2001
Where DE = the Decimal Equivalent that is also equal to the (BR) Binary
Representation. That is, the Subnet Mask, can only be assigned the IP
Address values summarized in the Table 7. Nonetheless, an example of this
Binary Difference is given in Figure 7. Where by, given 2^8 = 11111111 =
256 is the Minuend. Then the value of the 'Subnet Mask' is equal to the
value of the Difference between the Minuend and the Subtrahend, which
results in the Decimal Numbers: 2^7, 2^6, 2^5, 2^4, 2^3, 2^2, 2^1, and 2^0.
Summarized in Table 7, we have:
Figure 4
Binary Representation Decimal Equivalent
/ \ / | \
1. 11111111 - 0 = 11111111 = 256 = 2^8
2. 11111111 - 01111111 = 01111111 = 128 = 2^7
3. 11111111 - 10111111 = 00111111 = 64 = 2^6
4. 11111111 - 11011111 = 00011111 = 32 = 2^5
5. 11111111 - 11101111 = 00001111 = 16 = 2^4
6. 11111111 - 11110111 = 00000111 = 8 = 2^3
7. 11111111 - 11111011 = 00000011 = 4 = 2^2
8. 11111111 - 11111101 = 00000001 = 2 = 2^1
9. 11111111 - 11111110 = 00000000 = 1 = 2^0
Note: It should be clear that the Binary method of
Subtraction is quite different from the Bitwise
Anding method used by the Default Subnet Mask to
resolve an IP Address.
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Internet Draft December 13, 2001
Nonetheless, there is a logical rationalization for the choice of the
values of the Subnet Mask. Where by, the Binary Equations of Subtraction
yields functional results, which has a 'Least Significant Digit', that is
also the Factor use for the Translation of the Binary representation to its
Decimal (Integer) Equivalent.
TABLE 7
(The Resulting Modification of Table 7 noted above)
Least Binary Decimal: Number Number
Significant Representation Equivalent of Hosts*
Bit Subnets
| | | | |
0 0 0 0 0
2^7 01111111 256 - 128 = 128, 2 128
2^6 00111111 256 - 192 = 64, 4 64
2^5 00011111 256 - 224 = 32, 8 32
2^4 00001111 256 - 240 = 16, 16 16
2^3 00000111 256 - 248 = 8, 32 8
2^2 00000011 256 - 252 = 4, 64 4
2^1 00000001 256 - 254 = 2, 128 2
2^0 00000000 256 - 255 = 1, 256* X*
Note: The 'Asterisk' represents Values in which an account
for the Rule excluding All Binary '1's', that can
be maintained by a value of the 'Subnet Mask'. Here
we have conclusions resulting in an exception, as was
the case in the former use of '255.255.255.255' as the
Default Subnet Mask, being the derived Subnet Mask for
the Subnetting of the Parent Network's Hosts.
Nevertheless, the Number of Host per Subnet are
only approximations.
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Internet Draft December 13, 2001
Nevertheless, since there exist a Total Count of 256 Decimal (Positive
Integers), '0' not included, which are representations expressing the total
Number of available IP Addresses. That is, since this is the inclusive
count of the given Range 1 - 256. Where by, equation 1, which enumerates
this inclusive count, yields the Total number of IP Addresses in the Range
'1 û 256'.
1. 1 - 256 = 256, where '0' is excluded from the
actual inclusive Total.
Moreover, this is also the Binary Representation, which equal of the
inclusive count for the total addresses in the 1 - 256 Range. It can be
concluded, that the Minuend 256, is some Multiple of the Number of Total
Number of Hosts Bits. That is, given that calculation of this total, is
also the inclusive count of the range comprising the Octets. In which case,
the Binary Number of Hosts Available would be represented as 2^24, 2^16,
and 2^8. That is, provided these numbers represent a count relative to the
Total Number IP Bit Mapped Host Addresses. However, if the case is such
that, the total number of Host Bit available were, '65,536', and the Least
Significant Digit given as '128'. Then, the Total of IP Host Bit Addresses
available given by the equation 2 would represent the used to determine the
Number of Host resulting from the Subnetting of the Last 2 Octets in any
given IP Address.
2. [65,536 / 128 = 512]
Furthermore, given the definition of Supernetting, as being the Subnetting
of the Last Octet available in any IP Address. Then, the total number of IP
Host Bit Addresses available would equal the Least Significant Digit. In
which case, the results of equation 3 would translate to a total number of
IP Host Bit Addresses equal to '1', which would have an IP Bit Map Address
of 31 Binary Digits, as represented in Table 18 and the equation 3.
3. [256 / 128 = 2]
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Internet Draft December 13, 2001
Nevertheless, the procedures involving Supernetting, as outlined in the
Classless System, did not eliminate the Structure or concepts of the Class
System. Especially since, it did not define Supernetting as a derivative of
Subnetting, which is the Subnetting of the Last Octet of any IP Address.
Notwithstanding, the Definitions and Laws defining the Internet Protocol
Specifications for IPv7 and IPv8, which regarding their implementation, has
change the concepts of Subnetting and Supernetting. That is to say, the
definition of the Subnet Identifier imposes restrictions upon the
availability of the Octets, which can be Subnetted or Supernetted. Where
by, if only the Host Octets are available, then those that can be Subnetted
is the lasts two Octets within the IP Address. While Supernetting, is now
defined as the process of Subnetting the last Octet of an IP Address. In
other words, the definitions and laws of IPv7 and IPv8 describe an outline
for Supernetting and Subnetting, which can not violate the restrictions
imposed.
Needless to say, except for the laws, definitions, and the resulting
constraints imposed. The information provided herein, is essentially the
same as that which governed IPv4. Nevertheless, the Tables below summarize
the logical format, which outlines the results of the from the change in
Binary Enumeration that defines the concepts of Subnetting and Supernetting
in IPv7 and IPv8.
TABLE 16
Decimal Binary Difference LSD
and Resulting Results Factor ^
Subnets / Supernets ^ / ^ \ |
/ ^ \ /|\ / | \ |
/ | \ / ^ \ / ^ \ ^
/ | \ / | \ / | \ |
/ v \ / v \ / v \ /v\
1. 256 - 128 = 128 = 01111111, 256/128 - 128/128 = 1, 2^7
2. 256 - 192 = 64 = 00111111, 256/64 - 192/64 = 1, 2^6
3. 256 - 224 = 32 = 00011111, 256/32 - 224/32 = 1, 2^5
4. 256 - 240 = 16 = 00001111, 256/16 - 240/16 = 1, 2^4
5. 256 - 248 = 8 = 00000111, 256/8 - 248/8 = 1, 2^3
6. 256 - 252 = 4 = 00000011, 256/4 - 252/4 = 1, 2^2
7. 256 - 254 = 2 = 00000001, 256/2 - 254/2 = 1, 2^1
8. 256 - 255 = 1 = 00000000, 256/1 - 255/1 = 1, 2^0
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Internet Draft December 13, 2001
TABLE 17
Subnetting Results in IPv7 and IPv8
Number Binary Equation to Determine Available
Bit Hosts: Equivalent: Subnet Bit Mask Hosts*
/ | \ / | \ / | \ / | \
1. 8 = 2^3 (16 - 8 = 8) + 16 = 24 255
2. 9 = 2^3 + 2^0 (16 - 9 = 7) + 16 = 23 510
3. 10 = 2^3 + 2^1 (16 - 10 = 6) + 16 = 22 1020
4. 11 = 2^3 + 2^1 + 2^0 (16 - 11 = 5) + 16 = 21 2040
5. 12 = 2^3 + 2^2 (16 - 12 = 4) + 16 = 20 4080
6. 13 = 2^3 + 2^2 + 2^0 (16 - 13 = 3) + 16 = 19 8160
7. 14 = 2^3 + 2^2 + 2^1 (16 - 14 = 2) + 16 = 18 16,320
8. 15 = 2^3 + 2^2 + 2^1 + 2^0 (16 - 15 = 1) + 16 = 17 32,640
9. 16 = 2^4 (16 - 16 = 0) = 16 = 16 65,280
Note: The 'Asterisk' on the Available Host Column, is the
Mathematical Calculation having the Results, which does
not account the 'All '1's', or '0's' Exclusion Rule',
and results in the Host count as being some multiple
of '2^N'.
TABLE 18
Supernetting 'Last Octet' in Third IPv7 and IPv8
Number: Binary Equation to Determine Available
Bit Hosts: Equivalent: Subnet Bit Mask Hosts*
/ | \ / | \ / | \ / | \
1. 0 = 0^0 (8 - 0 = 8) + 24 = 32 0
2. 1 = 2^0 (8 - 1 = 7) + 24 = 31 2
3. 2 = 2^1 (8 - 2 = 6) + 24 = 30 4
4. 3 = 2^1 + 2^0 (8 - 3 = 5) + 24 = 29 8
5. 4 = 2^2 (8 - 4 = 4) + 24 = 28 16
6. 5 = 2^2 + 2^0 (8 - 5 = 3) + 24 = 27 32
7. 6 = 2^2 + 2^1 (8 - 6 = 2) + 24 = 26 64
8. 7 = (2^2)+(2^1)+(2^0) (8 - 7 = 1) + 24 = 25 128
9. 8 = 2^3 (8 - 8 = 0) + 24 = 24 256*
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Internet Draft December 13, 2001
Note: The 'Asterisk' represents Values in which an account
for the Rule excluding All Binary '1's', that can
be maintained by a value of the 'Subnet Mask'. Here
we have conclusions resulting in an exception, as was
the case in the former use of '255.255.255.255' as the
Default Subnet Mask, being the derived Subnet Mask for
the Subnetting of the Parent Network's Hosts.
Nevertheless, the Number of Host per Subnet are
only approximations.
Needless to say, any analysis of figure 4, tables 7, 16, 17, and 18 (From
Chapter V), would reveal that Subnetting or Supernetting concerns only the
Values maintained in either the whole of One Octet, or some fraction
thereof. In other words, while Table 17 and 18 shows the Subnet Bit Map
Range exceeding more than One Octet. It should be clearly understood that
some portion of this IP Address is the Network ID Portion. What this means,
is that, the Decimal Value of the Subnet or Supernet ID IP Address can only
consume either the whole or some fractional value of One Octet. Whose Range
is derived from the 8 Bits one Octet contains (Table 16), while its
respective Total Number of Hosts is a function of 2^N (Tables 17 and 18);
where the value of 'N' is equal to the Number of Bits used to derive its ID
IP Address. However, these calculations does not account accurately for the
Host Count when assigning '256.256.256.256' or
'11111111.11111111.11111111.11111111' as the IP Address for the Subnet or
Supernet, which is an acceptable practice used to assign Hosts to the
Parent Network IP Address.
Nevertheless, the values inherent and maintain by the implementation of the
IPv7 and IPv8 IP Specification that underlie its logical structure, derives
Routing Techniques, which yields a major performance gain over that
provided in IPv6. Furthermore, while there is a difference from that
described in IPv4. The inherent change is not so substantial, as to cause
a serious burden and tremendous growth in the learning curve. However,
because there yet remains strong similarities between IPv4 and IPv7. And
since, IPv8 is an enhancement of IPv7. The discussion regarding Routing,
shall focus upon IPv8, because its structure poses a challenge, which is
a departure from that seen in IPv4. Nonetheless, the methods derived for
Subnetting and Supernetting, above, should be understood as being
applicable to both, IPv7 and IPv8.
E Terrell [Page 76]
Internet Draft December 13, 2001
However, even with this being said, IPv8 clearly show its kindred to IPv4,
which is established through its relationship with IPv7. Hence, almost
everything that was familiar in IPv4 is retained, and the provisions, which
allows an 8 Bit growth rate approaching 128 Bit Addressing, yields a
staggering '3.40282 x 10^38' IP Addresses. Moreover, Incremental Growth is
a very significant factor, especially when considering the Routing and
Networking implications. Where by, Supernetting and the techniques of CIDR
attempts to improve Router performance through the use of the Subnet Mask,
and by looking at the Back End of an IP Address Aggregation. Thus, allowing
a reduction in the size of the Router's Table, and increasing the
thoroughfare by permitting the assignment of several IP Addresses to this
Back End Address.
However, the implementation of IPv8 suggests just the opposite, without the
elimination of CIDR. Where by, Router's become more specialized Address
Forwarding Computers belonging to 1 of 3 categories; The OuterCom, the
BridgeCom, and The InterCom. These categories houses three router types in
2 Divisions; the 'Primary' and the 'Secondary'. Where the 'Primary' and
'Secondary' divisions provides the clarity, which indicates the established
function and duties these Routers are to perform.
Nevertheless, the routers belonging to the 'OuterCom' category, is the
'Global' and the 'Internetwork' routers, which are assigned to the
'Primary' division. And while the 'Network' router does not have a
divisional classification. It is assigned to the 'BridgeCom' category,
because it serves both the 'OuterCom' and the 'InterCom' routers. Where it
functions as a LINK, which is used to establish the communications between
the 'Primary' and 'Secondary' divisional routers.
Nevertheless, this hierarchical structure concludes with the introduction
of the 'InterCom' category, which houses the 'Secondary' divisional
routers: the 'Inter-Domain' and the 'Intra-Domain'. These routers are used
to control the internal communications of the Networks defined as being
the smallest sections of this Network Hierarchical Architecture. Where by,
the 'Inter-Domain' router routes, when the communication is 'InterCom',
using only the IP Address of the Octets defined by the 'Subnet Identifier'.
While the Intra-Domain router, routes an 'InterCom' packet to its final
destination using the 'CIDR' technique.
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Internet Draft December 13, 2001
The defining purpose of these classifications provides not only an accurate
and functional description, but renders the Overview of the 'Network
Architectural' Layout, itself, as a major boost in the overall performance
of the Network. In fact, the implementation of this 'Network Architecture'
alone, would reduce the Router's Table, reduce Network Traffic, and enhance
System Management capabilities. Where by, the benefits inherent to these
specialized Routers is accomplished by programming each to perform there
individualized functions. While the Individualized Functions that the
programming procedure would encompass, entails segmenting the IP Address
into 'Routable Blocks' and creates 'Routable Blocks' portions of the 32 Bit
Address Block, which would also be routable. This method would allow all of
the OuterCom Routers to be programmed, for example, to Route only using the
Front End of the 8 Bit Blocks of IP Address format. This is the convention
and purpose for establishing the assignment, which defines the Global
Router to the 'Zone IP' section of the IP Address, and the 'Internetwork'
router to the 'IP Area Code' Address. Thus, achieving a significant
increase in the Router performance overall, which is a far superior
improvement over that which can be achieved using the CIDR technique alone.
The reality of these benefits becomes even clearer when an understanding of
Front End Addressing achieved. Where by, the Global Router would route
using only the first 8 Bits of an IP Address. The Zone IP, then remove the
Zone IP Address before forwarding the communication to the Internetwork
Router, which uses only the second 8 Bits to route by IP Area Code, and
strips this 8 Bit Block IP Address before routing to the Network Router.
This allows the Routers to determine if the communication is an Intercom or
an Outercom, which is a method use to determine Geographical Location. In
which case, if it is Outercom, the Router needs only to know the location,
and or Hop Count, of the nearest Internetworking Router(IP Area Code
Address), which in turn needs to know the location of the Global Router
(Zone IP Address). The benefits here, is that, in either case, these
Routers need only know, or be, 2 or 3 connecting Routes beyond the single
Point of Failure.
Nevertheless, while all Intercom communications are Routed as belonging
somewhere within the Domain of the Network Router, which also increases the
overall performance in Routing Communication's. The Network Router is
indeed the pivotal point of this Network Routing Hierarchical Structure.
In other words, it is assigned the task required to establish the Inter and
OuterCom Communications with the Global, the Internetwork, and the
Inter-Domain Routers. This makes the Network Router the line of
Debarkation, which is the necessary and fundamental focal point for all
Communication Traffic.
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However, the responsibilities this levies upon the Network Router and it's
routing Table, remains yet, far less than the Corporations today. Where by,
continuing with the '2 or 3 connecting Routes beyond the single point of
failure' scenario, or CRBSPF. At most, the Network Router need only
maintain 3 separate Routing Tables that contains the routes of the Global,
the Internetwork, and Inter-Domain Routers. This provision provides the
Network Router with the specificity that is necessary to improve Router
performance, while allowing it to maintain individually, the respective
knowledge of 2 or 3 connecting Routers and their Routes beyond the single
Point of Failure.
Nevertheless, once the packet has reached the Inter-Domain Router of the
Network, which lies outside the Boundary of any Private Network. In which
there exist 4 types; Commercial, Governmental, Public, and Private. The
Inter-Domain Router routes the communications packet, using only the first
16 Bits of the IP Address to route to the Intra-Domain Router of the
packet's destination. This method provides the Inter-Domain Router with the
same advantages of the 3 primary Router types. That is, it needs only to
maintain the knowledge of the location of the Global, the Internetwork, the
Network, and the Intra-Domain Routers, which comprise 4 separate Routing
Tables. This knowledge also includes the location of 2 or 3 of these
respective Router, and the associated connecting routes beyond the Single
Point of Failure.
The above methodology, described clearly, the most basic routing
hierarchical structure, and while this structure appears an
oversimplification. However, there are only '255 Zone IP' Routers and '255
IP Area Code' Routers, which maintains contention for providing a
performance increase, regardless. And while, these are the only Routers
that can strip portions of the IP Address to improve the speed of
transmission, which can be controlled in the Header, using Bits. Even
routing the entire IP Address will not deplete performance, which is
indeed, a boon for Security and Encryption Implementation, not to mention
Secure Single Line Communication. And this is judged a real possibility,
not only because of the increase in the transmission rates, but the
likelihood of the number of people using this technique.
Furthermore, if the 3 Primary Routers maintained permanent locations, then
clearly, this Routing Hierarchical Scheme would become a very plausible
reality. This is because, not one of the Primary Routers would need to know
the location of every Router, but if need be, could easily find them.
Especially if, this system were further enhanced with Transmitters, which
would Broadcast at regular intervals, or told by remote control, when to
broadcast. This procedure would allow Routers, when needed, to use one of
the Internet Discovery Protocols to find other Routers, or establish
communications. Needless to say, the inherent advantages of this
implementation are breathtaking, to say the very least.
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I mean, when considering just some of the implications; Mapping, Tracking,
Locating, and Navigation, which can all become possible through the use of
permanently located routers. In what would become, a 'Land Based Global
Navigation System', which uses ground based systems that communicates using
the Hardware Address of MAC Layer. The startling features of this system,
allows not only land, Air and Sea Navigation. But poses a serious challenge
to the development and deployment of Communication Satellites, questions
their high costs and significance. Especially since, this system could
easily provide the Terrain Maps, Tracking and Locating persons or vehicles
having the hardware to transmit a signal, and make real, the Reality of Un
-Manned Transportation System. Even pilot Airplanes remotely, or provide a
live monitor for every flight, as an added safety feature. And while
'LBGN', does poses a challenge to the current Satellite Communication
Systems. It can not eliminate their use, because they provide an
unquestionable visual observation ability, that a ground based system could
never compete against, and would always maintain a disadvantage from the
topological perspective.
However, the great advantage of this system, is that, it allows Emergency
Response Personnel, to locate people in trouble, and do so, using the
Hardware Address of the MAC Layer to find them, even while they are
talking. And this implies, that the communication could be Cellular or
Radio Wave. It really does not matter because, when Stationary Routers and
MAC Layer communication is implemented, it could also be controlled, to
prevent Traffic Congestion. Needless to say, while all of this might seem
startling at first. The worry regarding a shortage of MAC Layer Addresses,
is soon to become an issue. There's no cause for alarm however, because the
badly needed MAC Addresses has already been created. Remember IPv6? It has
all the MAC Addresses you will ever need, and then some to spare.
Especially since, the possibility exist, that perhaps, some time in the
future, or even now, the number of Hardware Devices will exceed the
population total.
Needless to say, a Computer could easily handle the cumbersome structure
and superfluous address definition. Which could be used to issue MAC
Addresses to manufactures, or written directly to the Hardware Device. This
would serve not only to reduce the errors, but save the people from the
aggravation of having to use and work with the IPv6 protocol.
Nevertheless, while the limelight has indeed revealed the possibilities
encompassing the 3 Primary Routers. It is clearly, the mandates commanded
by the Secondary Routers, which dictates the change that makes these
possibilities a Reality. However, given by today's performance standards,
the Global and Internetwork Routers have the advantage of being capable of
routing using only an 8 Bit IP Block Address, which is it also capable of
stripping from the initial IP Address. Needless to say, while these issues
might seem important by today's standards. There are similar advantages
employed in the Secondary Routers.
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Where by, the Network Router uses, at most, 16 Bits to route, and only 8
Bits are necessary for it to route to the Internetwork Router. This means
that, the Network Router requires 16 Bits to route to the Global Router,
and the first 16 Bits of the 32 Bit IP Block Address to route to the Inter
-Domain Router. And while the Inter-Domain Router is the only Router that
requires the use of the entire 32 Bit IP Block Address to route to the
Intra-Domain Router. It routes to the OuterCom Routers using the methods
they employ; the 8 Bit IP Block Address when routing to the respective
Global and Internetwork Routers, and the first 16 Bit of the 32 Bit IP
Block Address to route to the Network Router.
Nevertheless, the Intra-Domain Router uses at most, 16 Bits and CIDR
techniques to route the communications packet to its final destination,
and the same routing methods employed by the Global, the Internetwork, the
Network, and the Inter-Domain Routers, to route to their locations. In
other words, the Global Router uses only an 8 Bit IP Block Address for
normal communication routing, and the entire IP Address for Direct Routing.
While the Internetwork Router uses either an 8 Bit IP Block, the first 8
Bit of the 32 Bit IP Block to route. Where as the Network Router uses
either 8, or 16 Bits to Route. However, the performance load seems
displaced because, Inter-Domain uses either 8, 16, or 32 Bit IP Block
Addresses to route, which means greater demand. And while the final
destination should bare the brunt, the Intra-Domain Router uses only 8,
or 16 Bits to route. And of course, as with the Global Router, the
Intra-Domain Router must be capable of Direct Routing, which means, it must
also route the entire IP Address as well.
Nevertheless, the results mandates an enhancement in the overall
performance claimed by the Primary Routers, which are the requirements
imposed by the Secondary Routers, that also necessitates the simplification
of the existing wiring structure. These mandates are an extension of
demands encompassing the established concepts of "Ease of Use and
Implementation", and the 'Principle of Plug and Play'. In other words, this
is a 'Start from the Ground Up' implementation. That requires the
elimination of the present wiring system and "Junction Box". Where by,
'Bare Wires' would be replaced by either a 'Hub' or 'Connector Plugs', such
as the 'Splitter' 'SJ45-2, -3, -4, and -6', which connects 2 or more
distinct and separate 'Ethernet lines' in a network, and the 'SJ11-2, -3,
-4, and -6', which is similar the Ethernet arrangement, but connects
multiple and distinct telephone lines.
The obvious benefits notwithstanding, clearly, if IPv8 becomes the Standard
for the Global Telecommunication System Interface. Then the existing
Telephone Numbers in use today, would be replaced by the 32 Bit Block IP
Address, and the Analog Telephones by Digital Telephones, which utilizes
software to eliminate the need for anyone to maintain the obligation of
having to remember any number beyond 15 digits.
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In other words, the establishment of a sequential order having only an 8
Bit growth rate, is the ultimate boon for IPv8, which allows for a more
gradual and stable growth approaching the 128 Bit IP Addressing format.
Needless to say, its methods of Routing any form of Communication, clearly
caps its superiority well beyond any other IP Specification. The evidence
of this fact, is first established by its Front-End Routing techniques, and
while communications from an Intra-Domain to some OuterCom Location would
require the 48 Bit IP Address to remain intact. Its Front-End Routing
techniques would prove still, far superior than the methodology in use
today. Moreover, the second boon for Front-End Addressing, is derived from
the 'Block-Addressing' Structure of the IP Address. While this structure
allows only the Global and Internetwork Routers to Strip their respective
IP Block Addresses from the IP Address when the routed communication is the
direction of some Intra-Domain. The velocity at which these 8 Bit IP
Address Blocks can be Routed in any thoroughfare will prove, just as fast,
if not faster, than the Switches presently employed.
Chapter VI Conclusion: Outlining the Benefits of IPv7 and IPv8
The benefits from the implementation of IPv7 could be a reality now. This
is because there are absolutely no changes in its Header, or any of the
other specifications outlined in other RFC's pertaining to datagrams or its
relation to other protocols. And while, the underlying representation for
Enumeration remains the same, the process characterizing this method, the
Binary Representation, has indeed changed. What this means is that,
Software Upgrades required to implement IPv8, could be implemented now, to
take advantage of every aspect of both IPv7 and IPv8. This is required
because, regardless of whether or not IPv8 is used now, or 10 years from
today, the loss suffered exceeds 133,000,000 IP Addresses available in
IPv7, which is greater than IPv4. Needless to say, the validity of the
latter, is established by the foundations presented, which underlie the
logical foundations of IPv7 and IPv8.
Nevertheless, while the findings presented, are indeed confounding and
thought provoking issues, which represent the beginnings of what could
prove to become such a profound discovery. Whose impact could produce such
a measurable, and significant effect upon every aspect of the Theoretical
and Applied Mathematical Sciences. That every Industry caught in its wake,
could undergo a profound and dramatic change. In fact, every Industry in
every Technologically Advance Nation in the World, that succumb to the
dependencies imposed by this Technological Revolution, called the
Information Age, will indeed undergo such a profound and Revolutionary
change, that no other event in all of History will seem its equal.
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Notwithstanding the effects provided by the addition of a more stringent
adherence to the rules of Logic. The stability of a more gradual and
controllable growth in the number of available IP Addresses, will seem to
most, beneficial. However, the effects of changing the method of
enumeration in the Binary System, will boggle the minds of even the most
knowledgeable, and educated of persons, the world over.
Clearly, the result of the implementation of IPv7 and IPv8 will usher more
than a stable and gradual growth for the Global Telecommunications
Community. In fact, the elimination of the mistakes in IPv4 and the change
to the Binary System's method of enumeration, ushers new commitments and
promises that will ignite the Dawn of the Intellectual Revolution. Needless
to say, these promises are guarantees that will sustain not only the
promises of 'Internet', but will establish the necessary foundation, which
solidifies the gap that creates and maintains the cultural barriers and
differences present in the world today.
Furthermore, the benefits from the implementation of IPv8 will seem to
overshadow the number of available IP Addresses it provides. That is, its
implementation will foster the reality of dreams that were once thought the
fantasy found in the pages of a Science fiction novel. This includes such
simple problems as those experienced by the Telephone Companies, the
shortages in the supply of telephone numbers. Where by, the adoption of
this system would change the count in the number of digits from the present
11, to a maximum of 15. Nonetheless, while this eliminates problems
associated with growth and the constantly changing prefix. Its adoption
could also change every concept in the Structure, Use, and underlying
Foundations of the Entire Telecommunication Industry.
I mean, just think for a moment. Where, something as simple as the
'Junction Box' (MPOE), that now serves as the connecting and distribution
point, for homes, business, and apartment complexes. It could quite
conceivably, be replaced by a Network Server, a Router, and Hub, which
would lessen the burden associated with the cost of the present
arrangement. In short, the existing Private Telephone System would be
replaced with a Private Computerized Telecommunication System, and the
Public Telephone System would become the Computerized Information
Telecommunication Systems. These new systems could service the population
of the entire World with any information available from some assigned
Resource Distribution Center.
While at the same time, IPv8 continues to open many other avenues of
exploitation for the Industries of the Entire World. For example, the
Television Industry, Cable Television Industry, the Video Telephoning and
Video Teleconferencing Industry, are only a few of the many corporations
that could benefit from its implementation. Nevertheless, accompanying this
presentation, below, is a Table listing the Hardware and Software changes
mandated by the implementation of the IPv7 and IPv8 IP Specifications.
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Table of Changes and the Specifications
Required for Software and Hardware*
HARDWARE IMPLEMENTATIONS | INDUSTRY EFFECTED | SOFTWARE & HARDWARE
AND DEVELOPMENT | | CHANGES AND SPECS
-------------------------|-------------------|-----------------------
1: Digital Telephone /w |Software |Software Changes:
Video Display and |Manufactures, |1. Network TCP/IP
Optional Video Camera |Telecommunications | Configuration:
"Mini-Operating System"|Equipment |1a.Child Window to allow
(Such as 'Windows CE') |Manufacturers, | Choice Options having
|Computer and | Selection between;
Purpose: To Establish |Related Equipment | a. IPv4 Address mode
Telephone Communication|Manufactures, and | for "InterCom"
Using the 'Internet', |in all cases their | Communications
by Polling using MAC |products effects |
Hardware Address for |the Consumers. |2a. IPv7 & IPv8 Address
Status Check and Ringing.| | Mode for "InterCom" AND
------------------------|-------------------|"OuterCom" Communications
2: Design of SJ45 Splitter| | within the same
to Connect Multiple | | "IP Area Code", or
RJ45 Lines; SJ11 | | outside of the Zone IP
Splitter to connect | | Address.
Multiple RJ11 Lines | |
This would eliminate | |Note: Child Window to
individual wiring of | |allow Choice Options
Analog and, or Digital | |being either a 'Radial
Telephone Connections | |Button' and / or a
and allow this scheme | |"Question Message" asking
to be replace by Hubs, | |if communications either
Routers and Servers. | |a InterCom or OuterCom
-------------------------| |Transmission. Then,
3: Electronic Transponder | |asking for a Specific
that Broadcasts IP | |Location of Destination.
Address Location to | |(Locations are
Determine Geographical | |referenced from options
relative to some known | |
or Fixed Location | |Note: These changes
(Query having Response) | |effect the Computer
| |Operating Systems and
| |other communications
| |software.
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--------------------------|-------------------|
4: Design Of Language | Applies to all |
Translation Servers | the companies |2. Application Changes:
which will translate | |1a. All Mathematical
communications between | | software applications
different cultures | |and calculation programs.
| |Note: Changes effecting
| | Application Software
--------------------------| | performing some
5: Global Accessed | | function related
Resource Information | | to/in Mathematics,
Servers | | results from the
| | Change in the Methods
| | of Enumeration in the
--------------------------| | "Binary System".
6: Design of Super | |
Computer Controllers | |3. Network Operating
to control Routing and | | System
the Switching functions | | 1a."IOS" Internet or
to replace current | | 'Network Component
Telephone Systems | | Operating System'
| |
| | 2b. BIOS of Networking
--------------------------| |Components and Equipment
7: Automobile equipped | |
with Computer IP | |Note: The changes
Broadcast Transponder, | |effecting Network OS
Locator | |and BIOS of the
| |Connecting Components/
--------------------------| |Equipment which Connects
8: Medical Patients | |Computers in a Network
wearing Computerized | |must allow for the
Status Devices linked | |changes outlined in
Medical Response Teams | |Appendix III, as given
using IP Broadcast | |by the definitions.
Devices | |
| |4. Electronic
--------------------------| | Sub-Component
9: Computerized Homes and | |1a. "Gate Logic"
Appliances using IEEE | | "Binary Instruction"
1394 FOR connection and| | Set" for 'CPU' & 'IC'
IP Broadcast for Alarms | | Components.
and emergencies. | |
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| |This would be viewed
--------------------------| |as a reduction in the
10: OuterCom and IntraCom | |Number of 'Logic Gates'
Routers with Port | |required for a given
Assignment Control and | |circuit, which are the
allow Host connection /| |results from the
Direct connection to | |Analysis of the
OuterCom communications | |Conclusions yielding a
to reduce Multiple IP | |New Method of
Address to same Location| |Enumeration for the
(But there is plenty | |'Binary System'.
to be assigned) | |
--------------------------| |5. 'Discovery and
11: Change in the Binary | | Activation Protocol
Logic that Outlines | | Algorithm Design'
not only the Functions| |1a. Remote Location and
of the Central | | Control of hardware
Processing Unit, 'CPU'| | Devices.
but provides it the | |
ability to distinguish| |2b. Algorithm Design
the Operating System | | For the Method of
it uses. In other | | 'Triangulation' of
words, every 'CPU' can| | Land Based Global
now become a 'Hybrid',| | Positioning Systems
which can use any or | | which communicates with
every Operating System| | MAC Address of Hardware
available in the | |
Computer Industry. | |
And this also provide | |
the 'CPU' and its usual| |
Operating System with | |
the ability to share | |
programs or applications| |
other Operating Systems.| |
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--------------------------|-------------------|-------------------------
12:Transponders, Receivers| Wireless |The implementation and
and MircoWave | Technology |Design of Electronic
Transmitters placed in | and the companies |Components which allow
the Standing Lights | Listed in # 1 |MicroWave Transmission
on Roadways and in Cities| above |Between Dishes on top of
for the implementation of| |Standing Lights and
# 3, 7, and 8 noted above.| |Buildings or any Towering
Which could be made to | |Structure, manmade or Natural
Pilot and Navigate | |Which would offset the need
Driverless Vehicles and | |for Satellites as the
Trains, which Maps Terrain| |primary Communication medium
of the Roadways, which | |which maintains equal
control the Guidance | |Bandwidth / Thoroughfare
Transmitters implanted in | |Which can be implemented
the Reflectors of the | |without environmental
Roads Lane Dividers / or | |disruption. Noting the
Below. | |Frequencies which would be
| |less harmful. In which case,
| |this System would serve for
| |Fiber Wire, or use Wireless
| |if Fiber is not possible.
--------------------------|-------------------|-----------------------
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Security: The Relationship between IPv7 & IPv4, and the Security;
Suggested and Recommended Alternatives for IPv8
There are no differences between the security methodologies employed in
IPv4 and that of IPv7. In fact, IPv7 is nothing more than an IP Addressing
Scheme Overlay that exploits the format of the IP Address Scheme used in
IPv4. Nevertheless, while there is an existing difference between these
Addressing Systems, they pertain only to the mathematical operations
involving the calculation of their respective IP Addresses, which are now
governed by a Set of Logical Laws. Furthermore, when noting their version
numbers, since IPv7 is not an assigned version number and identical to
IPv4. It is not necessary to change from the present use of IPv4. In other
words, IPv7 is IPv4 having a different IP Addressing Schematic depicting
the number of available IP Addresses for distribution. That is to say, it
does not require even a version number change for compatibility, IPv7 is
IPv4. This also means that the rigorous testing required of a New IP
Addressing System can be eliminated.
Nevertheless, while IPv8 is an enhancement derived from IPv7, it does
maintain marked differences, as seen in the IP Addressing System employed.
However, this should not pose any challenges for the IP Community to
examine or test. But, this is not to say, that its implementation of
Security measures will not be different from that now used in IPv4. What I
am saying, is that, IPv8 will prove far less cumbersome than IPv6. This
fact will become even more pronounced when it is realized that the
consideration for any determination regarding the level of difficulty in
the implementation of a Security System, is indeed dependent upon the IP
Addressing methods of enumeration.
Moreover, it should be clear that another distinction maintained by IPv8,
which is a provision that allows for a separation or division of the
Security measures employed. This is a result of the 'Address Block'
configuration, which provides a way to Address, Separate and Distinguish
the Different Segments of the 48 Bit IP Address in IPv8. However, the
result of this method allows for the creation of 3 levels of Security,
because there are 3 separate and distinct IP Addresses that equal the total
of this 48 Bit configuration; YYY:JJJ:XXX.XXX.XXX.XXX or
256:256:256.XXX.XXX.XXX).
This however, emphasizes a greater the need for Security measures, which
should be employed to control InterCom and OuterCom communications of the
Global Internetwork. This reality is evinced by the fact that, the Global
Telecommunications Community for the first time, will assume its true
identity. Where by, because of the need for an ISP to establish the
connection to the Internet. We become impressed with the thoughts of the
Global Telecommunications Community (The Internet) as being a Dynamic
Communications System. That's always on, and never sleeps. However, this is
a miss conception, or interpretation of that which is truly as Static
System.
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That is to say, the Global Telecommunications Community (The Internet) is
only a thoroughfare, which is not unlike the cable connecting the
telephones presently in use. In other words, to have a single connection
requires a Link. It does not matter, if this Link or connection you dialed,
provides you with a Requester or an IP Address. The point to be made, is
that, a connection must be established with someone, who will grant access
to his or their location on the Party Line. What this means, is that, the
Internet is only a Cable. While the Global Telecommunication's Community,
is indeed a Community, which consists of several Millions of People who
have jointly agreed to become members of this Party Line. Thus, allowing
access to their Telecommunications Information System, to anyone whom has
agreed to become a member.
Nevertheless, IPv8 transcends this present and limited notion of the
Internet, and truly provides everyone with access to the Global
Telecommunications Community. Where by, everyone in the world having a
telephone today, would have controllable access to this Party Line.
However, everyone connected to the Global Telecommunications Community
would use the IPv8 Addressing Configuration related to the connection of
the Destination Address with whom they chose to communicate. In other
words, if the Destination was located within the Zone and IP Area Code of
the Source, then they would only need to use the 32 Bit portion of the 48
Bit IP Address. This is because the Router used to Transmit the
communication would be a InterCom Router, capable of routing the IP Area
Code Address Block and the 32 Bit IP Address indicating the Network IP
Address of both the Source and Destination locations.
Needless to say, this diverse functionality provides a greater expansion of
the IPv7 IP Addressing System without any sacrifice in the over all
Security, as would be the case if a significant departure from the IP
Addressing System now employed, were implemented. In fact, the knowledge
gained through the implementation of the Security measures in IPv4, should
provide a strong foundation for any transition to IPv8.
What this means, is that, the degree and type of Security can vary as a
matter of choice or concern. For example, an Administrator could use the
same level of Security for IntraDomain Communication (InterCom) and either
increase or use a different, more specialized type of Security measure for
the OuterDomain Communication (OuterCom).
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In other words, one suggestion that would create this possibility, is to
employ a software tool that would allow the user to differentiate the
locations they desire to establish a communication with, which is prefixed
by either or both, the Zone IP or IP Area Code. The software would then,
automatically configure the corresponding IP Addresses within the datagram,
which is identical to the current methods in use. This would allow all
communication that exists within the same Zone IP and IP Area Code Address
to be the same as that which is presently employed. The reality of this
process is derived directly from the concept of the Smart Router. Whose
programmed task, when routing any transmissions, is that of Striping either
the ZONE IP, the IP Area Code, and no part of the sequence of the Network
IP Address, which is related to its location for delivery of the
transmission to its destination.
Nevertheless, this method reduces somewhat, the complexities of
implementing Security measures for a 48 Bit System to that of a 32 Bit
System, which would resemble IPv4 and IPv7. Whose Security can be
controlled by the same methodology, that being, Software Encryption and
Access Rights, which is now employed. What this suggests, is that, IPv8
can have 3 distinct levels of Security, which can be implemented
automatically by the Routers, and, or controlled by Software.
What this implies, is that, every Domain must have a minimum of 2 types of
Routers to control IP routing and Security; the IntraDomain Router
(InterCom Router), the Inter-Domain, the Network, the Internetworking
Router (OuterCom Router), and the Global Telecommunications Router (Global
Router). Their functional purpose would not only facilitate Routing, but
enhance Security Communications as well. This is because the methods of
Routing employed would consist of the Front End of the IP Address, and
Encryption of the Data Segment of the transmitted Packet. Where by, each
type of Routers need only know the location of the next Router which routes
the either the same IP Address Block or the next IP Address Block in the
sequence. This would essentially have the effect of creating a One-Route
Path having a Multi-IP-Address-Thoroughfare. That would allow Decryption of
Datagrams either by specific Routers, or the Software of the intended
Destination.
Needless to say, this suggestion does not necessarily impose a challenge
upon the Firewall. Where by, Security could be a combination of both, or
just controlled by the Smart Router, and access to the InterCom from a
Hacker transmitting from some location on the OuterCom would be, for them,
the Fort Knox Challenge.
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In other words, the Router could be used for Decryption and Encryption of
the communications it receive and transmits, or Encryption can be performed
by the Router and Decryption could be performed by Software. Whose
decryption key code is transmitted, embedded in the Datagram. There by,
allowing the receiving destination's previous decryption code, to decrypt
the Key Code to be used to determine the decryption sequence of the current
transmission. The Cable Pay Television Industry could implement such a
process. In which the Encryption, Decryption Software would be supplied by
them to their customer. While the Global Router could control and be
programmed for random sequencing of the Encryption, and corresponding
Decryption Key to be sent with the transmission. Or, by using Direct
Communication, Encryption and Decryption could be accomplished from the PC
of the intended destination.
However, the latter could be the likely scenario used in a High Security
Area, such as the Military or some Top Secret Research Facility. Which
would have the need to maintain strict control of the InterCom and OuterCom
Transmissions. In other words, a Smart Router would be capable of
discerning the type of Traffic it is passing. That is, the difference
between a transmission that is Encrypted, not Encrypted, and that which has
the incorrect encryption. And then perform the necessary functions of
Decryption on one transmission, while being capable of sending both
transmissions to their destinations.
This would provide a common access control for Authentication and
Synchronization of the Encryption and Decryption Keys. Thus, providing the
necessary Security to control the Inter and Outer æCommÆ communications
within the same Zone and IP Area Code. Which would in essence, provide
places needing to regulate access to the Global Community or their
InterCom, with the Security control they need to regulate the traffic
entering or exiting their Domain. In other words, it is suggested that,
IPv8 IP Addressing System should be implemented with 3 levels of Security,
comprising 48, 40, and the 32 Bit IP Address possibilities it contains.
These benefits however, might possess an additional cost, which the long
run would prove it worthy.
Nevertheless, it can be concluded that the benefits offered by the
implementation of IPv8 within the same 'Zone IP Block Address' and 'IP
Area Code', changes none of the Security procedures, which are now present
in the use of IPv4 today. However, it is a Recommendation, since Global
Telecommunications does require the use of the ZONE IP and IP AREA CODE
BLOCK Addresses, that another 'DHCP*' be specified for use in conjunction
with the Global Router. This implementation is seen necessary not only for
the 48 Bit IP Address and Network Name Resolution, but also because of the
Additional Security Requirement that is fostered by the implementation of
this IP Addressing System.
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*Note: While inclusion of more that One DHCP Server, or Multiple DNS
Servers does maintain the advantage that would facilitate
Address Assignment and Address Name Resolution in the complex
Addressing environment of IPv8, or the Internet for that
matter. It will not however, supplant the requirement nor the
need of having to Re-Write (i.e. Patch) the Software for each
of the Respective Servers. Noting that, using only one of
these respective Severs may meet the requirements of any
Network. However, there can be 2 or more of each, but at least
one must exist, of each of the respective Servers used, whose
Software is written for compliance with the IPv7 and IPv8 IP
Specifications, which would establish or Link Communication
beyond the Domain of the Intra-Network or Private Network
Domain.
Needless to say, this would provide the necessary Security benefits of
having controlled access to the Global information in other Zones and or
IP Area Codes, which would allow the continued use and enjoyment of the
uniform security standard presently used in the 32 Bit IP Addressing System
today. Nevertheless, these Enhanced Security Control Features should be
viewed as a Boon, because they provide a much greater scrutiny and control
over Inter and Outer Comm Communications for every Network Connected to the
Global Telecommunications Community. However, this implementation is only
possible through the use of the 'Smart Router' and the services provided
from a second 'DHCP' Server. Which together, would provide the necessary
functions and ability to make these enhanced security features possible.
In other words, the recommendation is that, there should exist 2 'DHCP'
Servers, one for connection to the Global Community and the other for
Communications within the same 'Zone IP Address' and 'IP Area Code'.
Nevertheless, these are for the most part suggestions, which can be
considered as recommendations, and Standard implementations. The point made
however, is that, with IPv8, any Security Implementation can be Built upon
the foundation and knowledge gained from that existing in IPv4. This is to
say, IPv8 can be used, or implemented, without extensive testing. Because
it is a logical derivative of IPv7, which maintains same similarities that
IPv7 has with IPv4. And while there exist hardware configurations that can
remain in use. There exist other hardware concerns, which remain in
question.
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Be that as it may be! Whatever the selection is chosen from the multitude
of possibilities, as the best possible representation for the 'HEADER' used
in IPv8. It should be clearly understood, its choice is arbitrary, which
does not necessarily degrade, nor improve the efficiency or use of IPv8.
Needless to say, for every RFC written which entertains issues concerning
Security. The implementation of IPv8 that would become effected, or seen as
a change from IPv4, concerns only the Zone IP and IP Area Code Block
Addresses, which should not require any appreciable change either beyond
IPv4 or that which has been recommended. In other words, for the most part,
IPv8 is a supple change, which underlies a major Structural Departure from
that of IPv4. Which means that the Security methods implemented in the
latter, will retain a measurable degree of validity, use, and application,
in the former.
Nevertheless, every individual can have their personal IP Address, just
like the Phone Number exists today. Which does not exclude the existence
of the Disconnected Private Network Domain. Needless to say, the only
limitation for Implementation of Security Measures, is the imagination of
the Hardware and Software Designers.
Note: It is important to mention that the IP Addressing
Format of IPv8, has an inherent Security Feature,
which if used, would require an Independent
Login / Password / Authentication at the Zone IP
Address, the IP Area Code Address, and the 32 Bit
Block Network Address. And this could also include
the more advanced encryption methods, beyond the
standard now employed for Authentication. This is
analogous to perhaps, a Security Level of C-5, or
maybe higher (A-2), because other options can be
employed, and a greater control for Security exists.
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Appendix I: 'Graphical Schematic of the IP Slide Ruler'
======================================================================
= Octets 2nd 3rd 4th Figure 1
= 1st | | .......
= | | | . .
= ----- v | . 001 . The IP Addressing Slide Ruler clearly
= ^ ....... | ....... establishes the Differences between
= | . ** . | . . Decimal and Binary Calculations.
= | . 001 . v . 160 . Where, in this case, the Number of
= | ................... Rulers or Slides, represents the
= | ................... Maximum number of Hosts available in
= | . . . . an IP Address Range having an
= . 160 . 001 . 188 . Exponential Power of 3. That is, if
= IP ................... the First Octet is Defined by the
= Address ................... "Subnet Identifier", as providing
= Range . . . . a Network within the IP Address
= . 188 . 160 . 223 . Range assigned to this Class. That is,
= 1 - 255 ................... the individual Ruler or Slide, has a
= | ................... one-to-one correspondence with the
= | . . . . OCTET it represents, and is equal to
= | . 223 . 188 . 239 . an Exponential Power of 1. Which also
= | ................... maintains this one-to-one
= | ................... relationship. In any case, it should
= | . . . . be understood that the Decimal is an
= | . 239 . 223 . 256 . Integer representing the IP Address,
= | ................... and has only 1 value that occupies
= | ................... the given Octet. However, the Binary
= | . . . representation for the IP Address, is
= | . 256 . 239 . an 8 digit Logical Expression
= v ............. occupying one Octet. Where each digit
= ----- ....... has a 2-state representation of either
= . . a 1 or a 0. The distinction is that,
= . 256 . this is a Logical expression that has
= ....... no Equivalence. However, there is a
= Mathematical Method which resolves
=The ( ** ) indicates this distinction, and allows for the
=the Reference point Translation of each into the other.
=of the IP Side Ruler. In other words, one System can never
= be used to interpret any given value
= of the other, at least, not without
= the Mathematical Method used for
= Translation. But each, can separately
= be mapped to the structure of the 'IP
= Slide Ruler ', rendering a translation
= for one of the two representations.
= (Noting that the Binary Translation of
= its Decimal equivalent must be known
= first.)
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Note:[An example of the assignment of a 'ZONE' Number Prefix in IPv8
would be that of a Continent; North America or South America.
While the example of the location for an assigned 'IP AREA
CODE' in IPv8 would be some Sub-Region within a 'ZONE Prefix'
(Continent): New York or Chicago. The convenience of this
structure, is that, the Zone Prefix assigns an entire IP
Addressing Scheme to that Area (256 Locations), and the IP AREA
CODE allows for a further expansion or division of each IP
Address Class (256 Sub-locations) within the Addressing Scheme.
However, the assigned Zones and IP Area Codes are not
Variables, which means they are permanently assigned to the IP
Addressing Scheme. But the IP Addresses they prefix are
variables, which can be changed. Nevertheless, the IP Slide
Ruler is used only for IP Addressing, and not the Prefixes.]
Appendix II: The Beginnings of the Discovery; Mathematical
Anomaly
My work in the Mathematical Field of Number Theory, provided me with an
unprecedented insight of the underlying logical foundation existing in the
whole of mathematics today. Needless to say, the discovery, which sparked
another Revolutionary Change in the Mathematical Field, was once again, a
violation of some elementary concept.
Nevertheless, the mathematical issue that resulted in a change in the
methods of enumeration for the Binary System, started as an argument
concerning the existence of the 'One-to-One' Correspondence between the
Mathematical Calculations involving the Decimals (Positive Integers) and
those concerning the Binary Operators (Logical Expressions; the Truth Table
values of 1's and 0's). Needless to say, it is worth presenting once again,
the Analysis of this Mathematical Anomaly, which caused this Mathematical
Upheaval.
Please note the ongoing argument, which attempts a resolution of This
Mathematical discrepancy. Where by, given Class B as the starting point, we
have:
1. Class B; 128 -191, IP Address Range
Default Subnet Mask; 255.255.000.000
(Which yields: 2^14 Networks and 2^16 Hosts;
that is, 16,384 Networks and 65,536 Hosts.)
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However, this total is not the correct method of enumeration, and it is not
the actual number (Integer Number) of available networks. And this FACT
becomes even more apparent when the Binary Translation of the Decimal
(Positive Integers) Numbers is completed. That is, the result would yield
64 Binary Numerical Representations, ONE for each of the Decimal numbers
(Positive Integers) that are available in the IP Address for the Class B.
Where Class B should maintain the representation (Which provides the actual
Integer enumeration for the calculation of the total IP Addresses
available. In other words, their independent count, of their respective
totals for the Actual Number of Available IP Addresses in the Class B
should Equal '64'.) given by:
2. Class B: 128 -191, (Which equal the total of 64
possible IP Addresses for the given Address Range)
Default Subnet Mask: 255.255.000.000
(Which results in 64^2 Networks and 254^2 Hosts;
that is, 4,096 Networks and 64,516 Hosts.)
Nevertheless, an enumeration, or break down count association, of each
representation, that is, Binary and Decimal. Would indeed, provide a
greater support for the conclusion presented thus far. Where by, given the
Classes noted in 1 & 2 above. We have:
1a. (128 + 128 + 128 + 128 + ...+ 128) = 128 x 128 = 2^14
1 2 3 4 ... 128 = Total Count
Which equal the Total number of Networks for the Given Address Range.
And
1b. (255 + 255 + 255 + 255 +...+ 255) = 255 x 255 = 2^16
1 2 3 4 ... 255 = Total Count
Which equals the Total Number of Hosts for the Given Address Range.
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While noting that these equations represent the Binary Method for
determining the number of Networks and Hosts for the given Address Range of
Class B. However, keeping this in mind, notice the difference that exist
when this same calculation is used for the Decimal (Positive Integer)
representation.
2a. (64 + 64 + 64 + 64 +...+ 64) = 64 x 64 = 64^2
1 2 3 4 ... 64 = Total Count
This remains true regardless, that is, even if an argument regarding the
possible existence of a different value of the variable in the Second
Octet, which would account for the inclusive total of the range 0 - 254.
The error would exist still, because of the standing Rule, which does not
allow the Host or Network IP Address to maintain a value representing 'All
Binary '1's' or All Binary '0's'. In which case, the result of 2a, as noted
above, would be given as, 64 x 255 = 16,320. Needless to say, the count
given as the Binary representation of the total number of Hosts and
Networks IP Addresses for the IPv4 System, as concluded above, is still
wrong!
Where this number equals the number of Networks for the Given Address Range
assigned to Class B.
And
2b. (254 + 254 + 254 + 254 +...+ 254) = 254 x 254 = 254^2
1 2 3 4 ... 254 = Total Count
Where this equation represent the Total Number of Hosts for the Given
Address Range of Class B.
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In other words, given the equation (191 -128) + 1 = 64. We are then
presented with the Total Number of Addresses available for the given
Address Range, 128 - 191, for the Class B. Where it can be seen that,
any One-to-One mapping of the Numbers in the Address Range and the
Counting Numbers (Positive Integers), beginning with 1. Should yield
the Total Number of Addresses available in any Count, for the
Determination of the Total Number of Networks. And this same line of
reasoning applies to the Host count, as well.
['Where the Subscript Number equals the Value of the Total Number
of Available IP Addresses (a One-to-One Correspondence between
the Enumeration of, and the Address Ranges given) for the
Network and Host Ranges in Class B. Where both Binary and
Decimal Number representations are the given examples.']
Nevertheless, when the Decimal and Binary conversion is completed. That is,
when you establish a One-to-One relationship between the Binary and Decimal
Numbers. You would discover that the their respective totals would be the
same. That is, there can only be 64 Binary numbers and 64 Decimal numbers
for the calculation of the Total Number of Networks. And there can only be
254 Binary Numbers and 254 Decimal Numbers for the calculation of the Total
Number of Hosts. The difference is that, the former method reveals the
Binary calculation, while the latter is the Integer (called the Decimal)
Calculation. Needless to say, it should be very clear that the Binary
method is a Logical Expression, and does see the Integer Count, that is the
'Difference between the Range Boundaries Plus 1'. Which yields the total
number of available IP Addresses to be used to determine the actual number
of Hosts within a given IP Address Class Range. Clearly, the Decimal method
is indeed a Mathematical Expression representing the operations involving
the Positive Integers.
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Appendix III: The Reality of IPv6 vs. IPv8
Introduction
Any deliberation upon the foundational differences existing between any two
or more systems, is a daunting task, whose resulting dissertation would
require years just to complete a single reading. However, if such a study
first, begun by eliminating those portions of each system, which maintained
a universal application to every system in which such a study would
comprise. Then, the amount of time would be significantly reduced, because
the subject matter would only entail the analysis of those parts pertaining
to the differences each systems maintained relative to the other.
Nevertheless, it should be clear, that the outline of this Appendix will
only present a succinct view of this endless count, of what will be
concluded as the beneficial differences maintained by IPv8 when compared to
IPv6. Which will nonetheless, be shown far to be far superior to any
offering rendered by the implementation of IPv6.
In other words, the reality regarding the benefits or short comings of any
IP Addressing System, which is not a direct reference to the Mathematical
Methodologies entailing the Address themselves, are indeed the universal
and superficial extensions, which are not relative to any particular
system. Where by, issues such as the Header Structure, Functional
Definitions describing Address Classes, and other Operational Methods,
which are associated with the Addresses, are all Universal Extensions of
the Addressing System that maintains a universal application. Which can be
employed for use in any IP System of Addressing. Needless to say, these are
inherent facts regarding the discussion of any IP System of Addressing,
which necessitate an understanding of the over all implications relating
thereto. Where by, after the elimination and resolution of all matters
concerning the Universal Extensions, because they maintain or can become a
usage, function, or implementation shared by both systems. The focus of
attention regarding any implementation of a Global Telecommunications
Standard, would now center entirely upon the mathematical enumeration
methods of, and the IP Addressing System Schematic itself.
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Nevertheless, Hinden's work, "IP Next Generation Overview", made reference
to several possible uses for the IPv6 protocol. In fact, he tended to
ignore other specification, which would probably prove more suitable when
configuring Household Appliances; for example IEEE 1394. Needless to say,
while it is clear that his objective was to exemplify the possible uses and
applications of IPv6. He did in fact ignore, the amount of Network traffic,
or Bottlenecks, the inclusion of devices such as these would create.
Moreover, while household appliances would probably be connected to a
Computer System, which is Networked to the Global Telecommunications
Community. It will be the controlling application, which would be accessed
from some remote location and not the device itself. Needless to say, he
emphasized moreover, that the number of available IP Addresses in the
present IPv4 System and Routing, were the underpinning issues, which
promoted the need for another IP Addressing System.
Nevertheless, the only issues regarding IPv6 and IPv8, which shall embody
the topics of this Appendix are, Structure of the IP Address, Routing, and
their related issues.
The IP Addresses of IPv6 and IPv8 Compared
First and foremost, it should be noted that, IPv6 is not a Global
Telecommunication Standard, because it does not offer nor include, any
incorporation of the existing Telephone Communication System. However,
while it does expand the number of available IP Addresses to the Global
Internet Community. Its Default Addressing Structure however, is redundant,
and the definitions incorporated in this IP Addressing System, outlining
its underlying purpose / structure / use, lack the soundness of logical
support, which are indeed superfluous. In other words, the IPv6 IP
Specification, itself, lacks the logic foundation of Sound Mathematical
Reasoning, which would justify its Existence, and its total IP Address
availability is less than IPv8.
Where by, IPv6 offers a pure 128 Bit IP Addressing System, and a Backwards
compatibility comprising 96 Bits of IPv6 Address and 32 Bits of IPv4
Address. This yields, to say the very least, an unprecedented number of
available IP Addresses, with no mention of the possibility of individual IP
Address assignment for the general public, which comprises the total
population of the world. However, it does provide IP Addresses for business
uses, which can then make assignments for use by the general public.
Nevertheless, as a point of interest, a 128 Bit IP Address Scheme is
equated to '3.40 x 10^38'. Which is, given the total population of the
world as being '6.0 x 10^9', is approximately equal to assigning
3.64 x 10^28 IP Addresses to each and every individual person on the
planet.
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Nonetheless, one would assume that the purpose for a Global
Telecommunication System, was not only the concerns for free enterprise
and the ever growing number of people wanting the availability of a much
broader means of communication. But to address the needs of the public at
large, which the emergence of the 21st Century now mandates.
Needless to say, the overall structure of IPv6, bars the assignment of
individual IP Addresses. Where by, given that an individual location
represents a single NODE Connection. IPv6 almost commands that every Node
maintains several INTERFACES, which would allow the assignment of several
IP Address Numbers, one per Interface, to establish connections for the
services offered by different providers. This scheme almost certainly
guarantees, that the present cabling system will become an over burden
Network Highway of continuous Traffic Jams and Bottlenecks. This moreover,
does not even raise a Brow regarding the Backseat, that "The Nightmare on
Elm Street" must take, when the IT Professionals must consider the
Management of such a Network. Just forget about troubleshooting, component
failure, or some unforeseen catastrophe!
I mean, consider for a moment the layout of the defined Sub-Divisions,
nested might I add, which is the purported Hallmark of the IPv6 Addressing
Scheme. And which, is not employed by IPv8, because it is designed to
maintain a similar functionally as that of the present Telephone System.
All while retaining the ease of use and implementation corresponding to
IPv4.
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1. UNICAST ADDRESS; The One-to-One method of
communication, which exist between 2 Nodes.
a. Global Based Provider; Provider based unicast
addresses are used for global communication.
b. NSAP Address
c. IPX Hierarchical Address
d. Site-Local-Use; single site use.
e. Link-Local-Use; single link
f. IPv4-Capable Host; "IPv4-compatible IPv6 address"
g. With IP Addresses Reserved for Future Expansion
2. Anycast Addresses; an address that is assigned to
more than one interfaces (typically belonging to
different nodes), with the property that a packet
sent to an anycast address is routed to the
"nearest" interface having that address, according
to the routing protocols' measure of distance.
3. Multicast Addresses; a multicast address is an
identifier for a group of interfaces. A interface
may belong to any number of multicast groups.
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TABLE AI
Allocation Prefix(binary) Fraction of Address Space
Reserved 0000 0000 1/256
Unassigned 0000 0001 1/256
Reserved for NSAP Allocation 0000 001 1/128
Reserved for IPX Allocation 0000 010 1/128
Unassigned 0000 011 1/128
Unassigned 0000 1 1/32
Unassigned 0001 1/16
Unassigned 001 1/8
Provider-Based Unicast Address 010 1/8
Unassigned 011 1/8
Reserved for
Neutral-Interconnect-Based
Unicast Addresses 100 1/8
Unassigned 101 1/8
Unassigned 110 1/8
Unassigned 1110 1/16
Unassigned 1111 0 1/32
Unassigned 1111 10 1/64
Unassigned 1111 110 1/128
Unassigned 1111 1110 0 1/512
Link Local Use Addresses 1111 1110 10 1/1024
Site Local Use Addresses 1111 1110 11 1/1024
Multicast Addresses 1111 1111 1/256
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TABLE AII
SCHEMATIC DESIGN OF THE IPv6 IP ADDRESS
1. Provider Based Unicast Addresses
| 3 | n bits | m bits | o bits | p bits | o-p bits |
+---+-----------+-----------+-------------+---------+----------+
|010|REGISTRY ID|PROVIDER ID|SUBSCRIBER ID|SUBNET ID| INTF. ID |
+---+-----------+-----------+-------------+---------+----------+
2. Local-Use Addresses
Link-Local-Use
| 10 |
| bits | n bits | 118-n bits |
+----------+-------------------------+----------------------------+
|1111111010| 0 | INTERFACE ID |
+----------+-------------------------+----------------------------+
Site-Local-Use
| 10 |
| bits | n bits | m bits | 118-n-m bits |
+----------+---------+---------------+----------------------------+
|1111111011| 0 | SUBNET ID | INTERFACE ID |
+----------+---------+---------------+----------------------------+
3. IPv6 Addresses with Embedded IPV4 Addresses
"IPv4-compatible IPv6 address"
| 80 bits | 16 | 32 bits |
+--------------------------------------+--------------------------+
|0000..............................0000|0000| IPV4 ADDRESS |
+--------------------------------------+----+---------------------+
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"IPv4-mapped IPv6 address"
| 80 bits | 16 | 32 bits |
+--------------------------------------+--------------------------+
|0000..............................0000|FFFF| IPV4 ADDRESS |
+--------------------------------------+----+---------------------+
4. Multicast Addresses
| 8 | 4 | 4 | 112 bits |
+------ -+----+----+---------------------------------------------+
|11111111|FLGS|SCOP| GROUP ID |
+--------+----+----+---------------------------------------------+
We need not concern ourselves with Table AI, because its definitions are
arbitrary, and can be applied to any 128 Bit IP Addressing Scheme. However,
Table AII provides the reality, which relates the meaning of the MANY
SKELETAL (Default) STRUCTURES an IP Address can have in IPv6. While the
Default Skeletal Structure of an IP Address in IPv8 has only One Simple
Format, which is used throughout its Addressing Scheme. Needless to say,
these IP Address structures in IPv6, form the bases of the foundation for
another, yet undefined Class System. Which uses WORDS to define different
segments of the Skeletal (Default) IP Address, for which the numbering
system of the IP Specification must correlate. Furthermore, they exhibit
and maintain a repetitive definition having the same overall purpose, which
was achieved using the simpler methods in IPv4. To say the very least, this
is a more complex structure, differing markedly from IPv4, and the Skeletal
IP Address defined by the Default Subnet Mask, now the 'Subnet Identifier'
in IPv7 and IPv8.
Nevertheless, IPv8 defines a IP Addressing Structure, which is a 64 Bit IP
Addressing System using only 48 Bits, that 'Defaults' to a 32 Bit IP
Addressing System when the communications or transmissions are within the
predefined Block Addresses of the Zone IP and IP Area Code (for the
communicating entities). In other words, IPv8 retains the ease of use,
implementation, and simplicity of IPv4/IPv7. All while allowing a more
conservative expansion, for growth, in the number of available IP Addresses
approaching the 128 BIT Addressing Format.
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Moreover, while almost duplicating IPv4 in functionality, IPv8 derives its
strengths from the conceptualization of "Block IP Addressing". That is,
there are '4' '8 Bit Routable Address Blocks', representing four separate
Octets, which are complete individual IP Addresses. And they are
represented by the first 32 Bits of this 64 Bit IP Address Structure,
which reserves 16 Bits, or two separate Octets, for future expansion.
Furthermore, this 'Block IP Address' concept, comprises a 5 Block IP
Address Division (that can be further divided to enhance the Router's
overall performance). Which allows the entire IPv8 IP Addressing Schematic,
when fully implemented, a greater and more direct control over the Routing
(Not the Route Path) of an IP Address. Furthermore, each Zone IP Block
Address is allocated approximately '1.091 x 10^12 IP Addresses' for
distribution and assignment (See Table 15). Needless to say, this is only
a small fraction of the total number of available IP Addresses in the IPv8
Addressing Scheme (See Table 15).
Nevertheless, this implementation in essence, allows every existing entity
previously assigned an IP Address, to continue its use without any change.
In fact, IPv8 is the only true Global Telecommunication System Standard,
which incorporates every Industry within the Telecommunications Community
into one, World Wide Global Telecommunications System, through the use of
Block IP Addresses. Needless to say, what makes this all possible, is the
use of the Zone IP and IP Area Code Prefixing System. Which, to say the
very least, it is indeed one of the Hallmarks, that provides IPv8 its
notable distinction. Moreover, it should also be clear, that IPv8 offers
a smoother transition, the upgrade from IPv7, without the issues arising
from incompatibilities, backward compatibility, or any of the difficulties
resulting from having to learn the particulars of the implementation of a
new, entirely different IP Addressing System.
A Succinct Consideration Regarding Routing in IPv6 vs. IPv8
The Routing implementations recommended in IPv8, require the development of
3 types of Smart Routers, Global, OuterCom, and InterCom. These would
control 3 major methods of Routing: DIRECT-PPTP, CIODR-FEA and CIODR-BEA.
Which predicts moreover, a reduction in the size of the Router's routing
Table, and a reduction in the total number of Routers needing to be
deployed, regardless of the size of the Network Domain. Nevertheless these
routers are defined in Table AIII.
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TABLE AIII
1. Global Router: A "OuterCom' router having the dual routing path
capability defined by the Zone IP and IP Area Code Block IP
Addresses (CIODR-FEA). Which is programmed to discern the
differences in data types, capable encryption and decryption of
data, and would route the data by either stripping the Prefix Code
or transmitting the data to the next router governing the
destination.
2. Internetwork Router: A "OuterCom" router having the dual routing
path capability defined by the IP Area Code Block IP Address and the
First 16 Bits defined the Subnet Identifier of the 32 Bit IP Address
Block (CIODR-FEA). Which can also be programmed to discern the
Differences in data types, capable of routing encrypted and
decrypted data, and would route the data by either stripping its
associated Prefix Code or would be By-Passed for direct routed
transmissions.
3. Network Router: A " BridgeCom" router having the dual routing path
capability defined by the First 16 Bits of the 32 Bit Block IP
Address and Routing by Octets defined by the Subnet Identifier of
the 32 Bit IP Address Block (CIODR-FEA). Which can be programmed to
discern the differences in data types, capable of routing encrypted
and decrypted data, and would route the data by using its defined
functions or transmitting the data to the next router governing
intended destination (CIODR-BEA).
4. DIRECT-PPTP: An InterCom / OuterCom Transmission, which can be Routed
with IP Address intact to establish a direct Secure Peer to Peer
Conference on a OuterCom, or InterCom Communication.
5. CIODR-FEA: A Classless Inter/Outer Domain Routing Technique, which
routes using, First or Second 8 Bits, of Front End of the 48 Bit
Address Blocks comprising the Zone IP, IP Area Code, and the First 2
Octets of the 32 Bit Address Block. (FEA = Front End Address)
6. CIODR-BEA: A Classless Inter/Outer Domain Routing Technique, which
routes using the Back End of the 32 Bit Address Block, that comprise
the last 2 Octets. (BEA = Back End Address)
7. Inter-Domain Router: A "InterCom" Router is the first link outside
of a Private Network Domain.
8. Intra-Domain Router: A "InterCom" router that is use within a Private
Network Domain, and it is used to Route either InterCom or OuterCom
communications.
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Needless to say, the Routing techniques recommended for use in IPv8 are far
superior to those implemented in IPv6. Where by, the routing techniques
employed in IPv6 necessitate the use of "CIDR" because of the "Backward
Compatibility" underpinning its IP Addressing Format. It also provides an
ISP with the ability to choose a Route Path, which was formally left to the
Router. However, this direct Route Control over transmissions, which is
indeed a Security Risk, undermines the fundamental requirement(s) for
anyone seeking individual privacy and control of the information
transmitted while using this Global Thoroughfare. In addition, these
methods would require, if not mandate, a serious overhead on the design
and cost equipment.
Nevertheless, the benefits ascertained from the choice of IPv8 over IPv6,
are indeed a reflection of its unquestionable superiority, which is an
inherent feature in the foundation of the Mathematics supporting its
Logical Structure. Where by, the division of an IP Address Class (or its
representative; the Default Address Structure(s)), is indeed a Division of
the respective Number of IP Addresses associated with the Address Class
Range. In other words, it is a Mathematical determination founded upon the
Logic of the Method Of Quantification, which amounts to an increase in the
efficiency in the use of the Total Number of Available IP Addresses in
IPv8, overall. Which is approximately '99.99...+ %' efficient, compared to
IPv4's rating of less than '97%'. However, Tables AI and AII, shows no
clearly discernible efficiency determination for IPv6, and its use of the
Total Number of Available IP Addresses. This is because the Number of Bits
used to Define its Default Addressing Structure can be 128 or more. This is
an inherent problem of the IPv6 Specification, which lacks any discernible
Logical Structure that ONE would conclude as being supported by, or derived
from a Logically Consistent Mathematical Foundation. Even so, it could not
sustain an efficiency rating 'Greater Than nor Equal to 95%', because there
are 4 of the 6 pre-defined 'Default Address Class Structure(s)', in which
there is an assigned Prefix that limits the use of the Total Number of
available Addresses within the IPv6 IP Specification.
What this implies, is that, it is not possible for the IPv6 IP
Specification to be Mathematically Consistence, nor posses any Logical
Foundation based upon derivable premises, as is the case for the IPv7 and
IPv8 IP Specifications. Where by, the experience gained from the Addressing
Methods of IPv4, and those Mathematically derived and represented in IPv7
and IPv8, shows clearly the requirements Mandated by the Mathematical and
Logical reasoning of Quantification. Which has indeed demonstrated that the
Division of the Address Range into any number of Default Addressing
Structure(s), or the creation of a Sub-Division of Address Classes which
are associated with the Addressing System, will effect the Efficiency in
the utilization of the total Number of Available IP Addresses in the
Addressing System overall. In the strict sense, what this means is that,
while it is possible to create an Addressing System without the Rules of
Mathematics and or Logical Reasoning, without these rules or Laws there
can be No Continuity within the System itself. Needless to say, if this
were not true, then IPv6 would represent the 128 Bit version of the IPv8
IP Specification.
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In other words, there are Mathematical Laws in which the IPv6 IP
Specification clearly violates. These Laws, which are derived from the
Logic of the Method of Quantification, governs the Mathematical Operations
of the Binary System which relates the Addressing Schematic to the
Addressing System's Method of Enumeration. These results become the
foundational Premises, which imposes a boundary or limit, that clearly
defines and Determines the Structure of any IP Addressing System Schematic
whose foundation is derived from the Binary System.
Appendix IV: A Succinct Proof of the Fall of the Binary System
Overall, which questions the validity of
Machine Language
While I may possess an intuitive understanding of the Theoretical aspects
in the Mathematical and Physical Sciences. I also maintain an education in
the broad spectrum of the Theoretical Subject matters encompassing these
fields of study. In other words, I have elected a very simple proof to
present to the general audience, that commands only an understanding of
Basic Algebra and some of its laws. The argument thus presented, will
provide proof that the Current Method of Enumeration in the Binary System
is incorrect, and will establish beyond question that the method presented
above is indeed the correct method which should be applied.
Furthermore, this presentation, it should be understood, is not the only
proof that can be derived for the correction of the Error in the Method of
Enumeration in the Binary System. However, it seems to be well suited
overall for its intended purpose and objective, because I believe itÆs the
simplest and easiest to understand.
Nevertheless, the problem concerning the Error in the Method of Enumeration
in the Binary System, is not new. In fact, understanding the concept of
ZERO, itself, was such a great challenge for the entire Mathematical
Community, that it retains a measurable significance in the History of
Mathematics in general, if not overall. Where by, it should be understood
that the lack of an understanding of the difference between the concepts of
Set Theory, i.e. elements of a Set, and Positive Integers. Is indeed, the
problem underlying this reported Error, which is the same as not grasping
or understanding the Concept of ZERO.
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Needless to say, to understand how this miss representation of Zero effects
the Method of Counting, one only needs to understand that the Elements of
the Binary Set, '0' and '1', are Abstract Entities. Which, when combined
through the rules governing their usage, are then used to represent some
Number, but, they have No Numerical Value nor Meaning. In other words, the
Elements of the Binary Set, might just as well have been Sheep having
different Color Wool. The principle would have been the same, because if
the question of "How Many Sheep?" or " How many Sheep Wool Types?" were to
be posed. The answer would still be 2, which is the Number of Elements in
the Binary Set. Now to build upon this foundation, from Laws Elementary
Algebra:
Where by, from the Properties of Real Numbers of Elementary Algebra, the
Substitution Law for Equality states: "If A = B, then A may be replaced by
B and B by A, in any Mathematical Statement without altering the Truth or
Falsity of the Statement." This is seen true, and does indeed support the
usage and Concept of the Variable. (Which we are all so familiar.)
In other words, if we replaced the Elements of the Binary Set with another
Set of Elements, which renders or provides a different appearance or
graphical representation. Could we not achieve the same functional purpose
as that defined in the Binary System? Where by, from the Substitution Law
for Equality we have;
1. If '0' and '1' are elements of the Binary Set, {0,1}, and if There
exist a condition for the ({0,1} | {0,1} = {A,B}, where '0 = A'
and '1 = B', then from the Substitution Law for Equality above we
can perform the noted Substitution of the respective Elements of
the Binary Set without Altering the Truth of any Statement in the
Binary System. (Which is by Definition Equality of Sets.)
And from the Old Method of Enumeration in the Binary System we could
establish an Equality. Given by equation 2 we have;
2. ' BAA = 100 = 4 ', where '0 = A' and '1 = B', and '4' is a
Positive Integer.
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And while, this does not, by itself, resolve the Zero issue. What we have
accomplished, is to establish an EQUALITY and One-to-One Correspondence
between two Sets, {0,1} and {A,B}. Which is a valid Method of Counting in
the Binary System, and the Counting method presently used. (This also is
given by Definition in Set Theory.)
Nevertheless, by definition, any Set that contains NO Elements, then that
Set is said to be empty, and is called the 'EMPTY SET' or 'NULL SET'. Where
by definition we have;
3. "For Every Sets that Contain No Elements, the Set is said to
be Empty, and is called the Empty Set or Null Set, which is
represented by a Zero having a Diagonal Line Drawn through
it. (And for our purposes we will Equate it to '0', the
'Integer Zero'.
Nevertheless, one can easily see the confusion that does incur, as given by
3 noted above. Especially when anyone associates the 'Null or Empty Set'
represented by '0', with the Element Contained in the Binary Set; Zero,
represented in the Set {0.1}. Needless to say, there exist two simple
approaches which solves this dilemma.
The first approach would be a comparison between the inclusive Count of the
total Number of Elements Contained in the respective Sets; i.e. the Binary
Set and the Null or Empty Set. Given by equation 4 we have;
4. {0} = 'the Null or Empty Set' and {0,1} = 'the Binary Set'.
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From number 4 noted above. It is clearly seen that the Null or Empty Set
contains, at least for our purposes, only One Member, and is equal to Zero,
which represents No Elements. However, the Binary Set contains Two Members,
which is represented by the Abstract Elements, '0' and '1'. In other words,
if the Null Character could represent a Member, but Not an Element. Then
clearly, these Two Sets do not maintain a One-to-One Correspondence between
the total Count of their Respective Members, and since the Null or Empty
has No Elements, they are Not Equal. Hence, the Binary Set which contains
No Elements, is Empty, and can not contain any Members Equal to the
Abstract Elements, '0' or '1'. Therefore, the Binary Element '0' can not
be Equal to either the 'Null of Empty Set' or to the 'Zero Integer' of
Positive Numbers.
Nevertheless, the second Solution would be to Equate the Elements Contained
in the Binary set to those Belonging to the Null or Empty Set using numbers
1 and 2 noted above, which is derived by Definition and the Substitution
Law for Equality. Where by;
5. Since {A,B} = {0,1} then from the Substitution Law for
Equality and its corresponding definition in Set Theory,
we can use the Set {A,B} in lieu of the Set {0,1} and
still obey the rules in the Binary System.
Where by, if the conditions given by number 6 were true;
6. {A,B} = {0} = Null or Empty Set = 0 = Zero Integer of the
Positive Numbers.
Then the Binary Set would contain No Elements, and the Set {A,B} would not
be Equal to the Binary Set {0,1}. In other words, these Sets are neither
Equal nor Equivalent, and they are indeed Disjoint because they contain No
Common Members. Hence, the conclusions deduced for the first solution,
noted above, remain Valid and True.
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[What this implies, when accepting the Elements of the Binary
Set, {0,1}, as Abstract Entities, and not Numbers Representing
the Graphical Depiction associated with the Positive Integers.
Is that, a Positive Integer can be assigned or associated with
the Elements of the Binary Set, in such a way, that a One-to-One
Correspondence could be established, which would render a count
representing the Total Number of Elements Contained in the
Binary Set. Where by, such an Assignment would yield:
7. 0 = 1 , and 1 = 2, yielding an inclusive total count of 2.
Needless to say, the results shown could quite easily be used in
Another argument, which would yield results that are indeed the
conclusions this paper presents. However, this is a foundation for,
perhaps a book, because the constraints of this draft already swell
the limitations of the marginal boundaries. Notwithstanding, the
apology for demanding an educational prerequisite for the audience.]
Therefore the equivalent representation in Positive Integers for the Binary
Element represented in the Binary Set, {0,1}, given by 0, and defined as 00
in Chapter I, is Equal to '1'; the Positive Integer. Hence, the Null or
Empty Set in the Binary System is Equal to {0}, and is Equal to the Zero
Integer of the Positive Numbers. In other words, the methods of counting as
depicted in Table 8, as being derived from the conclusions in Chapter I,
remains valid, because there is no actual Binary Representation for the
Integer '0'. Moreover, it should be understood, that the actual value of
the Positive Integer, as derived in the equation noted in number 2 above,
equals the Positive Integer 5, as given in Table 8 of Chapter I. Which
reflects the Change in the Method of Enumeration for the Binary System.
Nevertheless, while this is a profound discovery, in itself. Regarding
Assembly Language however, the Addressable Memory by Address Register Size,
in Bits and Bytes, confirms the conclusions of this paper, which mandates
through Logical Analysis a change in the Method of Enumeration for the
Binary System. While further inspection yields as the possible reason,
which eliminates errors, is that, there appears to be absolutely No
association beyond the Calculation of Bits and Bytes, which use the Binary
System. Moreover, in retrospect, since Machine Language is Binary, and
while I doubt that the calculation of its Memory Address Register size may
not be in error. I would be hard pressed not to assume the worst,
especially since the underlying principle behind the concept of this
language is the Mathematical Calculations involving the Binary System. And
even this conclusion is drawn notwithstanding the Operating Systems or
Applications, which communicates with the Language of the Machine
rendering Mathematical results employing the Binary System.
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Needless to say, the Results and Conclusion(s) provided herein, are indeed
suggestive of a Problem far greater than those maintained by the initial
objectives. Where by, it can also be concluded that, any Mathematical
Computation involving either directly or indirectly, through translation or
whatever, the Binary System, would be in Error. And this is a Conclusion
notwithstanding the intended use or association. That is, it does not
matter whether the calculations concerned a Space Probe, a Genetic
Sequencer, or an IP Address. Because the Far Greater Problem not only
concerns Economic issues, which is the expense inured from changing the
Method of Enumeration for the Binary System in Operating Systems and
Software. But emphasizes the possibility of a Fatal Error resulting from
the use of the current Logic of the Binary System employed in Hardware
Devices, which could result in the loss of life. This would indeed become
the final result of this resounding reality if these changes are not made*.
*Note: The conclusion derived here is based upon an extreme case.
Where by, the Functional Purpose and Design of Electronic
Hardware is directly dependent upon the Logic of Binary
System, and does not account for the results its Logical
format will acquire from this change in the Method of
Enumeration.
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References
1. E. Terrell ( not published notarized, 1979 ) " The Proof of
Fermat's Last Theorem: The Revolution in Mathematical
Thought" Outlines the significance of the need for a thorough
understanding of the Concept of Quantification and the
Concept of the Common Coefficient. These principles, as well
many others, were found to maintain an unyielding importance
in the Logical Analysis of Exponential Equations in Number
Theory.
2. E. Terrell ( not published notarized, 1983 ) " The Rudiments
of Finite Algebra: The Results of Quantification "
Demonstrates the use of the Exponent in Logical Analysis, not
only of the Pure Arithmetic Functions of Number Theory, but
Pure Logic as well. Where the Exponent was utilized in the
Logical Expansion of the underlying concepts of Set Theory
and the Field Postulates. The results yield; another
Distributive Property (i.e. Distributive Law for Exponential
Functions) and emphasized the possibility of an Alternate
View of the Entire Mathematical field.
3. G Boole ( Dover publication, 1958 ) "An Investigation of The Laws of
Thought" On which is founded The Mathematical Theories of Logic and
Probabilities; and the Logic of Computer Mathematics.
4. R Carnap ( University of Chicago Press, 1947 / 1958 )
"Meaning and Necessity" A study in Semantics and Modal
Logic.
5. R Carnap ( Dover Publications, 1958 ) " Introduction to
Symbolic Logic and its Applications"
6. Authors: Arnett, Dulaney, Harper, Hill, Krochmal, Kuo,
LeValley, McGarvey, Mellor, Miller, Orr, Ray, Rimbey, Wang,
(New Riders Publishing, 1994) " Inside TCP/IP "
7. B Graham ( AP Professional, 1996 ) " TCP/IP Addressing "
Lectures on the design and optimizing IP addressing.
8. Postel, J. (ed.), "Internet Protocol - DARPA Internet Program
Protocol Specification," RFC 791, USC/Information Sciences
Institute, September 1981.
9. Cisco Systems, Inc. ( Copyright 1989 - 1999 ) "
Internetworking Technology Overview "
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10. S. Bradner, A. Mankin, Network Working Group of Harvard
University (December 1993) " RFC 1550: IP: Next Generation (IPng)
White Paper Solicitation "
11. RFC 791
12. Y. Rekhter (September 1993) RFC 1518: "An Architecture
for IP Address Allocation with CIDR".
13. S. Bellovin (August 1994) RFC 1675: " Security Concerns
for IPng"
14. R. Atkinson (August 1995) RFC 1825: " Security
Architecture for the Internet Protocol"
15. R. M. Hinden (May 1995) " IP Next Generation Overview"
Author
Eugene Terrell
24409 Soto Road Apt. 7
Hayward, CA. 94544-1438
Voice: 510-537-2390
E-Mail: eterrell00@netzero.net
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