ETT-R&D Publications E. Terrell
IT Professional, Author / Researcher April 2000
Internet Draft
Category: Proposed Standard
Document: draft-terrell-logic-analy-bin-ip-spec-ipv7-ipv8-06.txt
Expires October 10, 2000
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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Internet-Drafts are draft documents valid for a maximum of six months
and may be updated, replaced, or obsoleted by other documents at any
time. It is inappropriate to use Internet-Drafts as reference
material or to cite them other than as "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
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Conventions
Please note that the font size of the Tables are smaller than the
expected 12 pts. However, if you are using the most current Web
Browser, the View Section of the Title bar provides you with the
option to either increase or decrease the font size for comfort
level of viewing. (Provided that this is the HTML version.)
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. Nevertheless, their use
servers a functional purpose, which is not intended to undermine authority.
That is, they provide an ability to distinguish the difference(s),
not to mention the convenience, which serve to support the underlining
foundation of the logical argument justifying their existence. In other
words, I shall continue their use until a decision can be made by
"IETF/IESG/IANA", which would determine if such an assignment is
necessary.
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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 underlining Mathematical Logic of the Binary
System. It sustains a more pronounced Revolution, having such a profound
impact. That it produces Results which Mandates a Change in the Entire
Foundation for the Method of Enumeration in the Binary System. 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 its 'Default Addressing Structure' is
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 (eg.; 'F = 1111 = 15', See Table 8). Not
to mention, the employment of a Backwards Compatibility with the Error
Plague IPv4 IP Addressing System.
However, because IPv7 and IPv8 are logical derivations of IPv4. 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 IP Addresses; The controls that optimize IP
Address distribution and provide 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.
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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. However, it can be used, 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'.
[ 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 effect 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 effect 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 neccessary 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.
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 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 thier 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.
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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'.
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 its assimilation with the Current Foundation'.
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.)
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 underlining subject matters from which IPv4, and the
Binary System were derived. Hence, this paper should only be considered as
an excerpt of the underlining 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:
'The IPv4 Class Address Range'; 'The 32 Bit IP Address Format'; 'The
Method for Subnetting'; 'The Principle of the Octet'; and '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.
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.
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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.
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.
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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.
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.
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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.
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
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
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Note: There is no Division of Classes D or E. In fact, their
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.
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.
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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 underlining its functional purpose are assumed,
and based upon descriptive use, and not the soundness of Logical
reasoning derived from definitions.
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
underlining 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 underlining objectives
found upon the Internet Draft upon which this presentation resides.
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.
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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
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
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.
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.
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Notwithstanding, that the example above was a demonstration of the
concepts and the principles underlining Subnetting. However, its
principles and concepts needless to say, is the foundation from which
the principles underlining 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.
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 underlining 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 underlining the entire mathematical field,
and enhanced the use of the Exponent with the precise definition of
being a Logical Operator. Who's underlining 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 underlining Logic as well.
Moreover, while this conclusion was derived from, and served no direct
purpose in the first proof of Fermat's Last Theorem.
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 "Booleian 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 underlining
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
1 provides the platform from which this analysis shall begin.
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.
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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
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'.
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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.
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.
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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.
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'.
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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:
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 (Mathemetical) 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
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 "
Exponential Enumeration Binary Representation Positive Integer
^ ^ ^
/ | \ / | \ / | \
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
.. .......... .................. ...
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 ".
E Terrell [Page 25]
Internet Draft April 10, 2000
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.
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 N0
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 employes 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.
E Terrell [Page 26]
Internet Draft April 10, 2000
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 underlining 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.
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. This is because, they
can have IP Addresses Assigned as needed, which
can be derived from any one of the of the 3 Divisions
of the 5 IP Address Classes.
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Internet Draft April 10, 2000
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
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).
E Terrell [Page 28]
Internet Draft April 10, 2000
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 Suceeding the Primary Setion
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 Suceeding 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 existane 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.
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'
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.x.x.x can never be assigned as a Network
Address, because is the 'LoopBack' test IP Address
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.
E Terrell [Page 29]
Internet Draft April 10, 2000
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 April 10, 2000
TABLE 11
{" The Laws of the Octet "}
1. By definition, there exist 4 distinct Sections or Divisions
for every IP Address Class. However, the number of Sections
or Divisions is dependent upon IP Bit Address Range defined
for the IP Address.
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; B - E).
3. The Subnet Identifier assigns to any Octet it defines in any
Section or Division of every IP Address Class, when not use
as the Default Subnet Mask, only the value of the numbers
available in the IP Address Range assigned to that IP Address
Class.
4. For every OCTET in any Section or Division of any IP Address
Class, that the Subnet Identifier does not define, can be
assigned any value in the range of 1 - 256 (which excludes
only All Integer '0's', and not All Binary 1's.). That is,
provided that there is no succeeding Section or Division,
whose reference is the same OCTET, which is Defined by the
Subnet Identifier. Hence, if there is such an OCTET in the
succeeding Section or Division, then it can not be defined by
the Subnet Identifier and use All of the Address(es) in the
Address Range noted above. {This is seen true by Table 6a,
and the Definitions noted above.}
5. For every OCTET within any Section or Division of any IP
Address Class that is defined by the Subnet Identifier,
and is preceded by a Section or Division whose reference
is the same Octet. Where the case is such that, the Octet
of the preceding Section or Division is not defined by the
Subnet Identifier. Then the Octet of the preceding Section,
or Division, can not be assigned any value as given by the
IP Address Range assigned to that IP Class.
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Internet Draft April 10, 2000
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 Setions 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:
E Terrell [Page 32]
Internet Draft April 10, 2000
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
preceeds 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 for
all 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:
E Terrell [Page 33]
Internet Draft April 10, 2000
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 - 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'
E Terrell [Page 34]
Internet Draft April 10, 2000
Table 12.
"Reality of the 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 'Q - 64'; 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
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 'Q - 32'; 193 - 224 is not included in the
Address Range Rrepresented 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 'Q - 16'; 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
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 'Q - 15'; 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
E Terrell [Page 35]
Internet Draft April 10, 2000
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.
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. 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
the case if there was another section which followed, that which is now
the last section.
E Terrell [Page 36]
Internet Draft April 10, 2000
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.
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 37]
Internet Draft April 10, 2000
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
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
E Terrell [Page 38]
Internet Draft April 10, 2000
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 underlining foundations characterizing IPv4, intact.
E Terrell [Page 39]
Internet Draft April 10, 2000
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 underlining 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
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 40]
Internet Draft April 10, 2000
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 'SIX' 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 Setions of
the respective IP Address Classes. In other words, the
number of available Hosts IP Addresses is always a
'Constant', and is determined by 'Laws of the Octet'.
6. The existance 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, execpt 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 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'.*
E Terrell [Page 41]
Internet Draft April 10, 2000
*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] Broadasts only".
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.
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.
The advantages of IPv8 however, surmount far beyond any 32 Bit IP
Addressing System now employed, or ever conceived. Nevertheless, while
retaining the ease of use and implementation of 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 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 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, each 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 Hell...A Light Year Distance is only 5,873,960,000,000 miles ]
Furthermore, while the foundations underlining IPv8, 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 42]
Internet Draft April 10, 2000
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 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 | 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 |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
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.
E Terrell [Page 43]
Internet Draft April 10, 2000
IP Header for IPv6
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 | PRIO. | FLOW LABEL |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| PAYLOAD LENGTH | NEXT HEADER | HOP LIMIT |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
| |
| |
| |
| SOURCE ADDRESS |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
| |
| DESTINATION ADDRESS |
| |
| |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|-------------------------------------------------------------|
|+ + + + + + + + + + + + + DATA + + + + + + + + + + + + + + + |
|-------------------------------------------------------------|
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. of any is clear that IPv4
and IPv7 can share the same Header.
E Terrell [Page 44]
Internet Draft April 10, 2000
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.
Nevertheless, figure 6 outlines the 'Default IP Address Structure" that
is used in IPv8.
FIGURE 6
1. Source Addressing Structure: 256:256:256.000.000.000
2. Source Addressing Structure: 256:256:256.256.000.000
3. Source Addressing Structure: 256:256:256.256.256.000
4. Destination Addressing Structure: 256:256:256.000.000.000
5. Destination Addressing Structure: 256:256:256.256.000.000
6. Destination Addressing Structure: 256:256:256.256.256.000
E Terrell [Page 45]
Internet Draft April 10, 2000
Nevertheless, figure 6 depicts the 'Default IP Address Structure' for
the Primary, Secondary, and Ternary IP Address Classes, and the Zone
and IP Address Area Codes for the Source and Destination Addresses.
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 that they are Routable as
well. Now observe the Structure, given in Table 15, that this IP
Addressing Scheme yields, and compare its results with that of
Table 12.
E Terrell [Page 46]
Internet Draft April 10, 2000
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
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
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
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
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
E Terrell [Page 47]
Internet Draft April 10, 2000
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 8 equal 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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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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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 exeption, 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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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 - 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]
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.
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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 Subentting 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
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'.
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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*
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 exeption, 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 frational 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.
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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.
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.
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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.
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.
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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.
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, which 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 mandates that results in the enhancement in the
overall performance claimed by the Primary Routers, are the requirements
imposed by the Secondary Routers, which 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.
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.
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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 underlining
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.
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.
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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 Underlining 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 Slpiter | | within the same
to Connect Multiple | | "IP Area Code", or
RJ45 Lines; SJ11 | | outside of the Zone IP
Slpiter 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 communicationis 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
(Quiey having Response) | |effect the Computer
| |Operating Systems and
| |other communications
| |software.
--------------------------|-------------------|
4: Design Of Language | Applies to all |
Translation Servers | the companies |2. Application Changes:
which will transalate | |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 equiped with| |
Computer IP Broadcast | |Note: The changes
Transponder, Locater | |effecting Network OS
| |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. | |
| |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.| |
--------------------------|-------------------|-------------------------
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 | |Struture, 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 / Throughfare
Transmitters implanted in | |Which can be implemented
the Refletors of the Roads| |without environmental
Lane Dividers / or Below. | |disruption. Noting the
| |Frequenies 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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Note: The asterisk indicates Design Specification,
see accompanying Drawings and associated
documents, which are not available for
the "IETF" world notification.
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, which 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 we 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 her 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).
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.
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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.
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 Communiccation, 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.
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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 Comm
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.
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, 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 2st 3nd 4rd Figure 1
= | | .......
= | | . .
= ----- 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 - 254 ................... 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 underlining 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.)
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:
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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.
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!
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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.
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.
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.
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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 underlining 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 Existance, and its total IP Address
availibility 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.
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.
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 |
+--------------------------------------+----+---------------------+
"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 |
+--------+----+----+---------------------------------------------+
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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.
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 continued 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.
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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.
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.
Appendix IV: A Succinct Proof of the Fall of the Binary System
Overall, which questions the validity of
Machine Language
While I may posess 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 which can be derived for the corretion 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 beleive its the
simpliest 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 underlining this reported Error, which is the same as not grasping
or understanding the Concept of ZERO.
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:
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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 appearence 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 Subsittution 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.
And while, this does not, by itself, resolve the Zero issue. What we have
accomplished, is to establish an EQUALITY and One-to-One Correspondene
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 which 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;
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4. {0} = 'the Null or Empty Set' and {0,1} = 'the Binary Set'.
>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.
[ What this implies, when accepting the Elements of the Binary Set, {0,1},
as Abstract Entities, and not Numbers Representing the Graphial 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.
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Needless to say, the results shown here, 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 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 dreived 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, cconfirms 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 underlining 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 communiates with the Language of the Machine rendering
Mathematical results employing the Binary System.
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
Sequener, 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 Funtional Purpose and Design of Electrionic
Hardware is dircetly 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
underlining concepts of Set Theory and the Field Postulates. The
results yield; another Distributive Property ( i.e. Distributive
Law ) 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 "
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"
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Special Note from the Author:
[ The more this paper is read, and re-read, the number of benefits which
can be realized, seems grows at an astronomical rate. What this suggest,
I would imagine, is that the number of possible benefits, which can be
conceived, abounds even the boundaries of our imagination's. Needless to
say, one of the additional benefits, which is a direct result of these
IP Specification(s), is the elimination of the use, or need, for Country
Codes Designation in the Naming Scheme Translation for the IP Address
(i.e. '.us' for United States, which is normally attached to the End
of the Domain Name). In other words, this requirement is met through the
use of the 'Prefixes' assigned to the 32 Bit Block IP Address in IPv8.
Moreover, it is also behooving to note, that the number of Divisions or
Sections, Parts of the Whole, of an Address Class, is the Result of the
Logic from the Method of Quantification. Where by, the division of an IP
Address Class, 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. ]
Author
(Please comment, Written responses only, to:)
Eugene Terrell
24409 Soto Road Apt. 7
Hayward, CA. 94544-1438
Voice: 510-537-2390
E-Mail: eterrell00@netzero.net
(Personal Patent and Copyright is intended; do not attach
nor affix copyright information without expressed consent
of the Author noted above.)
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