Internet Draft E. Terrell
Category: Proposed Standard ETT-R&D Publications
Expires: October 27th, 2006 April 2006
The CIDR Network Descriptor expands the size of the IPtX Address
Space beyond the IPv6 IP Addressing Specification
'draft-terrell-cidr-net-descrpt-expands-iptx-add-spc-21'
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Requirements Terminology
The keywords MUST, MUST NOT, REQUIRED, SHALL, SHALL NOT, SHOULD,
SHOULD NOT, RECOMMENDED, MAY, and OPTIONAL, when they appear in
this document, are to be interpreted as described in [RFC-2119].
Conventions
Please note, the mathematical operators that cannot be represented
in the 'txt' file format, which represent; the '^' Carrot sign for
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This Internet-Draft will expire on October 27th, 2006.
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Abstract
This document, which Obsoletes RFC 2373, RFC 1517, RFC 1518, RFC
1519, and IEEE Specification 1541-2002 (Re-defining the
Electromagnetic Spectrum and the 'SI Units' as a Base 2 Exponential
Binary Conversion - defines the IPtX Bit-Map Specification and
Technique for Bit-Mapping any 'Decimal Fraction' - Page [93], [94],
[106] - ['DCE Unit' = ' 2E'Q ']), provides the final clarification
of the conclusions that redefines the 'CIDR' notation as the 'Network
Descriptor', and proves that the IP Address Pool Total for the IPtX
Specification is greater than IPv6. And more importantly, because
these conclusions reveal the actual design of the Binary
Communication System, the Revolutionary impact sustained, is an
upheaval affecting the entire field of Computer Science; 'The
Rudiments of Finite Quantum Computing and Finite Quantum Computer
Programming'. In other words, IPtX is a more powerful and cost
effective IP Addressing Specification, and when using the 'IPtX-MX
Protocol' {'2^X : 1'; the Compression Ratio for "The Intelligent
Quantum Tunneling Worm Protocol" - The Design of the 'Internet
Protocol telecommunications Xchange Specification'}, the interface
of the "Front-End" can mimic or simulate a 32 Bit-Mapped IP Address.
And this, in conjunction with the IPv4 IP Addressing Overlay,
provides a 100% Backward Compatibility with the IPv4 Specification
(Meeting the Requirements of RFC 1550), in the Backbone environment
approaching an unlimited size 'Bit-Map' Address Space.
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Table of Contents
Abstract
Introduction
1. The Classless Inter-Domain Routing Architecture, or CIDR
2. The Interpretation of the conclusions Expansion of 'CIDR';
Defining the "Network Descriptor"
3. The IPtX and IPv4 IP Addressing Schemes - 100% Compatibility
4. The Structural Comparison - IPv6 vs. IPtX
5. Security
6. IANA Considerations
6.1 Special IANA Consideration
6.2 Special IANA Consideration
- 6.2.1 - Closing Argument; 6.2.2 - Security; 6.2.3 - Summary
6.3 Special IANA Consideration
- Current Definition(s) for the Measurement of the Bit
7. References
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Introduction
The "CIDR" Concepts, the 'Network Descriptor' and the
'Bit-Mapped' IP Address, provided the bases for the comparison
between IPv4, IPv6, and the IPtX IP Addressing Specifications,
which concluded that these are different expressions of equal
definitions. That is, mathematically speaking, the IP Address
Pools of the IPv4 and the IPv6 Specifications, mathematically
defines the variable Coefficient of an Identical Base Pool of
IP Addresses, or X(2^32); given that 'X' respectively equals
'1' and '7.9228163 x 10^28'.
Where IPv4 = 1(2^32)
and IPv6 = 7.9228163 x 10^28(2^32) = 2^128 = 2^4(32).
However, the IP Address Pool for the IPtX Specification is
mathematically defined by the equation:
IPtX = X(2^32) + 16,500,000.
Nevertheless, these additional IP Addresses, because only the
"Network Descriptors" are different, (approximately 16.5 Million
Shared) are Host or Client IP Addresses, which cannot be used to
establish a direct Internet Connection because of the Logic
problems, the decisional conflicts with the Routers. In other
words, the expansion of the 'CIDR' concept(s), which
mathematically defines the expression; 'X(2^32)', can only
provide a Bit-Map that uniquely Identifies every IP Address
within every Address Class, or the IP Address Range the
expression defines, essentially availing the entire Range of IP
Addresses to the Global-Net.
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1. The Classless Inter-Domain Routing Architecture, or CIDR
The Classless Inter-Domain Routing Architecture, or CIDR, was
derived from the so called; "strategies for address assignment of
the existing IP address space with a view to conserve the address
space and stem the explosive growth of routing tables in default-
route-free routers" [9]. It was in reality, an Expansion of the
'Default Addressing Structures' existing in the Address Class
System. The popular claim nevertheless, boasted the elimination of
the Address Class System. These Claims needless to say, were
fashioned by the Authors, whose works represented their personal
interpretation(s), because the works comprising RFC's 1517, 1518,
and 1519 were never fully understood. The truth nonetheless, was
clearly explained in RFC 1519, whose discourse dealt specifically
with the way the Routers, and the Routing Protocols interpreted,
or dealt with the IP Address, and not the elimination of the
Address Class System per se. In other words, the Routers and the
Routing Protocols were limited to using only the 'Default
Addressing Formats', which represented Class A, Class B, and the
Class C Addressing Specification. And to deal with the prospect,
or the possibility of an IP Addressing Shortage, a plan was
devised (RFC's 1517, 1518, and 1519), which actually involved not
only the initial 'Default Addressing Formats', from Class A, B,
and C, but the remaining fractional subcomponents from each of
their respective Octets as well. In fact, while RFC 1519
specifically designed the CIDR Architecture to take advantage of
Class C, it did not weaver in its mention of the same
implementation for the Class A Specification. It could be said in
other words, that the CIDR Architecture represents an Un-Finished
version of the 'IPtX Protocol Family Specification'. However,
because of the MISNOMER, 'CLASSLESS', the process of SUB-DIVIDING
a Class (In particular; Class A, and Class C), was never fully
understood. Hence, the CIDR Architecture is the Sub-division of a
CLASS SYSTEM, or a Class Addressing System that has been
SUB-DIVIDED, which represents the Class, or the Whole, having a
Greater Number of Constituents.
In other words, the CIDR Architecture actually represents; The
'Inter-Domain IP Bit Mapped Address Routing Architecture'. Because
this, in essence, is what is really happening to the IP Address,
and this is the IP Addressing Format that the Router and the
Routing Protocols are dealing with. Therefore, the Class Addressing
System is a format that implements a Network IP Address using a
specified number of BITs, and in this case, it is either '8', '16',
'24', or '32' Bits. Needless to say, any further Sub-Division, or
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use of some Smaller Portion or Constituent, does not constitute a
departure nor eliminate the Existence of the Address Class System.
Hence, the CIDR Architecture actually reinforced the Class Concept
and proved that, without changing the entire Addressing Architecture
defining the 'IP Bit Mapped Address or the IP Bit Mapped Address
Space', the Whole, is indeed the Sum of its Parts.
2. The Interpretation of the conclusion's Expansion of 'CIDR';
Defining the "Network Descriptor"
When defining the New 'CIDR' Architecture as representing the
collective Extension for RFC's 1517, 1518, and 1519, we must
first list the functional components, or Highlights, noted as
the objectives or purpose supporting each of these papers,
individually. That is, there must be comparison between the
definition or description of the functional purpose of the
'CIDR' Architecture as represented in each of these papers,
compared with the New 'CIDR' Architecture this paper actually
represents.
RFC 1517 (Maintained promoted a fear of IP Address Loss, and
Astronomical growth in the size of the Routing Tables):
"- Exhaustion of the class-B network address space. One
fundamental cause of this problem is the lack of a network
class of a size that is appropriate for a mid-sized
organization. Class-C, with a maximum of 254 host addresses,
is too small, while class-B, which allows up to 65534 addresses,
is too large to be densely populated. The result is inefficient
utilization of class-B network numbers.
- Routing information overload. The size and rate of growth of the
routing tables in Internet routers is beyond the ability of
current software (and people) to effectively manage.
- Eventual exhaustion of IP network numbers."
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Argument in Opposition (Justification of the New 'CIDR' Architecture):
Clearly, using the expanded 'CIDR' Architecture, when using the
'CIDR Network Descriptor', the Reality of IP Address Exhaustion now
defines a wasted use of IP Addresses. In other words, Viable IP
Address that could have been use to establish an Internet Connection,
Connecting the Network's Backbone-Domain to the Internet, were
assigned for the Host IP Addresses. This is further clarified by a
Comparison of the "Internet Protocol v4 Address Space, and the use
of the CIDR Network Descriptor displayed in Table I:
TABLE I
IPtX - Internet Protocol t1 Address Space INDEX
IPaddNum = Network IP Address
CIDRNetDescrip = CIDR Network Descriptor
Current Number of IP Network Addresses Issued
Accounts for = 253 IP Network Addresses
CIDR
Network
Class A Descriptor
A-1: Issued = 127 , Remaining = 1,040,513,921 /0000:08
A-2: Issued = None, Remaining = 516,160,512 /0000:16
A-3: Issued = None, Remaining = 256,048,128 /0000:24
A-4: Issued = None, Remaining = 252,047,376 /0000:32
Class B
B-1: Issued = 64 , Remaining = 784,514,496 /1000:08
B-2: Issued = None, Remaining = 197,672,960 /1000:16
B-3: Issued = None, Remaining = 49,807,360 /1000:24
B-4: Issued = None, Remaining = 16,777,216 /1000:32
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TABLE I - Continued
CIDR
Network
Class C Descriptor
C-1: Issued = 32 , Remaining = 458,321,632 /1100:08
C-2: Issued = None, Remaining = 57,741,312 /1100:16
C-3: Issued = None, Remaining = 7,274,496 /1100:24
C-4: Issued = None, Remaining = 1,048,576 /1100:32
Class D
D-1: Issued = 16 , Remaining = 245,676,912 /1110:08
D-2: Issued = None, Remaining = 15,475,712 /1110:16
D-3: Issued = None, Remaining = 974,848 /1110:24
D-4: Issued = None, Remaining = 65,536 /1110:32
Class E
E-1: Issued = 15 , Remaining = 231,289,845 /1111:08
E-2: Issued = None, Remaining = 13,658,850 /1111:16
E-3: Issued = None, Remaining = 806,625 /1111:24
E-4: Issued = None, Remaining = 50,625 /1111:32
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RFC 1518 (Which deals more with the actual Structure of the Internet,
or its Hierarchical Structure , and IP Address allocation
and Routing, than the actual 'CIDR' Architecture) where by,
the points are specified as:
There are two aspects of interest when discussing IP address
allocation within the Internet. The first is the set of
administrative requirements for obtaining and allocating IP
addresses; the second is the technical aspect of such
assignments, having largely to do with routing, both within a
routing domain (intra-domain routing) and between routing domains
(inter-domain routing). This paper focuses on the technical
issues.
The architecture and recommendations in this paper are oriented
primarily toward the large-scale division of IP address
allocation in the Internet.
IP Addresses and Routing
Efficiency versus Decentralized Control
IP Address Administration and Routing in the Internet
Administration of IP addresses within a domain
Indirect Providers (Backbones)*
Continental aggregation*
Argument in Opposition (Justification of the New 'CIDR'
Architecture):
While there is a lot that can be said regarding RFC 1518,
especially since this is a proposal which advocates a great
deal of dependency upon ISP's, whose entire existence is
based upon the Economy, the Consumer, and a Volatile Market.
This actually means, an ISP has no guaranteed Future, regarding
either the use of the IP Address Base, or their Routers for a
thoroughfare. In other words, while this RFC did mention some
good points, these arguments are supported in the IPtX
Specification. It nevertheless, maintained more the soundings
of a White Paper Solicitation for a New System Overall, than an
actual presentation representing 'CIDR' Architecture. Needless
to say, some of the problems discussed, and emphasized
repeatedly, addressed the need for a Internet Hierarchy, while
dismissing the need to expand the number of Backbone connections,
this is the main point of consideration when addressing the
concept of an Internet Hierarchy.
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RFC 1519 (While this RFC should be the replacement for RFC 1517,
because it is clearly derived from RFC 1517, it claims to
Obsoletes RFC 1338, which I have not read. And while this
paper also disputes some of the proposals outlined in RFC
1518 {Noting Specifically the causes for a loss of
aggregation efficiency; Organizations which are multi-homed,
and Organizations which change service provider but do not
renumber.}. Nevertheless, one thing this RFC does, that the
others so far do not, is that, it Mathematically Introduces
the beginnings of Foundation for the 'CIDR' Architecture.)
Argument in Opposition (Justification of the New 'CIDR' Architecture):
Nonetheless, while this RFC introduces the basic Mathematical
Foundation for the 'CIDR' Architecture, and sets the fundamentals
for the hardware and software specifications for Networking in a
Supernetted Environment, it actually does nothing to prevent IP
Address wasted on Host Assignments. This is because the foundation
of the 'CIDR' Architecture was derived from the IPv4 specification,
which means there was no way, short of a New IP Addressing System,
could this waste be avoided. However, this is not the problem with
the IPtX specification, because it De-Emphasizes the HOST IP Address,
and gives it secondary functional value, which defines a dummy Host.
Needless to say, this was the foundation that was needed to get the
'Ball Rolling'. Nevertheless, while RFC 1519 developed the
Mathematical foundation for the 'CIDR' Architecture, it never fully
Exploited the benefits this Architecture maintains.
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Definitions
CIDR: Classless Inter-Domain Routing is an IP Address Resolution
Technique that provides a way to resolve any Binary Number(s)
into its the Integer Translation to verify an IP Address,
which is written in 'Dotted Notation' and defined by '4' 8 Bit
Octets.
CIDR Network Descriptor: It is a 2 Part Number used to resolve,
or discover the Integer representing
Binary Number defining the Network
Bit-Mapped IP Address.
[Where by, the Digits to the Right of the Colon Represents the
Starting Point for the IP Address Class Range in Binary Notation,
or Network IP Address assigned to the Specified IP Address Class
Range. And the Digits to the Left of the Colon represent the Count
of Bit Mapped Displacement, or the Number of Binary Digits the
Network IP Address uses. In which case, the '/XXXX:XX' notation
would be used to Identify the Bit-Mapped Address Class and the
Address Class Range of a Network IP Address.]
Nevertheless, the definitions noted above, concludes the argument by
providing logical support for Re-Defining the 'CIDR' notation as the
"Network Descriptor", which comprises a Switch, and a 2-part Number
that defines the entire Range of every IP Address, including the
Address Class Range mapping every Octet for the Network portion of
the IP Address defines.
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TABLE II
IPtX - Internet Protocol t1 Address Space INDEX
IPaddNum = Network IP Address (XXX.XXX.XXX.XXX)
CIDRNetDescrip = CIDR Network Descriptor (/XXXX:XX)
CIDRNetDesSwitch = CIDR Network Descriptor Switch (/)
CIDRNetDesClassID = A "4" place Binary Number (XXXX)
Identifying the 'Front-End' of the
Bit-Mapped Space of the Network Address
in the Range of the Address Class.
CIDRNetDesDivider = Statement End-Start New Statement (:)
CIDROctDesNetID = A "2" place, or variable Number (XX)
Identifying the entire Bit-Mapped Range
of an IP Address. (IPv6 has "3" places)
ZONEIPaddNum = Zone IP designates the Continent's location,
and it is the First of a 2 Octet configuration
defining the Prefix of a 32 Bit IP Address,
which is 8 Bit Number Terminated by a Colon
(XXX:)
IPAreaCodeaddNum = IP Area Code designates the second level
of the Continent's Sub-Region, and defines
the Second of the 2 8 Bit Octet
configuration Prefixing a 32 Bit IP Address
that is also Terminated by a Colon (XXX:)
GlobalIPaddNum = GlobalNet IP Address (XXX:XXX:XXX.XXX.XXX.XXX)
CIDRTrunkNetID = The combined use of the 'Zone IP' and the
IP Area Code to identify the "Trunk-Identifier",
which is assign to the 'TelCo-Xchge or Backbone
Routers'.
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3. The IPtX and IPv4 IP Addressing Schemes - 100% Compatibility
The IPtX IP Addressing Scheme is a logically derived 'Internet
Protocol Addressing Family' that is founded upon the IPv4 IP
Addressing Specification. In other words, because IPtX utilizes the
same Bit-Mapped Binary Addressing Format, which does not require any
deviation from the operational infrastructure of the IPv4 Address
Space. It maintains a 100% Backward Compatibility with IPv4, which
is retained throughout an expansion capability defining an
Infinitely Bit-Mapped IP Address Space using only a 64 Bit Header.
There is however, the one noted difference in the IPv4 and the IPtX
Specifications, which defines a distinction between the respective
"Subnet-Mask" and the "Subnet-Identifier" that allows the IPtX
Address Pool to be greater than IPv4 and IPv6, when using the same
Bit-Mapped IP Address Space. Needless to say, while this distinction
might at first, appear to be a strong departure from the IPv4 Format.
It's only a 'Binary Switch' that uses the elements from the Set,
{X,Y}, to provide the ability the Change ((between) or (Extend)) the
'Programmed Functions' or 'Operations' defining the "Subnet-Mask"
and the "Subnet-Identifier". In any case, it should be clearly
understood, the definition of the "Subnet-Identifier" extends the
definition of the "Subnet-Mask" by providing the ability to Change
the Range of the Subnet, which specifies the range of the Host IP
Address. And this, it should be noted, is the Distinguishing
Mathematical Hallmark that assigns every IP Address in the IPv4
Specification to the IP Address Pool, with the added benefit of the
creation of a Host IP Address Pool. Now, if the Address Spaces were
equal, the number of available IP Address in the IP Address Pool
assigned to the IPv4 Specification, given that IPtX is defined as
the extension of IPv4, exceeds the number of available IP Address
in the IP Address Pool assigned to the IPv6 Specification.
Nevertheless, the validity of the forgoing is supported by the
conclusions from the mathematical analysis and comparison of Tables
III, IV, and V.
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Table III
Decimal Structure of the IPv4 Representation IP Class System
IPv4 IP Address Pool = 4.145 x 10^9 Addresses
1. Class A: 1 - 126, Default Subnet Mask 255.X.X.X:
126 Networks and 16,387,064 Hosts: 0000
2. Class B: 128- 191, Default Subnet Mask 255.255.X.X:
16,256 Networks and 64,516 Hosts: 1000
3. Class C: 192 - 223, Default Subnet Mask 255.255.255.X:
2,064,512 Networks and 254 Hosts: 1100
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: 1111
15 x 254^3 = 245,805,960 IP Addresses available
Table IV
IPtX - 'Subnet-Identifier' = "Subnet-Mask" -
100% Backward Compatibility with IPv4
"IPtX Addressing System Using the Current Binary System."
[Note: The Law of the Octet defines the value, relative to Class,
of the 'Y' variable in the IP Address Pool containing;
4,145,927,192 = 4.145 x 10^9 Addresses, which should be:
2^32 = 4,294,967,296]
1. Total IP Addresses for Class A = 126 x 254^3 = 2,064,770,064
Total available IP Host Addresses Equals 126 x 254^N
[Where N = Number of Octet(s), and 'Y' equals the Address
Range '128 - 254', 1 - 126 is not included in the Address
Range Represented by the equation 'Y = 254 - 126'.]
Class A-1, 1 - 126, Default Subnet-Mask 255.Y.X.X /0000:08
126 Networks and 8,129,016 Hosts
Class A-2, 1 - 126, Default Subnet-Mask 255.255.Y.X /0000:16
15,876 Networks and 32,004 Hosts
Class A-3, 1 - 126, Default Subnet-Mask 255.255.255.Y /0000:24
2,000,376 Networks and 126 Hosts
Class A-4, 1 - 126, Default Subnet-Mask 255.255.255.255 /0000:32
252,047,376 Network / MultiCast IP Addresses / AnyCast
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Table IV - Continued
2. Total IP Addresses for Class B = 64 x 254^3 = 1,048,772,096
Total available IP Host Addresses Equals 64 x 254^N
[Where N = Number of Octet, and 'Y' equals the Address Range
'254 - Q'; 128 - 191 is not included in the Address Range
Represented by the equation 'Y = 254 - 64'.]
Class B-1, 128 - 191, Default Subnet Mask 255.Y.X.X /1000:08
64 Networks and 4,129,024 Hosts
Class B-2, 128 - 191, Default Subnet Mask 255.255.Y.X /1000:16
4,096 Networks and 48,260 Hosts
Class B-3, 128 - 191, Default Subnet Mask 255.255.255.Y /1000:24
262,144 Networks and 64 Hosts
Class B-4, 128 - 191, Default Subnet Mask 255.255.255.255 /1000:32
16,777,216 Network / MultiCast IP Addresses / AnyCast
3. Total IP Addresses for Class C = 32 x 254^3 = 524,386,048
Total available IP Host Addresses Equals 32 x 254^N
[Where N = Number of Octet, and 'Y' equals the Address
Range '254 - Q'; 192 - 223 is not included in the Address
Range Represented by the equation 'Y = 254 - 32.]
Class C-1, 192 - 223, Default Subnet Mask 255.Y.X.X /1100:08
32 Networks and 2,065,512 Hosts
Class C-2, 192 - 223, Default Subnet Mask 255.255.Y.X /1100:16
1,024 Networks and 8,128 Hosts
Class C-3, 192 - 223, Default Subnet Mask 255.255.255.Y /1100:24
32,768 Networks and 32 Hosts
Class C-4, 192 - 223, Default Subnet Mask 255.255.255.255 /1100:32
1,048,576 Network / MultiCast IP Addresses / AnyCast
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Table IV - Continued
4. Total IP Addresses for Class D = 16 x 254^3 = 262,193,024
Total available IP Host Addresses Equals 16 x 254^N
[Where N = Number of Octet, and 'Y' equals the Address
Range '254 - Q'; 224 - 239 is not included in the Address
Range Represented by the equation 'Y = 254 - 16'.]
Class D-1, 224 - 239, Default Subnet Mask 255.Y.X.X /1110:08
16 Networks and 1,032,256 Hosts
Class D-2, 224 - 239, Default Subnet Mask 255.255.Y.X /1110:16
256 Networks and 3,048 Host
Class D-3, 224 - 239, Default Subnet Mask 255.255.255.Y /1110:24
4,096 Networks and 16 Hosts
Class D-4, 224 - 239, Default Subnet Mask 255.255.255.255 /1110:32
65,536 Network / MultiCast IP Addresses / AnyCast
5. Total IP Addresses for Class E = 15 x 254^3 = 245,805,960
Total available IP Host Addresses Equals 15 x 254^N
[Where N = Number of Octet, and 'Y' equals the Address
Range '254 - Q'; 240 - 254 is not included in the Address
Range Represented by the equation 'Y = 254 - 15'.]
Class E-1, 240 - 254, Default Subnet Mask 255.Y.X.X /1111:08
15 Networks and 967,740 Hosts
Class E-2, 240 - 254, Default Subnet Mask 255.255.Y.X /1111:16
225 Networks and 3,810 Hosts
Class E-3, 240 - 254, Default Subnet Mask 255.255.255.Y /1111:24
3,375 Networks and 15 Hosts
Class E-4, 240 - 254, Default Subnet Mask 255.255.255.255 /1111:32
50,625 Network / MultiCast IP Addresses / AnyCast
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The mathematical analysis of the result from Table III and Table IV
reveals that when the "Subnet-Mask" is equal to the "Subnet-
Identifier". The division of the Address Classes in the IPv4
Specification, is defined by the "Network Descriptor" as; the
Logical Expansion of each of the Address Classes in the IPv4
Specification, through the use of the Network ID designation, "255",
in remaining Octets. And because the requirement of the "Subnet-
Mask" mandates that 'only a Number from the Range of the Address
Class' can be assigned a Network ID, then every Octet specifies one
of the '4 Sub-Division' created in the Range of every Address Class.
In other words, because the "Subnet-Mask" specifies the uses of the
"255" designation in conjunction with the 'Range of the Address
Class', to identify the Address Class associated with the Network
ID. The logical use of the Octets remaining in the Range of every
Address Class in conjunction with the "Subnet-Mask", is the logical
consequence of the conclusion derived from the expansion, or
sub-division of the 'Address Class Range' that was outlined in RFC
1517, 1518, and 1519. Needless to say, since 'the Quantified Sum of
the 'Product of the Network and Host IP Addresses' for every Address
Class in Table IV, is equal to the Total Number of IP Address
assigned to the Range of the Address Class defined by Table III,
then the Addressing Specifications shown by these Tables are
mathematically equal. In which case, mathematically speaking, it
should be concluded that the IPtX Specification, by RFC 1517, 1518,
and 1519, is the interpretation of the IPv4 Specification derived
from the use of the "Subnet-Mask".
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4. The Structural Comparison - IPv6 vs. IPtX
The handicaps from using an askew Binary System, the Loop-Back
Address (127), and the Subnet-Mask (255), makes it impossible for
the IPv4 Specification, even through the progressive expansion using
32 Bit additions for an equal Address Space, to match the IP
Addresses available in the IP Address Pool of the IPv6 Specification.
And clearly, the same fate, according to Figures 1 and 2, will befall
the IPtX Specification. However, because the IPtX Specification
maintains an expansion capability defining an Infinitely Bit-Mapped
IP Address Space using only a 64 Bit Header. In which, the
'TelCo-Xchge or Backbone Routers' would be assigned a Network ID,
which would absorb the Bit-String of the Address Space beyond the 32
Bit-Mapped IP Address Space defined by the IPt1 Specification. And
since, the losses represented by Figures 1 and 2, at infinity, are
not discernable. The IPtX Specification maintains an IP Address Pool
Capacity, which is theoretically, infinitely larger than the IP
Address Pool availability in the IPv6 Specification (See Figure 3).
IPv4 Specification
IPv4 = 32 Bit Address Space
IPv4 IP Address Pool = 253(254^3)
= 4,145,927,192
= 4.145 x 10^9 Addresses
IPv4 IP Address Pool Specification = 4,294,967,296
= X(2^32)
This represents a loss: 4,294,967,296 - 4,145,927,192
= 149,040,104 IP Addresses
IPv6 Specification
IPv6 = 128 Bit Address Space
IPv6 IP Address Pool = (2^32) x (2^32) x (2^32) x (2^32)
= 2^128 = X(2^32)
IPv6 IP Address Pool Specification =
340,282,366,920,938,463,463,374,607,431,768,211,456 IP Addresses
= X(2^32)
Figure 1
E Terrell Internet Draft [Page 18]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
IPtX Specification
IPt1 = 32 Bit Address Space
IPt1 IP Address Pool = (255^4)
= 4,228,250,625 + 16,500,000 IP Addresses
IPt1 IP Address Pool Specification
= X(2^32) + 16,500,000 IP Addresses
= 4,294,967,296 + 16,500,000 IP Addresses
This represents a loss: 4,294,967,296 - 4,228,250,625
= 66,716,671 IP Addresses
IPtX Specification
IPt2 = 64 Bit Address Space
IPt2 = 48 Bit IP Address = (255^2)(255^4)
= X(2^32) + 16,500,000 IP Addresses
IPt2 IP Address Pool = (255^2)(255^4)
= 65,025(2^32) + 16,500,000 IP Addresses
= 65,025(4,228,250,625) + 16,500,000
= 2.7494200 x 10^14 + 16,500,000 IP Addresses
IPt2 IP Address Pool Specification
= X(2^32) + 16,500,000 IP Addresses
= (256^2)(2^32) = 2.8147498 x 10^14
This represents a loss: 2.8147498 x 10^14 - 2.7494200 x 10^14
= 6.5329799 x 10^12 IP Addresses
IPt2 = 64 Bit Address Space = (255^4)(255^4)
= X(2^32) + 16,500,000 IP Addresses
IPt2 IP Address Pool = (255^4)(255^4)
= 1.7878103 x 10^19 + 16,500,000 IP Addresses
= 4,228,250,625(4,228,250,625) + 16,500,000
= 1.8160198 x 10^19 + 16,500,000 IP Addresses
IPt2 IP Address Pool Specification
= (256^4)(2^32) = 1.8446744 x 10^19
=(256^4)(2^32) = 1.8446744 x 10^19
This represents a loss: 1.8446744 x 10^19 - 1.8160198 x 10^19
= 2.8654592 x 10^17 IP Addresses
Figure 2
E Terrell Internet Draft [Page 19]
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'IPtX IP Specification'
(Topology of the Internet Backbone Hierarchy)
Trunk-Id Zone IP Bit-Mapped Network
Address IP Area Code IP IP Header IP Address IP Address
Size Address Address BITS Size Space Size Size
Spec. Spec. Spec. Spec. Spec. Spec.
| | | | | |
None = None = IPt1 = 32 Bit = 32 Bit = 32 Bit
32 Bit = 16 Bit = IPt2 = 64 Bit = 64 Bit = 32 Bit
64 Bit = 16 Bit = IPt3 = 64 Bit = 96 Bit = 32 Bit
96 Bit = 16 Bit = IPt4 = 64 Bit = 128 Bit = 32 Bit
128 Bit = 16 Bit = IPt5 = 64 Bit = 160 Bit = 32 Bit
: : : : : :
3.168k Bit = 16 Bit = IPt100 = 64 Bit = 3,200 Bit = 32 Bit
: : : : : :
159,968 Bit = 16 Bit = IPt5000 = 64 Bit = 160,000 Bit = 32 Bit
: : : : : :
XXXXX Bit = IPt 1.00 x 10^11 = : 3.200 x 10^12 Bits :
: : : : : :
XXXXX Bit = IPt 1.00 x 10^14 = : 3.200 x 10^18 Bits :
: : : : : :
Infinity = 16 Bit = IPtX = 64 Bit = Infinity = 32 Bit
+-----------------------------------------------------------------+
The "Trunk-Identifier" Specification (Spec.) contains the Zone IP
and IP Area Code. And given that Software can assign the Zone IP
and IP Area Code to any location/destination. Eventually it will
be necessary to know the 18 Digit IP Address: ZoneIP, IP Area Code,
Network IP Address. And noting that any Trunk-Id beyond 96 Bits
might seem ridiculous, because of the inherent limitations of the
design specifications for the "Network Descriptor", (+/0000:00).
However, assigning a 'Router-ID' that requires Special
Authentication between communicating Routers could easily absorb
any Number of Bits beyond the IPt4 Specification.
+-----------------------------------------------------------------+
Figure 3
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INTERNET PROTOCOL t2 (64 Bit) ADDRESS SPACE
IPt2 IP Address Prefix IPt1 Address
/ \ \ Schematic Distribution
Reserved CIDR Zone IP IP Area IP Address Purpose Date
BITS Network | Code Assignment | |
/ \ Descriptor V | / | \ / V \ V
---+---+--------+-------+--------+----------------+-----------+------
8 | 8 | None 000: 000: 000.000.000.000 None 4/2002
8 | 8 | All 001: 256: XXX.XXX.XXX.XXX NA 4/2002
8 | 8 | All 002: 256: XXX.XXX.XXX.XXX SA 4/2002
8 | 8 | All 003: 256: XXX.XXX.XXX.XXX EU 4/2002
8 | 8 | All 004: 256: XXX.XXX.XXX.XXX OS 4/2002
8 | 8 | All 005: 256: XXX.XXX.XXX.XXX AU 4/2002
8 | 8 | All 006: 256: XXX.XXX.XXX.XXX AF 4/2002
8 | 8 | All 007-256: 256: XXX.XXX.XXX.XXX IANA/RSRVD 4/2002
8 | 8 | NO-IDs 001-256: 000-256: 000.XXX.XXX.XXX IANA/EMGNCY 4/2006
8 | 8 | ±/XXXX:XX 256: 256: 127.000.000.000 IANA/LopBck 4/2002
SA = South America, NA = North America,
EU = European Union, AU = African Union,
AF = Asian Federation, OS = Oceania States
Figure 4
Note: The IP Addressing Design Specification implements the
IP Addressing Operational Design Procedures for the
"Front-End" and the "Back-End"... Specifically noting
that; IPv6 is a "Back-End" only, Addressing Specification:
IPv4 is a "Front-End" and "Back-End" IP Addressing
Specification: The IPtX Design however, is a Dual
Addressing Specification that offers a choice between a
design specification that is 100% backward compatible with
the "Front-End" and the "Back-End" of IPv4, or a design that
to mimics the "Front-End" of IPv4, with a new "Back-End"
design specification that defines an Alternate
"Electro-Magnetic Spectrum", which is a (New) "Binary"
Interpretation of the "Electro-Magnetic Spectrum"
{"Quantum Theoretical Physics"; the Logical Foundation
resulting from the discovery of the "Quantum Scale"}.
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Nevertheless, it should be clearly understood, that if the
'TelCo-Xchge or Backbone Routers' were assigned to the
"Trunk-Identifier", then there must be a way to verify, resolve,
or confirm the "Zone IP and the IP Area Code" Address defining the
"Trunk-Identifier". In other words, the IPtX Specification can
maintain the "Subnet-Identifier", use the "Network Descriptor"
to verify the "Trunk-Identifier", and exhaust, without loss, every
available IP Address in the Address Pool defined by the equation 1
(eq-1):
eq-1: IPtX = X(2^32) + 16,900,000 = Infinity
eq-2: IPv6 = X(2^32)
= (2^128)
= (256^16)
= 3.4028237 x 10^38
The process of maximizing the Address Pool defined by equation 1,
is a '3' Step procedure, in which the first step exhaust all of
the available IP Addresses in the IPv4 Specification. The second
step requires changing the Symbol used as the "Network Designator"
for the "Subnet-Identifier" (255 Or 256), and the third step
requires expanding the function of the Switch for the "Network
Descriptor". To achieve the first goal, multiply the Network and
Host IP Addresses from Table IV, and use the product to represent
the total number of Networks, leaving the Host total unchanged.
And after the "Network Descriptor" and the "Subnet-Identifier"
has been redefined, as provided in Table V. The adjusted results
now reveals that the total number of available IP Addresses in
the Address Pool for the IPtX Specification is equal to equation
1, and it exceeds the amount assigned to the IPv6 Specification,
when the size of the Bit-Mapped Address Space is equal to both
Addressing Specifications (See Table VI).
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TABLE V - Definitions
+--------------------------------------------------------------------+
| |
| "Network Descriptor": A method derived from the CIDR notation, |
| which is used to resolve and identify every part of a Network |
| IP Address. And when it defines the use of '2' State Switch, |
| comprising a 'Statement 'End-Start' New Statement Command |
| symbol' and a 2 Part numeral, it separates an IP Address into 2 |
| components, which identifies the Network IP Address and the |
| Trunk-Identifier. |
| |
| |
| CIDR Network Descriptor ' ±/0000:00 ' |
| |
| 1) '2' State Switch: " ±/ " - CIDRNetDesSwitch |
|Front-End: a) "Network-Identifier" Switch: ' -/ ' - CIDRGetIPaddNum |
|Back-End: b) "Trunk-Identifier" Switch: ' +/ ' - CIDRGetTrunkIDNum|
| |
| 2) 'End-Start', Flip/Flop Command symbol: '(:)'- CIDRNetDesDivider|
| |
| 3) Network ID': ' 0000 ' - CIDRNetDesClassID |
| |
| 4) 'Octet Bit-Map': ' 00 ' - CIDROctDesNetID - Address Length |
+--------------------------------------------------------------------+
| |
| "Subnet-Identifier": Defines the Overlay that is used in |
| conjunction with a "Network Designator" and the 'X' and 'Y'|
| variables to resolve a Network(s) IP Address. |
| |
| 1) "Network Designator": The symbol for the Null Set, ' F ', |
| which is used as the 'Place Holder', identifying |
| the OCTET(s) that define the Network ID, or |
| the Network portion of the 32 Bit IP Address. |
| |
| 2) "Octet using entire Address Range: ' X ' |
| |
| 2) "Octet cannot use "Network Designator" Addresses: ' Y ' |
| |
+--------------------------------------------------------------------+
E Terrell Internet Draft [Page 23]
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Note: From Table V, the "Network Designator", which is symbolized
as; ' F ', could just as easily, been assigned to defined
any symbol, (e.g.; '257') except for ' 0 '(representing
' 00 ', the Binary equivalent of ' 1 ') and any assignment
represented in the Range of the Addressing Specification. In
any case, it should be clearly understood that when every
available IP Address is used for IP Addressing. The IPtX
Addressing Schematic, (where fig. 5 and fig. 6 respectively
denotes IPt1 and IPt2 Specifications) becomes nothing more
than an OVERLAY, which is used to facilitate the
visualization of the Topology for the Structure of the
Network Design. And this is an extremely important advantage
when designing a Network containing hundreds (or thousands)
of Servers and several thousand (or Million) Hosts assigned
to Subnets. [It is important to note, ' F ' represents the
'NULL SET' or TRUE ZERO {the Traditional European
Representation for True Zero}, and ' 0 ' is EQUAL to ' 00 ',
which defines the Binary equivalence of ' 1 ':
'00' = '0' = '1'.]
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TABLE VI : ' IPt4 ' 128 Bit-Mapped Space
"The Logically derived Structure of the 'Synthetic' Decimal
Representation of the IPt4 IP Addressing Specification"
IPt4 Address Pool Size = 2^32(256^12) = 256^16
= 4,294,967,296(256^12) = 3.4028237 x 10^38
NOTE: IPt4, by FIGURE '5' contains;
'7.9228163 x 10^28' COPIES of the 'IPt1' Specification
CLASS A - 'Address Range 1 - 128'
A-1; Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.Y.X.X -/0000:08
- Networks: 128 x (128 x 256^2)(256^12)
- Host: 128 x 256^2 = 8,388,608
A-2; Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.Y.X -/0000:16
- Networks:(128^2)(128 x 256)(256^12)
- Host: 128 x 256 = 32, 768
A-3; Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.Y -/0000:24
- Networks:(128^3) x 128(256^12)
- Host: 128 = 128
A-4; Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.FFF -/0000:32
- Networks: 128^4(256^12)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks ID - 2^7 = (256^12)(128 x 16,777,216)
= 1.7014118 x 10^38
Hosts = (128 x 256^2) + (128 x 256) + 128 = 8,421,504
E Terrell Internet Draft [Page 25]
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TABLE VI : ' IPt4 ' 128 Bit-Mapped Space - Continued
CLASS B - 'Address Range 129 - 192'
B-1, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.Y.X.X -/1000:08
- Networks: 64(256 - 64)(256^2)(256^12)
- Host: 64 x 256^2 = 4,194,304
B-2, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.Y.X -/1000:16
- Networks: (64^2)(256 - 64) x 256(256^12)
- Host: 64 x 256 = 16, 384
B-3, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.Y -/1000:24
- Networks: 64^4(256 - 64)(256^12)
- Host: 64 = 64
B-4, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.FFF -/1000:32
- Networks: 64^4(256^12)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks ID - 2^6 = (256^12)(64 x 16,777,216)
= 8.5070592 x 10^37
Hosts = (64 x 256^2) + (64 x 256) + 64 = 4,210,752
E Terrell Internet Draft [Page 26]
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TABLE VI : ' IPt4 ' 128 Bit-Mapped Space - Continued
CLASS C - 'Address Range 193 - 224'
C-1, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.Y.X.X -/1100:08
- Networks: 32(256 - 32)(256^2)(256^12)
- Host: 32 x 256^2 = 2,097,152
C-2, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.Y.X -/1100:16
- Networks: 32^2(256 - 32) x 256(256^12)
- Host: 32 x 256 = 5,888
C-3, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.Y -/1100:24
- Networks: 32^3(256 - 32)(256^12)
- Host: 32 = 32
C-4, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.FFF -/1100:32
- Networks: 32^4(256^12)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks ID - 2^5 = (256^12)(32 x 16,777,216)
= 4.2535296 x 10^37
Hosts = (32 x 256^2) + (32 x 256) + 32 = 2,105,376
E Terrell Internet Draft [Page 27]
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TABLE VI : ' IPt4 ' 128 Bit-Mapped Space - Continued
CLASS D - 'Address Range 225 - 240'
D-1, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.Y.X.X -/1110:08
- Networks: 16(256 - 16)(256^2)(256^12)
- Host: 16 x 256^2 = 1,048,576
D-2, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.Y.X -/1110:16
- Networks: 16^2(256 - 16) x 256(256^12)
- Host: 16 x 256 = 4,096
D-3, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.Y -/1110:24
- Networks: 16^3(256 - 16)(256^12)
- Host: 16 = 16
D-4, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.FFF -/1110:32
- Networks: 16^4(256^12)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks ID - 2^4 = (256^12)(16 x 16,777,216)
= 2.1267648 x 10^37
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
E Terrell Internet Draft [Page 28]
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TABLE VI : ' IPt4 ' 128 Bit-Mapped Space - Continued
CLASS E - 'Address Range 241 - 256'
E-1, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.Y.X.X -/1111:08
- Networks: 16(256 - 16)(256^2)(256^12)
- Host: 16 x 256^2 = 1,048,576
E-2, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.Y.X -/1111:16
- Networks: 16^2(256 - 16) x 256(256^12)
- Host: 16 x 256 = 4,096
E-3, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.Y -/1111:24
- Networks: 16^3(256 - 16)(256^12)
- Host: 16 = 16
E-4, Subnet Id - 256:256:256:256:256:256:256:256:256:256:256:256:
FFF.FFF.FFF.FFF -/1111:32
- Networks: 16^4(256^12)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks ID - 2^4 = (256^12)(16 x 16,777,216)
= 2.1267648 x 10^37
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
Note: Since, the "Subnet Id" = the "Subnet Identifier", the Shared
Host IP Address Pool increases by a factor equal the number of
available Network IP Addresses assigned to every sub-division
within the Overlay defining the Address Class Range, given
that No Host Address is assigned a direct Internet Connection.
E Terrell Internet Draft [Page 29]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
eq-1: IPtX = X(2^32) + 16,900,000 = Infinity
eq-2: IPv6 = X(2^32) = (2^128) = (256^16) = 3.4028237 x 10^38
eq-3: IPt4 = X(2^32) + 16,900,000
= (2^128) + 16,900,000
= (256^16)+ 16,900,000
= 3.4028237 x 10^38 + 16,900,000 Host Addresses
eq-4: IPv4 = X(2^32); when X = 1.
FIGURE 5 : 'IPt1'
"The Logically derived Structure of the 'Synthetic' Decimal
Representation of the IPt1 IP Addressing Specification"
'IPt1' Address Pool Size = 2^32 = 256^4
= 4,294,967,296 = 4.294967296 x 10^9
CLASS A
1. A-1, 1 - 128, Subnet Identifier FFF.Y.X.X -/0000:08
- Networks: 128 x (128 x 256^2)
- Host: 128 x 256^2
A-2, 1 - 128, Subnet Identifier FFF.FFF.Y.X -/0000:16
- Networks: 128^2(128 x 256)
- Host: 128 x 256
A-3, 1 - 128, Subnet Identifier FFF.FFF.FFF.Y -/0000:24
- Networks: 128^3 x 128
- Host: 128
A-4, 1 - 128, Subnet Identifier FFF.FFF.FFF.FFF -/0000:32
- Networks: 128^4
- Host: 0
Total Number of Available Network and Host Addresses:
2^7 Networks = 128 x 16,777,216 = 2,147,483,648
Hosts = (128 x 256^2) + (128 x 256) + 128 = 8,421,504
E Terrell Internet Draft [Page 30]
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FIGURE 5 : 'IPt1' - Continued
CLASS B
2. B-1, 129 - 192, Subnet Identifier FFF.Y.X.X -/1000:08
- Networks: 64(256 - 64)(256^2)
- Host: 64 x 256^2
B-2, 129 - 192, Subnet Identifier FFF.FFF.Y.X -/1000:16
- Networks: 64^2(256 - 64) x 256
- Host: 64 x 256
B-3, 129 - 192, Subnet Identifier FFF.FFF.FFF.Y -/1000:24
- Networks:64^3(256 - 64)
- Host: 64
B-4, 129 - 192, Subnet Identifier FFF.FFF.FFF.FFF -/1000:32
- Networks: 64^4
- Host: 0
Total Number of Available Network and Host Addresses:
2^6 Networks = 64 x 16,777,216 = 1,073,741,824
Hosts = (64 x 256^2) + (64 x 256) + 64 = 4,210,752
CLASS C
3. C-1, 193 - 224, Subnet Identifier FFF.Y.X.X -/1100:08
- Networks: 32(256 - 32)(256^2)
- Host: 32 x 256^2
C-2, 193 - 224, Subnet Identifier FFF.FFF.Y.X -/1100:16
- Networks: 32^2(256 - 32) x 256
- Host: 32 x 256
C-3, 193 - 224, Subnet Identifier FFF.FFF.FFF.Y -/1100:24
- Networks: 32^3(256 - 32)
- Host: 32
C-4, 193 - 224, Subnet Identifier FFF.FFF.FFF.FFF -/1100:32
- Networks: 32^4
- Host: 0
Total Number of Available Network and Host Addresses:
2^5 Networks = 32 x 16,777,216 = 536,870,912
Hosts = (32 x 256^2) + (32 x 256) + 32 = 2,105,376
E Terrell Internet Draft [Page 31]
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FIGURE 5 : 'IPt1' - Continued
CLASS D
4. D-1, 225 - 240, Subnet Identifier FFF.Y.X.X -/1110:08
- Networks: 16(256 - 16)(256^2)
- Host: 16 x 256^2
D-2, 225 - 240, Subnet Identifier FFF.FFF.Y.X -/1110:16
- Networks: 16^2(256 - 16) x 256
- Host: 16 x 256
D-3, 225 - 240, Subnet Identifier FFF.FFF.FFF.Y -/1110:24
- Networks: 16^3(256 - 16)
- Host: 16
D-4, 225 - 240, Subnet Identifier FFF.FFF.FFF.FFF -/1110:32
- Networks: 16^4
- Host: 0
Total Number of Available Network and Host Addresses:
2^4 Networks = 16 x 16,777,216 = 268,435,456
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
CLASS E
5. E-1, 241 - 256, Subnet Identifier FFF.Y.X.X -/1111:08
- Networks: 16(256 - 16)(256^2)
- Host: 16 x 256^2
E-2, 241 - 256, Subnet Identifier FFF.FFF.Y.X -/1111:16
- Networks: 16^2(256 - 16) x 256
- Host: 16 x 256
E-3, 241 - 256, Subnet Identifier FFF.FFF.FFF.Y -/1111:24
- Networks: 16^3(256 - 16)
- Host: 16
E-4, 241 - 256, Subnet Identifier FFF.FFF.FFF.FFF -/1111:32
- Networks: 16^4
- Host: 0
Total Number of Available Network and Host Addresses:
2^4 Networks = 16 x 16,777,216 = 268,435,456
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
E Terrell Internet Draft [Page 32]
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Special Note: The simplification of the Network IP Addressing
format into the 'Zone IP', the 'IP Area Code',
and the 'Network IP Address', as provided by the
IPtX Specification, could also REPLACE the format
currently being used by the Telephone Systems all
over the World. In other words, there is an EASY,
'Off-The-Shelf' procedure for DIALING any Telephone
Number defined by the 18 Digit String from the
'IPtX' Specification {See "TELe-RIP" Protocol}:
1. Dial First - Key in the digits representing the 'ZONE IP'
2. Dial Next - Key in an Asterisk " * " the 'End-Start Statement'(:)'
3. Dial Second - Key in the digits representing the 'IP AREA CODE'
4. Dial Next - Key in an Asterisk " * " the 'End-Start Statement'(:)'
5. Dial Third - Key in the All '12' digits of the 'NETWORK IP ADDRESS'
e.g. Direct Trunk-Identifier, and respective Local "ENUM" Dialing:
a. Dial Zone IP: '123:213:121.0.12.3' =
'123 * 213 * 121-000-012-003';
b. Dial IP Area Code: '123:213:121.0.12.3' =
' * 213 * 121-000-012-003';
c. Dial Local '123:213:121.0.12.3' = ' * * ' 121-000-012-003';
Where it is not possible to define the Zone IP,
IP Area Code, or Network IP Address with ' 0 '.
E Terrell Internet Draft [Page 33]
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FIGURE 6 : 'IPt2'
"The Logically derived Structure of the 'Synthetic' Decimal
Representation of the IPt2 IP Addressing Specification"
'IPt2' Address Pool Size = 2^32(256^2) = 256^6
= 4,294,967,296(256^2) = 2.814798 x 10^14
NOTE: IPt2, by FIGURE '5' contains;
' 256^2 ' COPIES of the 'IPt1' Specification
CLASS A
1. A-1, 1 - 128, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.Y.X.X -/0000:08
- Networks: 128 x (128 x 256^2)(256^2)
- Host: 128 x 256^2
A-2, 1 - 128, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.Y.X -/0000:16
- Networks: 128^2(128 x 256)(256^2)
- Host: 128 x 256
A-3, 1 - 128, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.Y -/0000:24
- Networks: 128^3 x 128(256^2)
- Host: 128
A-4, 1 - 128, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.FFF -/0000:32
- Networks: 128^4(256^2)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks 2^7(256^3)(256^2) = (128 x 16,777,216)(256^2)
= 2,147,483,648(256^2)
Hosts = (128 x 256^2) + (128 x 256) + 128 = 8,421,504
E Terrell Internet Draft [Page 34]
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FIGURE 6 : 'IPt2' - Continued
CLASS B
2. B-1, 129 - 192, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.Y.X.X -/1000:08
- Networks: 64(256 - 64)(256^2)(256^2)
- Host: 64 x 256^2
B-2, 129 - 192, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.Y.X -/1000:16
- Networks: 64^2(256 - 64) x 256(256^2)
- Host: 64 x 256
B-3, 129 - 192, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.Y -/1000:24
- Networks: 64^3(256 - 64)(256^2)
- Host: 64
B-4, 129 - 192, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.FFF -/1000:32
- Networks: 64^4(256^2)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks 2^6(256^3)(256^2) = (64 x 16,777,216)(256^2)
= 1,073,741,824(256^2)
Hosts = (64 x 256^2) + (64 x 256) + 64 = 4,210,752
E Terrell Internet Draft [Page 35]
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FIGURE 6 : 'IPt2' - Continued
CLASS C
3. C-1, 193 - 224, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.Y.X.X -/1100:08
- Networks: 32(256 - 32)(256^2)(256^2)
- Host: 32 x 256^2
C-2, 193 - 224, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.Y.X -/1100:16
- Networks: 32^2(256 - 32) x 256(256^2)
- Host: 32 x 256
C-3, 193 - 224, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.Y -/1100:24
- Networks: 32^3(256 - 32)(256^2)
- Host: 32
C-4, 193 - 224, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.FFF -/1100:32
- Networks: 32^4(256^2)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks 2^5(256^3)(256^2) = (32 x 16,777,216)(256^2)
= 536,870,912(256^2)
Hosts = (32 x 256^2) + (32 x 256) + 32 = 2,105,376
E Terrell Internet Draft [Page 36]
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FIGURE 6 : 'IPt2' - Continued
CLASS D
4. D-1, 225 - 240, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.Y.X.X -/1110:08
- Networks: 16(256 - 16)(256^2)(256^2)
- Host: 16 x 256^2
D-2, 225 - 240, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.Y.X -/1110:16
- Networks: 16^2(256 - 16) x 256(256^2)
- Host: 16 x 256
D-3, 225 - 240, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.Y -/1110:24
- Networks: 16^3(256 - 16)(256^2)
- Host: 16
D-4, 225 - 240, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.FFF -/1110:32
- Networks: 16^4(256^2)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks 2^4(256^3)(256^2) = (16 x 16,777,216)(256^2)
= 268,435,456(256^2)
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
E Terrell Internet Draft [Page 37]
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FIGURE 6 : 'IPt2' - Continued
CLASS E
5. E-1, 241 - 256, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.Y.X.X -/1111:08
- Networks: 16(256 - 16)(256^2)(256^2)
- Host: 16 x 256^2
E-2, 241 - 256, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.Y.X -/1111:16
- Networks: 16^2(256 - 16) x 256(256^2)
- Host: 16 x 256
E-3, 241 - 256, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.Y -/1111:24
- Networks: 16^3(256 - 16)(256^2)
- Host: 16
E-4, 241 - 256, Subnet Id - 8 Bit Reserved:8 Bit Reserved:256:256:
FFF.FFF.FFF.FFF -/1111:32
- Networks: 16^4(256^2)
- Host: 0
Total Number of Available Network and Host Addresses:
Networks 2^4(256^3)(256^2) = (16 x 16,777,216)(256^2)
= 268,435,456(256^2)
Hosts = (16 x 256^2) + (16 x 256) + 16 = 1,052,688
E Terrell Internet Draft [Page 38]
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Special Note: In the IPtX Specification any Contiguous String of
ZERO(s) is not a mathematically viable IP Address,
because the IP Address Pool equation, X(X^32),
defines a sequence of counting by successive
additions of '1'. That is, using Zero(s), while not
a problem for the IPtX Specification, it is however,
a problem for IPv6. In other words, the problems
inherent in the IPv6 Specification pertain primarily
to the difficulties arising from the 48 Digit Number
used to represent the Default format of an IP Address.
And while there are Rules which define the use of the
" :: " as the replacement for the Contiguous ZERO(s)
String, because they are not mathematically viable,
the problem is exacerbated. Furthermore, since I have
not found any documentation that specifically defines
how to distinguish between 2 or more Addresses
defining a different number of ZERO(s) in the
Contiguous String, which might occur in the Start,
Middle, or Trailing portion of the Address. Clearly,
the " :: " cannot be used as the solution for the 'Size
Reduction' of an IPv6 Address, or the replacement for a
Contiguous String of ZERO(s), at least, not without
the necessary Rule(s) explaining its use. Nevertheless,
these inadequacies are further compounded by defining
the IP Addressing Format as having a variable length,
which may be greater than 128 Bits, and the "::" as a
compressor of the leading and/or trailing zeros, or as
the replacement for the multiple 16-bit Zero Groups
with a specification that limits its use, number of
occurrences, in an address. And this, needless to say,
defines the gist of the mathematical failings of
every supporting document, including RFC 2373, and
more importantly, the reasons the Chinese developed
the IPv9 Addressing Specification.
E Terrell Internet Draft [Page 39]
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It should have been quite clear from documents expounding the
development of the design for the 'IPtX' Specification that the
"Network Descriptor" provided the means to identify the
"Trunk-Identifier", which defines the IP Address assigned to
the 'TelCo-Xchge or Backbone Routers'. In other words, from
'Table V - Definitions', the "Network Descriptor" allows for the
resolution of the Trunk-Identifier ID and the resolution of the
entire Length of the Network IP Address String. And while the
"CIDR" notation was exploited even further during the creation
of the IPv6 Specification; because the symbol, ' /128 ',
specifies the length for the Bit-Mapped IP Address, which defines
the size of the 128 Bit-Mapped IPv6 Address Space. The "Network
Descriptor" provided the ability to separate, or distinguish
between the addresses assigned to the 'TelCo-Xchge or Backbone
Routers' and the 'Network IP Address'. And this specified the
Length defining the Network IP Address as '32 Bits' in the IPtX
Specification, even if the size of its Address Space was equal to
or greater than the 128 Bit IPv6 Specification.
Nevertheless, this procedure allows the retention of the more
familiar structure defining a Network IP Address, which is similar
to the 'Telephone Number' and defined by the IPv4 Specification.
And clearly, this mathematically clarifies the interpretation of
the IPtX Specification (See Table VII), which is logically derived
from IPv4, by proving that the number of available Addresses in
its IP Address Pool is greater than the IPv6 Specification.
Furthermore, since it was only in the configuration of the Router
where "CIDR" was addressed, "CIDR", as with the "Network
Descriptor" can be automatic, and remain only as the concerns for
the Network Engineer, because its affect lies outside the boundary
of the Network Domain. In other words, IPtX is a more powerful and
cost effective IP Addressing Specification, which allows the
interface of the "Front-End" to mimic or simulate the IPv4
Specification, a 32 Bit-Mapped IP Address, in the Backbone
environment of an unlimited size IP Address Space.
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TABLE VII
+----------------------------------------------------------------+
| |
| IPtX - "Network IP Address" Bit-Mapped Length |
| Specification: ' 32 Bits ' |
| |
| |
| IPt2 - "Trunk-Identifier" = "Reserved":"Reserved":256:256: |
| = 16 Bit-Mapped Address String |
| "Network-Descriptor" = +/0000:16; Range '00 thru 16' |
| |
| |
| IPt4 - "Trunk-Identifier" = |
| 256:256:256:256:256:256:256:256:256:256:256:256: |
| = 96 Bit-Mapped Address String |
| "Network-Descriptor" = +/0000:96; Range '00 thru 96' |
| |
| |
| Given that the first ' 0000 ' defines the '8 Bit' String |
| Identifying: |
| |
| "Trunk-Identifier" : 'Class Range' - A, B, C, D, E - using the |
| ' +/ ' Switch |
| |
| |
| "Network ID" : 'Class Range' - A, B, C, D, E - using the |
| ' -/ ' Switch |
+----------------------------------------------------------------+
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5. Security Considerations
This document, whose only objective was the deliberation of the
final explanation for the development of the IPtX Specification,
which resulted from the Mathematics of Quantification, does not
directly raise any security issues. Hence, there are no issues
that warrant Security Considerations.
E Terrell Internet Draft [Page 42]
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6. IANA Considerations
The complete Anatomy of a IPtX Address String*
+---------------------------------------------------------+
1. 'Router-ID + Trunk-Identifier + Network IP Address*':
Total Address Length - IANA Specifications
2. 'TelCo-Xchge or Backbone Routers' - Router-ID: 'DNS ZONE'
" ID + Trunk-Identifier + ZONE IP + IP AREA CODE "
Total Segment Address Length - IANA Specifications
CIDR Network Descriptor /0000:00
3. 'Trunk-Identifier' - ID: 'DNS ZONE Address Block Specification'
" ID + ZONE IP + IP AREA CODE "
a. 'ZONE IP' - ID ' - Segment Length - IANA Specifications
b. 'IP AREA CODE - ID ' - Segment Length - IANA Specifications
Total Segment Address Length - IANA Specifications
CIDR Network Descriptor +/0000:00
4. 'Network IP Address' - ID: Segment Length - IANA Specifications
CIDR Network Descriptor -/0000:00
E Terrell Internet Draft [Page 43]
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6.1 Special IANA Consideration
While Router Authentication may prove vital for Security
Considerations. However, Address resolution could be accomplished
more easily using a '3 State CIDR Network Descriptor Switch'
identified as; {0, -1, +1}:
a) Router-ID: /0000:00 or
'E' Exponential Operator: /0000:00E00; 00E00 = 00^(00 thru 99)
{e.g. 96E99 = 96^99 Bits ~ (7.9228163 x 10^28)^99 copies of IPt1}
b) Trunk-Identifier: +/0000:00 or
'E' Exponential Operator: +/0000:00E00; 00E00 = 00^(00 thru 99)
{e.g. 32E10 = 32^10 Bits ~ (4,294,967,296)^10 copies of IPt1}
c) Network IP Address: -/0000:00 or
'E' Exponential Operator: -/0000:00E00; 00E00 = 00^(00 thru 99)
d) 'ANSI Trace-Ping-ID: Multi-Conditional Switch
defining Additional Command Statements -
±//0000:00|? and //0000:00|? {Where '|?' = HELP!}
The above considerations represent the conclusions derived from
the foundation of 'RFC(s) 1518 and 1519', which actually define
'Address Segment Routing'. Given that in the Binary System of
counting, sums by the addition of '1's' are from the Right, and
leading Zeros to the Left are insignificant. The conclusions
clearly establish the above mathematical expressions as a viable
representation of the Router's interpretation of an IPtX
'Bit-Mapped' IP Address. That is, the 'CIDR Network Descriptor'
provides the Router's depiction of an IP Address, which only
acknowledges the routing of the Network-ID according to the
structure of the Network's IP Address defined by the Address Class
Range: '±/0000:00E00 and /0000:00E00'. Hence, this is the gist of
an extremely powerful method, 'Address Segment Routing', which
provides the translation of the Network Address defined by the
Schematic representing the IPtX IP Addressing Specification, and
any length of one or more additional Address Segments defining the
total length of the IPtX Bit-Mapped Address.
E Terrell Internet Draft [Page 44]
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In other words, the 'CIDR Network Descriptor', in addition to
defining the mathematical expression of the routed Address, it
also acts as the Address Mask, resolving the Integer, one Bit at
a time, in a process that defines every Address defined by the
Schematic of the IPtX Addressing Specification. And finally,
these conclusions also confirm the necessity of the 48 Bit-Mapped
IP Address (18 digits), as the required identification to
specifically determine the exact location/destination of the
communicating nodes.
Nevertheless, the method of Counting that is defined by
'±/0000:00E00 and /0000:00E00', defines a 'One-to-One'
Correspondence with the Unary Element, ' 1 ', which defines the
Sum of the Elements contained in the Set defining the 'CIDR
Network Descriptor, as the Cardinality representing the count of
the number of elements the Set Contains. Thus, yielding the exact
depiction, from the Sum of the number ' 1's ', this equals the
Number representing the IPtX IP Address. In other words, the Sum
of the Bit Count defined by the '00E00' String is equal to the
Number representing the remaining portion of the IP Address that
is not defined by the Address Class Range, which defines the 8
Bit '0000' Prefix of the IP Address defined by the Network
Descriptor. However, allowing the '00E00.0000' String to be equal
to the method defining 'Exponential Enumeration' would be easier,
because an Exponential Equation could Mask and Un-Mask the Integer
representing the IP Address(s); '±/0000:00E00.0000 and
/0000:00E00.0000'. And this method would also represent an exact
count of the Sum of the ' 1's ', because it equals the one-to-one
relationship that assigns only one Number from the result of,
'2^X', the 'Exponent', to one IP Address. Furthermore, it is also
behooving to note, that since ( ±/ )'0000:00E00.0000' and
( / )'0000:00E00.0000' is Routable, its Function as the 'Network
Descriptor' still remains useful, because it allows for Address
Segment Routing, and retains the original definition of its
Address String Length; '±/0000:00'. In other words, the expansion
of the 'CIDR Network Descriptor' defines a Routable Mathematical
Expression, defining a '2^X : 1' 'Exponential Compression Ratio',
which can be used in either a Static or Dynamic Mode.
Note: The logical expansion of the 'CIDR Network Descriptor'
defines a Routable 'Universal Expression', which is a
Mathematical Expression defined by an 'Exponential
Equation', expressing the value of the result that
uniquely represents the value of the Quantified Sum
of the Component Strings defining the numerical value
of every IP Address defined by the IPtX Specification.
And this, as it will be clearly realized, changes the
calculation for the Bit/Data Transfer Rate.
E Terrell Internet Draft [Page 45]
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In any case, it should by quite clear that the foregoing uniquely
defines the IPtX Specification, a distinct difference from IPv4,
that provides the exact rendering of Binary Enumeration, which is
equal to the sequential incrimination resulting from the summation
of the progressing using ' 1's '. In other words, since the Binary
equivalent of the Unit displacement, given by eq-5, defines the
'Exponential Expression' derived from the Binary Equation defined
by the Mathematics of Quantification, which defines an
incremental progression using the result from the summation of
' 1's '. It defines the result, 2^Q, from the equation as
representing the Quantified Sum of the Binary Expressions defining
the Numerical Displacement of the 8 Bit Segment that defines the
Octet represented in an IP Address {see eq-6 and eq-7}.
eq-5: 2^X = 1; respectively denoting the Binary and Unary Sets
eq-6: 2^X = 8 Bit String = " 1 thru 256 "
eq-7: (2^X) + (2^X) + (2^X) + (2^X) = 2^Q = 2^N,
given that { . } = { + }, then
8 Bit. 8 Bit. 8 Bit. 8 Bit = 32 Bit = 2^Q,
XXX + XXX + XXX + XXX = 2^Q = 00E000.0000...,
2^Q now defines an incremental progression,
using the summation from the additions of
' 1's ', which approaches a Bit displacement
defining an infinite length; see eq-9.
And clearly, given that 2^Q = 00E000.0000..., where 2 = 00 and
Q = E000.0000..., the Masking and Un-Masking procedure for
protocol encapsulation is extremely elementary, because it is a
comparison defined by the laws of addition and subtraction. In
other words, the Sum of any number of the Binary Expressions
equaling the value of the 8 Bit Address Segment defining an Octet
of an IP Address, {where the 00E00.0000 = IPtX IP Address as the
Sum of the Binary Expressions defining the Total Number of Octets
the IP Address contains.) is equal to the value of the Integer
defining an IPtX IP Address. Hence, if there is a difference
between any of the values defining an Octet or their resulting
Sum, 2^Q, it would be determined, confirmed, or verified by the
Translation / Resolution of an IP Address from the Masking or
Un-Masking of the 'Exponential Expression(s)'. And this uniquely
defines, by eq-8, the 'IPtX Mathematical Expression' Routing
Protocol, and the ability of IPtX Specification to define an
Un-Limited IP Address Pool: see 'The Anatomy of the IPtX-MX
Routing Protocol'.
eq-8: 0000:00E000.0000... ; 2^X + 2^X + 2^F + 2^F = 2^Q
2^Q = IP Address value = the Sum of the Octets.
E Terrell Internet Draft [Page 46]
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The Anatomy of the IPtX-MX Routing Protocol
+-------------------------------------------+
The Number of 8 Bit Address Segments - IANA Specifications
0000:00E000.0000... = 2^999.99987654321 IP Addresses = 2^Q
or: Theoretical Number of available IP Addresses =
2^2(999.99987654321) copies of IPt1 = [('/0000:00') x ('+/0000:00')]
1. ' 0000: ' ID: 8 Bit Address Segment - Address Class Range
Total Segment IP Address Length - IANA Specifications
2. ' 00 ' ID: 4 Bit Address Segment - The Base 2, in 2^Q
Total Segment Address Length - IANA Specifications
3. ' E ' ID: 4 Bit Address Segment - Binary Exponential Operator
Total Segment Address Length - IANA Specifications
4. ' 000.0000...' ID: 48 Bit Address Segment - 2 Part Exponent Q
a.' 000 ' ID: 3-4 Bit Address Segment - Integer Part of Exponent
Segment Length - IANA Specifications
b.'.0000...' ID: 36 Bit Address Segment - Decimal Part of Exponent
"Payload Capacity" Segment Length - IANA Specifications
Total Segment Address Length - IANA Specifications
E Terrell Internet Draft [Page 47]
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5. 'Router-ID + Trunk-Identifier + Network IP Address*
0000:00E000.0000... + 0000:00E000.0000... + 0000:00E000.0000...
3(8 + 20 + 36) = 3(64) Bit Strings
a. 0000:00E000.0000... /0000:00 - Masked Routable Router-ID
b. 0000:00E000.0000... +/0000:00 - Masked Routable Trunk-Identifier
c. 0000:00E000.0000... -/0000:00 - Masked Routable Network IP Address
Total Address Length - IANA Specifications
eq-9: 0000:00E000.0000... ; The Reality of "2^X : 1"
Compression Ratio of the IPtX-MX Protocol
a. (2^X)v1 + (2^X)v2 + (2^F)v3 + (2^X)v4 = 2^Q
b. (2^X)v1 + (2^X)v2 + (2^F)v3 + (2^X)v4 + (2^F)v5 + (2^F)v6 = 2^Q
c. (2^X)v1 + (2^X)v2 + . . . + (2^F)vN = 2^Q
Given that 2^X defines Binary Enumeration, as the
result from an Exponential Equation that defines
the Unary incremental progression of addition,
or counting, using ' 1's '.
Note: The comparable analogy the Computing Power defining
the payload capacity of the '00.E000.0000... String'
is equivalent to having 2^999.99987654321 3-State
Logical Transistor Switches in the Core of '1' CPU.
And this, should be duly noted, is equivalent to
the ability of programming every Transistor, or
allowing every Transistor to become the CPU. However,
since every 4 Bit segment can equal any number in the
range of '0 thru 16', the '00.E000.0000... String'
Theoretical Number of available IP Addresses now equals:
E Terrell Internet Draft [Page 48]
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[('/0000:00') x ('+/0000:00')] = 16^2(161,616) = (2^4)^2(161,616) =
2^2(646,464) = 2^X = 2^1,292,928.99987654321 copies of IPt1
In which case, this means; A 64 Bit Address String can
define the Number or Data Stream that represents the
Sum of the incremental progressions, using '1's ', which
equals the count of a 2^646,464 Bit-Mapped displacement.
And if the Address total defined by IPt1; 4,294,967,296,
equaled a book containing 67,108,864 64 Bit words, then
the '00.E000.0000... ' 64 Bit Address Block defines
a Bit-Mapped Address String equaling approximately
2^646,464 Books; when a book contains approximately
50,000 pages.
+------------------------------------------------------------------+
+ [The Genetic Equation representing the Formula for Life? ...Yep.]+
|Encryption and Decryption - The Binary Enumeration Algorithm - 2^N|
+------------------------------------------------------------------+
1) X(2^X) - Encryption and Decryption Key
a. X - Counts the Number of Octets - 00 thru 2^X
b. (2^8) - Encodes and Decodes Bit-Map Octet String
2) 00.E000.0000... - Binary Enumeration Compression Algorithm
a. Encryption of the Integer defines a Unique Bit-Map Length -
e.g. - 123.123.123.123 = 1111011.1111011.1111011.1111011 = 2^Q
b. Every Integer has a Unique '00.E000.0000...' Translation
3) ' + ' and the ' . ' Symbols: "Put it Together & Take it Away"
a. String Assembler - ' + ' "Put it Together" -
e.g. - '123 + 123' = '123.123' = '123123' = 2^Q
b. String Delimiter - ' . ' "Take it Away" -
e.g. - '123123' = '123.123' = '123 + 123' = 2^Q
E Terrell Internet Draft [Page 49]
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In other words, Binary Enumeration, the method of incrimination
using ' 1 ' that defines the ' 2^X : 1 ' Ratio, sustains a
practical limit, which is defined by the current technology.
However, with the current technology it might be easier if the
Exponent of the ' 2^X : 1 ' Ratio defined a Payload Capacity of
256 Bits, or the equation, 2^256, which defines a Payload
capacity equaling 256 copies of a 50,000 page Book. And this,
it should be reasoned, with the appropriate upgrades would allow
the Ratio defining the current Data Transmission Rates, and a
host of related technological products, to obtain a performance
increase by that might be greater than a ' 4 : 1 ' Ratio.
E Terrell Internet Draft [Page 50]
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6.2 Special IANA Consideration
- 6.2.1 - Closing Argument
The proof of the mathematical validity for the Ratio defining
the ' 2^X : 1 ' relationship between Binary and Unary counting
is given by:
Since; 2^0 = 1, and (2^0) + (2^0) = 1 + 1 is True,
then; If 1 + 1 = 2, 1 + 2 = 3, ..., and 1 + N = IvN, is True,
there is a relationship; defining every 'X', in '2^X',
such that; for every value that the element 'Q' defines,
also defines a unique element in I, the Set of Integers,
then; '2^X' also defines an element of the Set of Integers,
given that; for every '2^X' of the Set I, '2^X = Q',
and; If 'X' defines an Element of the Set of Integers and an
Element of the Set of Real Number,
then; 'X' is Greater Than, or Equal To 'NvN + 1' and
'NvN + 1.000...NvN + 1'.
Hence: The Binary Set defines an Equation, '2^X', that
equals the count defining the Sum of the incremental
progression resulting from the Addition of '1's',
which is equal to the progressive counting sequence
defined by the Unary Set.
This concludes the design specification(s) for the IPtX
Addressing Protocol Family, with the implementation of the
E Terrell Internet Draft [Page 51]
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logically derived 'Intelligent Quantum Worm', which mimics the
'Payload Carrying Capacity' of the 'Instruction Set' carried by
a Cell of DNA. In other words, this discovery represents the
capability of compressing a number of any length (Compression of
the Set, Q = {1,2,3,4,...,N}, having a count of 'N' Members in
it's Set, into Q = {1,2,3,4,...,N} = 1, by Nesting Encryptions
of the Exponential Translation representing the exact Numerical
arrangement of the members of the Set, Q. And more importantly,
this discovery, when the correct Mathematical interpretation of
the encoding for the Binary System is used, defines the 64 Bit
Address as the Mask of the 'Intelligent Quantum Worm', the
'IPtX-MX Universal Routing/Routed Protocol' Specification,
which has a 'Theoretical Payload Carrying Capacity'
(Data Stream 'Bit-Count' Capacity) equal to the Bit size
specification defining a Backbone Environment having an
unlimited size 'Bit-Mapped' Address Space.
Polymorphing the 'Intelligent Quantum Worm' Protocol
+------------------------------------------------------+
"The Biological Depiction of the 3 Divisions of a Cell
and the Exponential Compression Algorithm is the Nucleus"
+---------------------------------------------------------+
Calibrating the Unit Bit Size to the measurement of the Displacement
Frequency Characterizing any one or more Unit measures from the
Frequencies of the 'Electro-Magnetic Spectrum of the Nucleus of an
Atom.
+--------------------------------------------------------------------+
The Polymorphing "Metamorphosis" Encryption Compression Algorithm
1. ' 0000:00E000.0000... ' becomes;
"Metamorphosis" Encryption Compression Algorithm;
2. ' 0000:00.0000...E000 '
And this can be programmed to imitate Virus or Bacteria
Prorogation, which can be Transformed, or adapt...,
because this Algorithm provides the Binary representation,
translation, or interpretation of every Element contained
in the Set of Real Numbers, including the Rational and the
Irrational numbers.
Which means, at some Point:
3. 0000:00.0000...E000 = 0000:00E000.0000...
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In other words, the Binary Equation in the Ratio, '2^X : 1',
actually defines the Unary Process of successive Additions of
' 1 ', which the counting by 1, represents every Numeral.
However, the benefits of the Exponential Algorithm is that,
regardless of the Numeral's length, it requires only 64 Bits
to represent the count of the Integer depicting the Numeral.
Nevertheless, the pointed fact is that, the mathematical
translation of the foregoing conclusions in terms of the number
of available IP Addresses, dramatically increases. In other
words, the IP Address Pool representing the 64 Bit IP Address
of the IPt2 Address Space, which is defined by the IPtX
Specification, more closely approximates:
16 Prefix Addresses
99,987,654,321 Addresses in each Prefix Address Set
And this means, there are;
2^646,464(16 x 99,987,654,321) Encryption Keys, or;
because this defines the Number of Encryption Keys for each
Address in the Address Pool given by;
" 0000:00E000.0000... "
then the Total Number of Addresses in the IPt2 Specification equals:
(2^(646,464.99987654321) x 2^646,464 (16 x 99,987,654,321) = 2^N
Or, The 'Payload Capacity' of ONE
Intelligent Quantum Worm - Payload Capacity =
2^646,464 X (16 x 99,987,654,321) Bits,
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Or, The Number of Copies of the IPt1 Specification;
2^(646,464.99987654321) x 2^(646,464) x (16 x 99,987,654,321)
Or; each Address Segment of the IP Address,
'Router-ID + Trunk-Identifier + Network IP Address**,
which is defined by;
0000:00E000.0000... + 0000:00E000.0000... + 0000:00E000.0000...,
and equals;
2^2(646,464) = 2^X = 2^(1,292,928.99987654321) copies of IPt1
the 'Polymorphing Intelligent Quantum Worm Protocol Data Compression
Engine', now defines each Address Segment with having either an
individual Encryption Algorithm, or a Data Compression Algorithm(s);
e.g. One Address Segment defines;
(0000:00E000.0000...) X (0000:00.0000...E000)
or each Address Segment of the Intelligent Quantum Worm's
Payload Capacity would equal;
2^(646,464) X (16 x 99,987,654,321) Bits.
Given that each Segment's Address Pool Capacity equals;
2^(646,464.99987654321) = (0000:00E000.0000...) = 2^X = 2^N
Addresses.
E Terrell Internet Draft [Page 54]
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6.2 Special IANA Consideration
- 6.2.2 - Security
Even still, possible interpretation(s) notwithstanding,
mathematically speaking however. The (" 00.0000...E000 ") String
can only define the "Payload Carrying Capacity" of a Data
Compression Engine. In which case, the Encryption Coding Strings
can be included and defined as an integral part of the Data Stream
Code, which has a 'Bit-Count Length' determined by the Scaleable
'Payload Capacity' of the 'Polymorphing Intelligent Quantum Worm
Protocol Data Compression Engine' (P-IQWP-DCE). Nevertheless,
this clarification completes the design specification for the
'Intelligent Quantum Worm Protocol', founded upon the logical
derivation of the Binary System of Enumeration from the Mathematics
of Quantification; it finalizes the unique design structure of the
IPtX Protocol 'Family' Specification.
And this is true since;
' 00.0000...E000 ' = 2^X = 2^N = ' 00E000.0000... *';
Noting more specifically that the Set of Points at which these Sets
are equal, is Finite. Hence, the number of occurrences in which
these Sets are equal is defined by;
'2^X = 2^N ':
"The Special Case defining the Distributive Laws representing the
Binary and the Unary Sets*". Furthermore, there is a broader
interpretation of the " P-IQWP-DCE " Binary Algorithm, in which the
Ratio, {2^X : 1} defining this engine represents the Probability or
Likelihood of the occurrence of a 'Security Event' vs. "Quality of
Service/Product" to prevent it, because 'Security Protection Coding'
is packaged in the "Payload": with an excellent Virus Protection
Software, e.g., - Consumes Limited or Balanced Security Code to
Message Space Ratio - Possible Number of Virus Combinations vs.
Anti-Virus Combinations ; This is an Absolute Protocol Protection
Environment Ratio defining the " P-IQWP-DCE " Space -
'2^X = 2^N ';
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Balance is Achievable or the Time required to perform a 'Security
Event' could be of such a duration, it would seem infinite! In
which case, the {2^X : 1} Ratio represents the scale of
comparison, providing the odds of determining the Probability of
preventing a 'Security Event', when using the currently available
Security Safe Guards. And more importantly - This Ratio {2^X : 1}
actually depicts a 'Fully Cognizance Autonomous Artificial
Intelligence', a True Binary Coding Environment, defining a
logical mathematical foundation derived from the Laws of Set
Theory and the Mathematics of Quantification. In other words,
the spectrum of possibilities defined by '2X' is unlimited;
since '2^X' represents the Binary equation defining the
incremental progression by successive additions of '1', and if
2^X is an Element of the Real Number Set, then
'2^X = 3^X = 4^X = 5^X = N^X + 1'.
In other words, since nesting is inherently defined, the 'DCE's'
Payload could define a series of Binary Equations representing a
Nested or Encapsulated Data Stream Transmission.
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6.2 Special IANA Consideration
- 6.2.3 - Summary
In summary, the conclusions from Mathematics of Quantification that
established a true Binary Environment, produced a Revolutionary
method of Coding, using the Exponential Expression '2^X',
correlating the Mathematical Language of the Binary System,
defining a Unary progression, resulting in the unique logical
design of the IPtX Protocol Family Addressing Specification.
Hence, the final imperative is to display "IPt2's" remaining 64
Bit-Mapped Protocol Specifications design for the 'Intelligent
Quantum Worm Protocol', all of which measure a different size
Address Pool correlating with the Address Class Specification
of IPv4 - Furthermore, the additional benefits this expansion
yields, magnifies the potential of the IPtX-MX Universal Protocol.
In other words, there are 5 Sub-Level Divisions of the ' IPt2 '
Specification, and each contains an 'Address Class Sub-Division';
Set = {A, B, C, D, E}:
+ -- TABLE VIII -- +
- Class A Address Pool Allocation -
1) (0000:0E0000.0000...), or (0000:0.0000...E0000)
- Class B Address Pool Allocation -
2) 00.0000...E000 ' = 2^X = 2^N = ' 00E000.0000... *
- Class C Address Pool Allocation -
3) (0000:000E00.0000...), or (0000:000.0000...E00)
- Class D Address Pool Allocation -
4) (0000:0000E0.0000...) , or (0000:0000.0000...E0)
- Class E Address Pool Allocation -
5) (0000:00000E.0000...), or (0000:.0000...E00000)
E Terrell Internet Draft [Page 57]
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Note... Because the Mathematical relationship between the ' 4 '
Unit structure of an IP Address defined in the IPv4
Specification represents the identical, ' 4 ' Unit
Pattern defining the divisional structure for the
'DCE' Unit defining the 'IPtX-MX Universal Protocol'
in the IPtX Specification - The Address Pool Allocation
table defining the Address Class Distribution in Table
VIII actually represents the definition of the '5'
Sub-Divisions - 'Address Scaling Division'; a
'Mathematical Scaling Communication Protocol' that
defines a procedure matching the specifications related
to the parameters defining 'Data Transmission Performance
Rates' of the Communicating Nodes - by Table VIX;
+ ---- TABLE VIX ---- +
1) IPt2-a - Class A Address Pool Allocation -
1.1) (0000:0E0000.0000...), or (0000:0.0000...E0000)
Address Class Sub-division - Set = {A, B, C, D, E}
2) IPt2-b - Class B Address Pool Allocation -
2.1) 00.0000...E000 ' = 2^X = 2^N = ' 00E000.0000...*
Address Class Sub-division - Set = {A, B, C, D, E}
3) IPt2-c - Class C Address Pool Allocation -
3.1) (0000:000E00.0000...), or (0000:000.0000...E00)
Address Class Sub-division - Set = {A, B, C, D, E}
4) IPt2-d - Class D Address Pool Allocation -
4.1) (0000:0000E0.0000...) , or (0000:0000.0000...E0)
Address Class Sub-division - Set = {A, B, C, D, E}
5) IPt2-e - Class E Address Pool Allocation -
5.1) (0000:00000E.0000...), or (0000:.0000...E00000)
Address Class Sub-division - Set = {A, B, C, D, E}
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[If X^X = 2^X, then X = 2^1/X, when 1/X = ' .00000... ':
and this is valid because each Address Class Allocation
will contain a different number of Binary, '2^F',
definitions.]
In other words, the IPtX Addressing Protocol "Family" is defined
by a mathematical foundation that defines an incremental
progression using successive additions of '1', which also defines
the sequence of counting defined by the Unary set. In which case,
if the mathematical laws defining the relationships for the Address
patterns of the IPtX Specification are mathematically consistent,
then Table VIX defines a mathematical expansion for every Address
Class Specification defined by the IPtX Protocol "Family".
The Additional benefits from the IPtX Mathematical Foundation
+--------------------------------------------------------------+
1) Data Transmission Rates = 'DCE' Unit Classification
2) 'Performance' & 'Dimensional Design' = 'DCE' Unit Classification
3) Data Transmission Communication Rates = 'DCE' Unit Classification
4) Data Transmission Rates Coefficient = ' X '
5) Data Transmission Rate(s) Equation = 'X(2^X) = 2^X = 2^N = X^X'
6) Control Data Transmission Rates / Matching the Node(s) Rate(s)
7) 'DCE' Unit Classification determines Bit Transmission Scale
8) 'DCE' Unit Classification = 'Storage Capacity Scale' Unit
9) 'DCE' Unit = "Hardware Compatibility Scale" Classification;
- Matching Data Transmission Communication Rates
- 'HEX' Numbering System Replacement
- Matching Binary Numbering System Scale = X(2^X)
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10) 'DCE' Unit Classification = "Calibrating the Encoding of Code"
a) Defines New Binary Coding Operator for Software Construction
and Design.
b) Defines New Binary Definition for Instruction Set and Scale
for CPU Design.
c) Defines New Data Communication Hardware Orientation
Connectivity Association Specification - Eliminating Device
Drivers, USB, ATA, SCSI, etc, and a host of additional
Hardware Control Protocols.
d) Scaleable 'DCE' Unit Defines a New Host IP Addressing
Specification, which provides a functional use, by TABLE VIX,
for the IPtX-MX Universal Protocol, that would allow Host
IP Address Activation for a Direct Internet Connection
- The Activation of every Host defined in the Overlay of
IPtX Specification {See TABLE VIX} - Adding a Host
designation function to the CDIR Network Descriptor, which
assigns the DCE Unit Protocol Specification to the trailing
end Switch; 'h': e.g. ' /0000:00-h ' - and this allows every
Network and Host IP Address to have a unique Identification
in the IPtX Specification.
e) Binary Encoding Conversion example; '1111 = 'DCE' Unit' = 2^X,
or ' 8 ' = 111 = 'DCE' Unit' = 2^X = 2^3 '; the Benefits are
easily realized when the Conversion represents a large Number.
Note: Assigning DCE Unit Protocol(s) -
Host Address Activation - IANA Specifications
CIDR Network Descriptor Host Activation Switch -
Host Switch 'h' - ' /0000:00-h ' - IANA Specifications
e.g. the respective reduction and expansion of the 'DCE' Unit:
a) IPt1 Specification - 4 Bit Address Class ID: 2 Bits Base in 2^X.
- 4 Bit 'E'- Exponent - Exponent Parts:
- 2 Bit Integer. - 20 Bit Decimal String - 32 Bit Address
- 0000:00E00.00... - 32Bit Intelligent Quantum Worm
b) IPt4 Specification - 16 Bit Address Class ID: 8 Bit Base in 2^X.
- 4 Bit 'E' Exponent - Exponent Parts:
- 28 Bit Integer. - 72 Bit Decimal String - 128 Bit Address
- 00.00:0000E0000v28.000...v72 - 128 Bit Intelligent Quantum Worm
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Nevertheless, the Intelligent Quantum Worm Technology maintains
a scaleable range that defines 5 Address Class Specifications,
which represent a different and independent copy of the IPt1
Specification. And this defines the Address Pool of the 64 Bit
IPt2 Specification, with a capacity equal to 5 copies of IPt1;
or 5(2^32) = 5(4,294,967,296) = 2.147836 x 10^10;
or "2.147836 x 10^10 'Intelligent Quantum Worms'"
that can all share or be assigned to service
4,294,967,296 IP Addresses. That is, this defines
a { 5 : 1 } Ratio, a mathematical relationship
sustained throughout the IPtX Specification, which
defines approximately 5 different Worm Configurations
for every IP Address Class defined by the IPtX
Addressing Protocol Family Specification.
Note: This defines the Theoretical Address Pool Capacity of
the IPt2 Specification as being equal to:
(0000:000E00.0000...), or (0000:000.0000...E00)
'Router-ID + Trunk-Identifier + Network IP Address*
0000:00E000.0000... + 0000:00E000.0000... + 0000:00E000.0000...
Router-ID = 2(2.147836 x 10^10)(2^646,464) x (4,294,967,296)
+
Trunk-Identifier = 2(2.147836 x 10^10)(2^646,464) x (4,294,967,296)
+
Network IP Address = 2(2.147836 x 10^10)(2^646,464) x (4,294,967,296)
= 12[(2.147836 x 10^10)(2^646,464)] x (1.2884902 x 10^10)
approximately available IP Addresses.
This is a good approximation, because this value
(2^646,464) changes, Higher to Lower, values defining
5 Categories of the IPt2 Specification.
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In other words, this essentially provides the 'Intelligent
Quantum Worm' Protocol with a Scalable "Payload Capacity",
which defines a 3-D Spatial Distortion that mimics a Tunneling
Effect. In which case, perhaps the "IPtX-MX Universal Protocol"
should rightfully be called:
An "Intelligent Quantum Tunneling Worm".
Nevertheless, the ability to program or construct a 3-D Space,
implies the possibility that today's 'Bit-Mapped' Specification
associates a Bit with a displacement equal to an extremely large
Electron Surface Area, one that encompasses the measurement of an
extremely large Pool (approximately 2^646,464) or Group of
Electrons. In other words, the "Intelligent Quantum Tunneling
Worm" Protocol, in such an environment, would define the Unit
Bit as the minimum excitation energy required to displace an
Electron One Electron-Mass Displacement Unit [6]. And then,
if it's A.I., there is the possibility that it could morph
itself, acquiring the specifications to accommodate a 3-D
Spatial Environment. - The Illusion by Shading, rendering
any picture or video with a 3-D effect when displayed.
Note: The actual difference the Theory of the IPtX
Specification presents, is defined by the
difference between Linear and Non-Linear
Coding, or the choice between Encoding the
Bit-Map of the Data Stream or Encoding the
Bit-Map of the Equation for the Data Stream.
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Nevertheless, while the foregoing proof are confirmed by the
conclusions from the proof of "Fermat's Last Theorem": However,
a more thorough understanding of the results from the successive
additions of '1', and the Basic Theory of Mathematics, which define
Sequential Counting is required to understand the error in the
current definition of Infinity; where 1/0 = INFINITY. And how is
it possible to define an Infinitely Large Address Pool to the
IPtX Specification.
The proof;
First, accepting that 1/0 = INFINITY, is not true, since Division
is defined [3] as Subtraction, then the results from the
continuous operation defined by eq-a, is pointless, because the
result from this equation defines the REMAINER, and if the
difference between the Remainder and the Quotient equals Zero,
then the solution, by eq-b, of 1/0, is equal to Zero.
eq-a. 1 - 0 = 1 - 0 = ... = (1 - 0)vN = 1
eq-b. 1 / 0 = 1 - 1 = 0
And if it can be said that the relationship between the
Unary Set and the Binary defines a { 1 : 11 } Ratio, where
Cardinatility representing this Ratio, given by eq-c, is True.
eq-c. ' 1 = 2 ' - Unary Set = {1}, Binary Set = {11}
"Given that: 11 = 1 + 1 = 2"
Then the Definition of a Prime Number is Given By:'
eq-d. '1 = 2' - 'Prime Numbers'
A 'Prime Number' or 'Prime Integer', is a positive
integer, 'p Greater Than or Equal to 1', that has
no positive integer divisors other than itself, 'p',
and '1'.
In which case, from the definition of a Prime Number, it can be
concluded that if every Number except '1', is defined as the
Progressive Additions of '1', then "1" defines the Absolute
Number, which is equal to the Cardinal Number that defines the
Universal Multiplicative Identity Element, representing every
Item defining itself [2].
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Clearly, the Modern Numbering System evolve defining the Zero
distinction as the Multiplicative Coefficient defining the
Count of the Members in the Set of ' 1's ' containing 10
Elements. Nevertheless, Nature's Mathematical System defines
the Binary pair {0, 1}, as the symbols to be used for numerology,
which ultimately refined into the more mathematical symbolic
numerical representation used today.
In other words, since '1' is the absolute Numeral, and the Binary
and Unary Sets must, if they are equal and enumerate to infinity,
map equally, in a One-to-One Correspondence with the Real Number
Set, which is counted using successive additions of '1'.
Then the Ratio defining the relationship between the Binary and
the Unary Sets, and represented in the mathematical expression
defining eq-c, since any One-to-One defines a sequential count
defined by the Unary Set as the successive additions using 1's,
also defines 2 Infinities.
eq-c. ' 1 = 2 '
Unary Set = {1} = Infinity = Binary Set = {11} = Infinity
Furthermore, since Infinity is not enumerable, then Infinity
must define a Prime Number, because only the mathematical
operations involving 'ITSELF' and '1' are defined.
Hence, "Given that: 11 = 1 + 1 = 2", and since eq-c is true,
then by eq-e, we have;
eq-e. 'Infinity' = (Infinity + Infinity) = 'Infinity'
And from eq-d, since multiplication is equal to the quantified
sum of addition, we have by eq-f;
eq-f. 'Infinity' = (Infinity + Infinity) = Infinities,
(Infinity + Infinity) = 'Infinity'
Therefore, since eq-d, " 1 = 2 - Prime Numbers ", is true, then;
Infinity = Infinity
E Terrell Internet Draft [Page 64]
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And this, since division is the quantified difference of the
repeated subtractions performed on a constant, further implies;
Infinity/Infinity = ' 1 ' and (Infinity - Infinity) = ' 0 '
Nevertheless, since the foregoing equations defines the
mathematical operations involving Infinity, and since these
operations also defines the enumeration of the Elements defining
the respective members contained in the Binary and Unary Sets.
Then the Elements these Set respectively contain, each
enumerate an individual count using successive additions of '1'
in a One-to-One Correspondence, to reach an Infinite Count of
the Members each Set contains.
In other words, by definition [3], since the
Unary Set = {1},
and the
Binary Set = {0, 1}
Then Infinity is the definition of 2 Sets, which defines;
The Binary Set defines; 1 either followed by an Infinite Zero
String, or a Decimal Point followed by an Infinite Zero String
terminated with a 1.
1) A '1' followed by an Infinite String of Zeros
2) 1 + 0vINFINITY...00000000000000000000000000000000000000.0
3) A '1' proceeded by an Infinite String of Zeros
4) 0.00000000000000000000000000000000000000...0vINFINITY + 1
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The Unary Set defines an Infinite String of ' 1's ', either before
or after the Decimal Point.
5) A '1' followed by an Infinite String of '1's'
6) 1 + 1vINFINITY...1111111111111111111111111111111111111.0
7) A '1' proceeded by an Infinite String of '1's'
8) 0.1111111111111111111111111111111111111...1vINFINITY + 1
Note: Both examples define every element contained in the Set
of Real Numbers. And more importantly, if the Infinite
Zero String is countable, then succeeding or following
the Zero String is also countable... Also, this proof
can be construed as equating the Count of the '1's' in
the Unary Set with the Zeros, and the '1' (occurring at
a Count one unit beyond the Infinite Zero String) in
the Binary Set - where Infinity defines; "Forever Plus
'1' " - Forever Plus '1' = ' 1 + Infinity ' [3].
"Intelligent Quantum Tunneling Worm"
+-------------------------------------------------------------+
Base of Exponent
Address Class | Decimal Part of Exponent
\ v |
Infinity: Infinity E Infinity .Infinity
/ \
/ Integer Part of Exponent
Exponential Operator
+-------------------------------------------------------------+
FIGURE 7
"Current Binary Translation"
'Showing examples of the Concept of "Footprint" Size Reduction'
32 + 32 = 64 = 2^X + 2^X = 2^5 + 2^5 = 8^2 = 2^6
32 Bit String + 32 Bit String = 64 Bit String
which means; - 32 Bit String + 32 Bit String = 2^6,
and - 32 Bit String = 2^5
' e.g. ' a 32 Bit String =
" 1011100110000100111111100010101011000111000111000111000111000111 "
= 32 Bit String = ' 11111111111111111111111111111111 ' = 2^5
32 Bit String = 2^5 = '2E5' = 111111111 '9 Bit String Displacement'
= 32 Bit String = ' INTEGER ' = 2^5
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---------------------------------------------------------------------
[Special NOTE: Possible Concerns of IANA, IESG, and IETF - 'How Does
the IPtX / IPtX-MX Protocol comply with the Octet Rule?' Noting
specifically that, IPv4 Bit-Maps to the current Backbone, and the
proposed structure for the IPv6 Backbone adds another difference.]
The Difference between Binary & Unary Systems of Counting
"Multiplication is the Quantified Sum of Addition"
1. 2. 3.
Binary Binary & Unary Unary
Representation for Counting Representation for
Counting is Multiplication Counting is Addition
+--------------------+------------------------+----------------------+
0^X = 0 | 0 | 0+0 = 0
| |
1. 2^0 = 1 | 00 = 1 | 1 = 1
| |
2. 2^1 = 2 | 01 = 11 | 1+1 = 2
| |
3. 2^F = 3 | 10 = 111 | 1+1+1 = 3
| |
4. 2^2 = 4 | 11 = 1111 | 1+1+1+1 = 4
| |
5. 2^F = 5 | 100 = 11111 | 1+1+1+1+1 = 5
| |
6. 2^F = 6 | 101 = 111111 | 1+1+1+1+1+1 = 6
| |
7. 2^F = 7 | 110 = 1111111 | 1+1+1+1+1+1+1 = 7
| |
8. 2^3 = 8 | 111 = 11111111 | 1+1+1+1+1+1+1+1 = 8
: | : | :
: | : | :
16. 2^4 = 16 |1111 = 1111111111111111| 16 = 1+1+1+1+1+1+1+1
| | +1+1+1+1+1+1+1+1
+--------------------+------------------------+----------------------+
Clearly, since Nature's method of Counting, just as in Particle
Physics, and Electronics, uses the Base 2 in Exponential
Enumeration - I wonder; 'How else could a Binary Pair be Counted?'
In other words, only SOFTWARE (Station or Node Location) can
represent or define the ZERO Concept, because a Zero Signal cannot
[true for the Binary as well as the Unary Systems] be Transmitted
Electronically [ 0 = EX = 0EX; Or if, 'X = 0', then 0 = 0E0 = E, as
in; 0000:00E0000.0000... = 256:00E0000.0000... = '256: E (+ Padding
to the Bit-Mapped Specification)...' ]. Hence, when an Electronic
Signal represents Binary Zero, '00' (where 2^0 = 2E0 = ' 1 ' =
'00'); it has a value equal to the Unary Set, or '1'.
E Terrell Internet Draft [Page 67]
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Exponential System
Binary System Zero of Counting
--------------------+-----------------+-----------------------
No Definition 0 0^X = 0 = 0EX
1. 00 = aa No Definition 2^0 = 1 = 2E0
2. 01 = ab No Definition 2^1 = 2 = 2E1
3. 10 = ba No Definition 2^F = 3 = 2EF
4. 11 = bb No Definition 2^2 = 4 = 2E2
: : :
: : :
8. 111 = bbb No Definition 2^3 = 8 = 2E3
9. 1000 = baaa No Definition 2^F = 9 = 2EF
10. 1001 = baab No Definition 2^F = 10 = 2EF
[Given that: E = Exponential Operator; F = Variable Irrational Number;
and X = Any Variable defined as a Member of the Real Number Set]
IPt2 vs IPv6 Protocol
IPv6 IP Addressing Specification;
= 128 Bit-Mapped Displacement
= [ 11111111.11111111.11111111.11111111.11111111.11111111.
11111111.11111111.11111111.11111111.11111111.11111111.
11111111.11111111.11111111.11111111 ]
= 2^128 ~ 3.403 x 10^38
= 2^128 ~ 340,282,366,920,938,463,463,374,607,431,768,211,456
= Total Number of Available Addresses in the IPv6 Specification
= A 48 Digit Number = 128-bits = 16 Octets
- More typically, the IPv6 addresses are written as eight groups
of four hexadecimal digits; e.g.:
= 2001:0db8:85a3:08d3:1319:8a2e:0370:7334 - 'valid IPv6 address'
= [ 11111010001:110110111000:1000010110100011:100011010011:
10100100111:1000101000101110:101110010:1110010100110 ]
[Note: Just Imagine the difficulty trying to Configure, or
Troubleshoot a 7,000 Node Network using 'valid IPv6 addresses']
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CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
Now, retaining the Octet Rules, IPt2 / IPt2-MX represents;
IPt2 IP Addressing Specification;
64-Bit length = 64 Bit-Mapped Displacement
= [ 11111111.11111111.11111111.11111111.
11111111.11111111.11111111.11111111.]
= [11111111 ( 8 Bit Prefix ): = 2^8
11 ( 2 Bit Base ) = 2^2
11111111 ( E = Exponential Operator - 8 Bits ) = 2^8
111111111111111111111111111111 ( Exponent - 30 Bits ) = 2^30
.1111111111111111 ( Decimal String Accuracy - 16 Bits ) = 2^16]
= 0000:2EX.000 = XXX:2EX.000 = 256:4^1,073,741,824.65536
= XXX:2EX.000 = 256(4^1,073,741,824).65536
= XXX:2EX.000 = 256(2^2,147,483,648).65536
= Total Number of Available Addresses in the IPt2 Specification
= XXX:2EX = 256(2^2,147,483,648) = 2^2,147,483,656 IP Addresses
- Or - This translates into a Number representing;
2,147,483,656 Bit-Mapped Length
- Or - A Number containing;
268,435,457 Octets
805,306,371 Digits
And if you will take note; This represents a Number so Large,
No Computer TODAY, can determine or calculate its actual value -
64 Bit-Mapped Displacement = 0000:00E0000.0000...
28 "Or" 30
8 Bit Prefix Bit Exponent
\ 2 "Or" 4 /
\ Bit Base /
\ | /
0000 : 00 E 0000 . 0000...
| \
8 Bit Exponential Operator \
\
16 Bit Exponential Decimal String
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- The 'DCE UNIT'; 4 BIT BASE, 2^4 = 4EX = 16EX -
256:16 E 28 Bits .XXX... = 0000:00E0000.0000...
256:16 E 268,435,456 . XXX... = 256(16^268,435,456) . XXX...
256(16^268,435,456).XXX... = 256(2^4(268,435,456) . XXX...
256(2^4(268,435,456).XXX... = 256(2^1,073,741,824) .XXX...
And a Bit-Mapped Displacement of 1,073,741,824 Bits,
contains 134,217,728 Octets -
134,217,728 Octets represents a Number
Approximately ( 3 x 134,217,728 )
402,653,184 Digit Number
256(402,653,184) = 103,079,215,104 Digit Number
- Or -
- The 'DCE UNIT'; 2 BIT BASE, 2^2 = 2EX = 4EX -
256:4 E 30 Bits .XXX... = 0000:00E0000.0000...
256(4^1,073,741,824).XXX... = 256(2^2(1,073,741,824) . XXX...
256(2^2,147,483,648).XXX... = 0000:00E0000.0000...
And a Bit-Mapped Displacement of 2,147,483,648 Bits,
contains 268,435,456 Octets -
268,435,456 Octets represents a Number
Approximately ( 3 x 268,435,456 )
805,306,368 Digits Long ... !
256(805,306,368) = 206,158,430,208 Digits Long ... !
Total Number of Available IP Addresses in the Address Pool for
the IPt2 Specification.
Yep! This number only has a 64 Bit Foot-Print - vs 128 Bit Length
---------------------------------------------------------------------
E Terrell Internet Draft [Page 70]
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There is no doubt that the profoundness of Figure 7 seems to
overshadow the simplicity and flexibility of the design of the
IPtX Addressing Protocol Family Specification. In which case,
and rightfully so, I must conclude the Summary of the IPtX design
specification with the explanation of the description defining the
32 Bit version of IPtX-MX Protocol, and how it applies to the IPt1
Specification. And this, it shall be seen, will provide a more
gradual interpretation, elaborating the procedural change defining
the steps of the expansive effects describing how "The CIDR Network
Descriptor expands the size of the IPtX Address Space beyond the
IPv6 IP Addressing Specification" - concluding more importantly,
with the correct mathematical expression reflecting these changes,
which is supported by a logical argument derived from the proof
of "Fermat's Last Theorem", and defined by the Mathematics
of Quantification.
+--------TABLE X--------+
IPt1; The preferred IPtX
Open - ClassLess - Bit-Mapped Routing Architecture
++---------------------------------------------------------------++
- IPt1 Address Class -
'Network Connection - Addressing "Location/Destination" Protocol'
- IPtX-MX 32 Bit {Masked} Universal Protocol -
'Masked Address Protocol -
Data Streaming Packet -
Variable "Payload" Encapsulation Capacity -
Encapsulation of Linear Programmed
Information/Instruction Code -
(e.g. IP Header, TCP/IP Encapsulation Protocols,
Else Encapsulation Protocols, Info etc.)'
- CIDR Network Descriptor "RIP" "TELe-RIP" "AS-RIP" Protocol -
"RIP" - Routing Information Protocol
"AS-RIP" - Address Segment Routing Information Protocol
"TELe-RIP" - Internet Telephone "ENUM" Routing Information Protocol
"TELe-ARP" - eTelephone "DCE-Unit" Address Recognition Protocol
"MUM-ARP" - Masking/Un-Masking "DCE" Address Recognition Protocol
'Initiating the Binary Algorithm Choosing and Encoding
the "P-IQWP-DCE" "DCE" Unit for "MUM-ARP" Identification'
- Distribution Overlay -
++---------------------------------------------------------------++
Note: The conjecture leading to the possibility of a 'Quanta
Electron', or 'Electron' Particle Size Variation is clearly
a rational assumption, defined by the "Rudiments of Finite
Physics", as defining the Pattern of the Accelerated
Particle as a function of its "Mass-Displacement" Unit [6].
E Terrell Internet Draft [Page 71]
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+--------TABLE XI--------+
CDIR Network Descriptor - Scaling IPt1 Address Space
'Scaling the Anatomy of a IPtX Address String'
++++++++---------------------------------------------------++++++++
Router - ID + Trunk-Identifier - ID + Network - ID
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
Copies of 'IPt1' = 1 'Total Address Length 32 Bits'
2) /0000:00 = 0 + +/0000:00 = 1 + -/0000:00 = 1
Copies of 'IPt1' = 256^4 'Total Address Length 64 Bits'
3) /0000:00 = 1 + +/0000:00 = 1 + -/0000:00 = 1
Copies of 'IPt1' = 256(256^4) 'Total Address Length 96 Bits'
++++++++---------------------------------------------------++++++++
+ -- IPt1 -- +
IPtX-MX Universal Protocol Allocation
+++----------------------------------------+++
- Class A Address Pool Allocation -
1) (0000:0E000.0000...) = 0^X, or (0000:0.0000...E000)
- Class B Address Pool Allocation -
2) 00.0000...E00 ' = 2^X = 2^N = ' 00E00.0000... '
- Class C Address Pool Allocation -
3) (0000:000E0.0000...), or (0000:000.0000...E0)
- Class D Address Pool Allocation -
4) (0000:0000E.0000...) , or (000.000.000.000 - IPt1/IPv4)
- Class E Address Pool Allocation -
5) (0000:0000E.0000...), or (0000:.0000...E0000)
E Terrell Internet Draft [Page 72]
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+--------TABLE XII--------+
IPtX Addressing Specification - '1)'
'CDIR Network Descriptor - Scaling IPt1 Address Space'
- IPtX-MX 32 Bit "Masked" Protocol Specification -
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
'Total Address Length 32 Bits - '1' Copy of the IPt1 Specification'
Network - ID: Address String Length - IANA/FCC Specifications
'Network ID Address Mask Bit-Mapped Specification'
- IPtX-MX 32 Bit "Masked" Bit-Mapped Specification -
- "Front-End" - "Back-End" Address Masking Specification -
- IANA/FCC Specifications -
'(0000:0E000.0000...) = 0^X, or (0000:0.0000...E000)'
- IANA/FCC Specifications -
'OverLay Design/Address Bit-Mapped Specification'
- See FIGURE 5 -
+--------TABLE XIII--------+
IPtX Addressing Specification - '2)'
'CDIR Network Descriptor - Scaling IPt1 Address Space'
- IPtX-MX 32 Bit "Masked" Protocol Specification -
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
'Total Address Length 32 Bits - '1' Copy of the IPt1 Specification'
Network - ID: Address String Length - IANA/FCC Specifications
'Network ID Address Mask Bit-Mapped Specification'
- IPtX-MX 32 Bit "Masked" Bit-Mapped Specification -
- "Front-End" - "Back-End" Address Masking Specification -
- IANA/FCC Specifications -
' 00.0000...E00 ' = 2^X = 2^N = ' 00E00.0000... '
- IANA/FCC Specifications -
'OverLay Design/Address Bit-Mapped Specification'
- See FIGURE 5 -
E Terrell Internet Draft [Page 73]
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+--------TABLE XIV--------+
IPtX Addressing Specification - '3)'
'CDIR Network Descriptor - Scaling IPt1 Address Space'
- IPtX-MX 32 Bit "Masked" Protocol Specification -
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
'Total Address Length 32 Bits - '1' Copy of the IPt1 Specification'
Network - ID: Address String Length - IANA/FCC Specifications
'Network ID Address Mask Bit-Mapped Specification'
- IPtX-MX 32 Bit "Masked" Bit-Mapped Specification -
- "Front-End" - "Back-End" Address Masking Specification -
- IANA/FCC Specifications -
' (0000:000E0.0000...), or (0000:000.0000...E0)'
- IANA/FCC Specifications -
'OverLay Design/Address Bit-Mapped Specification'
- See FIGURE 5 -
+--------TABLE XIV--------+
IPtX Addressing Specification - '4)'
'CDIR Network Descriptor - Scaling IPt1 Address Space'
- IPtX-MX 32 Bit "Masked" Protocol Specification -
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
'Total Address Length 32 Bits - '1' Copy of the IPt1 Specification'
Network - ID: Address String Length - IANA/FCC Specifications
'Network ID Address Mask Bit-Mapped Specification'
- IPtX-MX 32 Bit "Masked" Bit-Mapped Specification -
- "Front-End" - "Back-End" Address Masking Specification -
- IANA/FCC Specifications -
' (0000:0000E.0000...) , or (000.000.000.000 - IPt1/IPv4)'
- IANA/FCC Specifications -
'OverLay Design/Address Bit-Mapped Specification'
- See FIGURE 5 -
E Terrell Internet Draft [Page 74]
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+--------TABLE XIV--------+
IPtX Addressing Specification - '5)'
'CDIR Network Descriptor - Scaling IPt1 Address Space'
- IPtX-MX 32 Bit "Masked" Protocol Specification -
++++++++---------------------------------------------------++++++++
1) /0000:00 = 0 + +/0000:00 = 0 + -/0000:00 = 1
'Total Address Length 32 Bits - '1' Copy of the IPt1 Specification'
Network - ID: Address String Length - IANA/FCC Specifications
'Network ID Address Mask Bit-Mapped Specification'
- IPtX-MX 32 Bit "Masked" Bit-Mapped Specification -
- "Front-End" - "Back-End" Address Masking Specification -
- IANA/FCC Specifications -
'(0000:0000E.0000...), or (0000:.0000...E0000)'
- IANA/FCC Specifications -
'OverLay Design/Address Bit-Mapped Specification'
- See FIGURE 5 -
Now, take another Look at the IPt1/IPt1-MX Protocol Specification,
and then compare it to the IPv6 Specification:
Back-End 'Only' Protocol Format
/ / /
32 Bit-Mapped Displacement = 0000:00E0000.0000... = IPt1/IPt1-MX
32 Bit Length = 11111111.11111111.11111111.11111111 = IPv4 / IPt1
/ / /
Back-End 'Only' Protocol Format
2^6 = 6 Bit Exponent = 64 Bits
2^8 = 8 Bit Prefix /
\ 2^2 = 2 Bit Base /
\ | /
0000 : 00 E 0000 . 0000...
| \
8 Bit Exponential Operator \
\
2^8 = 8 Bit Exponential Decimal String
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256:4 E 64.XXXX = 0000:00E0000.0000...
256:4 E 64.XXXX = 256:4E64.XXX... = 256(4^64).XXX...
256:4 E 64.XXXX = 256(4^64).XXX... = 256(2^128)
= 256(3.4028236692093846346337460743177e+38)
= 8.7112285931760246646623899502533e+40
= 256 Copies of a '48 Digit Number'
{Maximum Number of Available IP Addresses Contained in a 32
Bit Foot Print... which is Greater than the IPv6 Specification.}
[Note: Regardless of the Backbone Configuration, the IPtX
Specification eliminates IP Address loss by; using only
the Base 2 Exponential methods for Enumeration, then
using: The IPtX-MX Protocol; A 'Non-ZERO Prefixed'
Addressing System that counts sequentially starting with
'1', and when using the current Backbone Configuration,
the lost IP Addresses are converted to Host Addresses.]
+++---TABLE XV---+++
|- Omni Directional Linear Flat Space
/
/- Omni Directional Linear Layered Flat Space
'DNS ZONE' --
\- Omni Directional Non Linear Layered Flat Space
\
|- Omni Directional Non Linear 3-D Space Cloud;
"The Mathematical proof establishing equality
between the measured dimensions associated
with the 'Circle and the Square' and the
'Sphere and the Cube' [7]."
'DNS ZONE - Address Block Specification'
- ZONE IP - Primary Node of the 'DNS ZONE' Bit-Mapped Space
- IP AREA CODE - IPt1 Address Block Specification - X(2^32)
IPtX-MX UNIVERSAL PROTOCOL - Specification Bit-Map
- Identifiable Bit-Mapped Address Classification
- Range Scaling Data Stream Classification
- Ratio Matching Copies of IPtX Specification {5 :1}
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Clearly, while the Address Pool equation, X(2^32), which provides
the design of the IPtX Addressing Protocol Family Specification
with an impressive IP Address Pool address count availability.
eq-1: IPtX = X(2^32) + 16,900,000 = Infinity
eq-2: IPv6 = X(2^32) = (2^128) = (256^16) = 3.4028237 x 10^38
eq-3: IPt4 = X(2^32) + 16,900,000
= (2^128) + 16,900,000
= (256^16)+ 16,900,000
= 3.4028237 x 10^38 + 16,900,000 Host Addresses
eq-4: IPv4 = X(2^32); when X = 1.
However, it is from the revised definition of the role of the
"CIDR Network Descriptor", by TABLE XVI, which actually expands
the Address Space of the IPtX Specification beyond IPv6.
TABLE XVI
Table of Scaleable/Expandable Switch Function
defined for the "CIDR Network Descriptor"
"CIDR Network Descriptor" - /0000:00
Scaleable/Expandable Switch Function {'|', '?', '+', '-', h, s, etc}
"CIDR Network Descriptor" - /0000:00 {'|', '?', '+', '-', h, s, etc}
Current Definitions of the "/0000:00" {'Switch'(s)}
- 's' - Subnet Network IP Address Encapsulated by Network-ID
- Pointer for Encapsulation Network -ID --> Subnet-ID
- Pointer for Encapsulation Network -ID --> Host-ID
- Switch - Network-ID /0000:00 s - Network Subnet Address Pool
- Switch - Subnet-ID = Network-ID /0000:00 -s
- Switch - Network-ID /0000:00 +s - Subnet Host Address Pool
- Switch - Host-ID = Network-ID /0000:00 -h
- Switch - Network-ID /0000:00 +h - Network Host Address Pool
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In other words, Activation of the Host Address Pool by
Encapsulating the Host IP Address (or Subnet IP Address) with
the Network-ID (Network IP Address), designs a method for every
Address Class Network IP Address with the ability to uniquely
identify and Activate every Host-ID from a Shared Host IP
Address Pool.
Nevertheless, from the Mathematics of Quantification, in which
derivation of the "Distributive Law of the Binary System" (The
Distributive Law for Exponential Functions) resulted from the
use of "Pythagoras Theorem" to proved the conjecture involving
"Fermat's Last Theorem" is true, also changes, and redefines,
the resulting IPtX Address Pool equation; in a table of
comparisons given below;
eq-1.1: IPtX = X[(2^32) + (2^32)16,900,000] = Infinity
eq-2.1: IPv6 = X(2^32) = (2^128) = (256^16) = 3.4028237 x 10^38
= 3.4028237 x 10^38 - Address Pool Total
eq-3.1: IPt4 = X[(2^32) + (2^32)16,900,000 Host Addresses]
= (2^96)[(2^32) + (2^32)16,900,000 Host-ID]
= (2^96)[(2^32) + (2^32)16,900,000 Host-ID]
= (2^96)(2^32) + (2^96)(2^32)16,900,000 Host-ID]
= 3.4028237 x 10^38 + 5.7507720 x 10^45 Host-ID
= (2^96)(2^32) + (2^96)(2^32)16,900,000 Host-ID]
= 5.7507723 x 10^45 IP Address Pool Total
= X(Y + Y) = XY + XY - The Distributive Law
eq-4.1: IPv4 = X(2^32); and since X = 1, then;
eq-4.2: IPt1 = [(2^32) + (2^32)16,900,000 Host-ID]
= (2^32) + 7.2584947 x 10^16 Host-Addresses
= 7.2584952 x 10^16 - Address Pool Total.
eq-5.1: IPt2 = (2^32)[(2^32) + (2^32)16,900,000 Host-ID]
= 3.1174999 x 10^26 - Address Pool Total
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And more importantly, the flexibility of the Switch implemented
for the "CIDR Network Descriptor" allows the possibility of
incorporating the definitions of every 'Router Protocol' into '1'
functional Protocol Specification: e.g. - IGMP, ICMP, RARP, TOP,
All Query Messages, Redirects, Errors, and Router Solicitation
and Queries; etc.
Note: Because the "DCE" Unit of the "IPtX-MX Protocol" can
also act as the Bit-Mapped Translation of a 'Carrier
Wave', it can also be assigned as the 'Streaming Voice
Transport of an Analog Signal' (or a Synchronized Audio
Video Wave). And this would provide the means to identify
a true Universal Internet-Tel (IP Telephone)
Specification, which would, using the 'CIDR Network
Descriptor', eliminate the need for Voice and Data
Signal Filtering. And more importantly, the 'Omni
Directional Non Linear 3-D Space Cloud', it should be
noted, can accommodate Multiple Bit-Mapped Address
length Specifications; multiple (or Multiple Bands
and Different Band Widths) Bit-Mapped Address length
Specifications of the Intelligent Quantum Worm
Protocol(s) {See - TABLE XV}:
1) allowing a direct Bit-Map Specification
equating "e911" and "911" dialing
2) Establishes the a 3-D Spatial Grid for the
Internet, mimicking a GPS 'like' Mathematical
Coordinate System, which provides the ability
to Triangulate, using Trigonometry, the
Location or Destination of any Internet
Connection; Cellar Phone(s) included.
3) Emergence Broadcast Beacons - Seismic Monitoring
4) By Identifying every Node or Internet Connection,
every Node becomes a Location Broadcast Beacon;
or 'LBGNS' - Land Based Global Navigation System
Connection, in the Real Time Environment of a
3-D Space. {This requires Network Synchronization:
to Locate and establish Permanent Connections;
to Locate and establish Roaming Connections
with a 'Location Roaming History', which must also
have an 'Established Permanent Connection Location
Record' - 'No User Control or Access' with/to; the
'Zone IP', 'IP Area Code', or the 'CIDR Network
Descriptor'. [10] - The IPtX DNS Specification)
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6.3 Special IANA Consideration
- Current Definition(s) for the Measurement of the Bit
{Information provided as a Courtesy of; "Wikipedia, the
free Encyclopedia"}
Currently defined mathematical relationship(s) defining the Unit
Bit:
Binary Digit -
Claude E. Shannon first used the word bit in a 1948 paper. He
attributed its origin to John W. Tukey, who had written a Bell
Labs memo in 9 January 1947 in which he contracted "binary digit"
to simply "bit", forming a portmanteau. Interestingly, Vannevar
Bush had written in 1936 of "bits of information" that could be
stored on the punch cards used in the mechanical computers of that
time. A bit is like a light switch; it can be either on or off.
A single bit is a one or a zero, a true or a false, a "flag" which
is "on" or "off", or in general, the quantity of information
required to distinguish two mutually exclusive states from each
other. The bit is the smallest unit of storage currently used in
computing.
Unit Bit -
The bit, as a unit of information, is the amount of information
carried by a choice between two equally likely outcomes. It is
the capacity of one binary digit. One bit corresponds to about
0.693 nats (ln(2)), or 0.301 hartleys (logv[10](2)). The name bit
is mostly used when discussing data capacity, emphasizing the
storage of data as individual binary digits. The name "Shannon",
referring to the same unit, is mostly used when discussing
information content, emphasizing aggregate information quantity.
A bit refers to a digit in the binary numeral system (base 2).
For example, the number 1001011 is 7 bits long. Binary digits
are almost always used as the basic unit of information storage
and communication in digital computing and digital information
theory. Information theory also often uses the natural digit,
called either a 'nit' or a 'nat'. Quantum computing also uses
'qubits', a single piece of information with a probability of
being true.
The bit is also a unit of measurement, the information capacity
of one binary digit. It has the symbol bit, and less formally b
(see discussion below). The unit is also known as the 'shannon',
with symbol 'Sh'.
E Terrell Internet Draft [Page 80]
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Ban -
A ban, sometimes called a 'hartley' (symbol Hart), is a
logarithmic unit, which measures information or entropy, based
on base 10 logarithms and powers of 10, rather than the powers
of 2 and base 2 logarithms, which define the bit. Like a bit
corresponds to a binary digit, a ban is a decimal digit. A
'deciban' is one tenth of a 'ban'. One 'ban' corresponds to about
3.32 bits (logv[2](10)), or 2.30 'nats' (ln(10)). A deciban is
about 0.33 bits.
Nat -
A nat (sometimes also nit or even nepit) is a logarithmic unit of
information or entropy, based on natural logarithms and powers of
e, rather than the powers of 2 and base 2 logarithms which define
the bit. The nat is the natural unit for information entropy,
corresponding to Boltzmann's constant for thermodynamic entropy.
When the Shannon entropy is written using a natural logarithm,
H = E pv[i] ln pv[i]
i
it is implicitly giving a number measured in nats. One nat
corresponds to about 1.44 bits (logv[2](e)), or 0.434 hartleys
(logv[10](e)).
TABLE XVII
Measurement of the Quantities of Bits
SI Prefix and Binary Interpretation - Binary IEC Prefix Standards
Name - Symbol - Quantity | Name - Symbol - Quantity
kilobit kb 10^3 (2^10) | kibibit Kibit 2^10
megabit Mb 10^6 (2^20) | mebibit Mibit 2^20
gigabit Gb 10^9 (2^30) | gibibit Gibit 2^30
terabit Tb 10^12 (2^40) | tebibit Tibit 2^40
petabit Pb 10^15 (2^50) | pebibit Pibit 2^50
exabit Eb 10^18 (2^60) | exbibit Eibit 2^60
zettabit Zb 10^21 (2^70) | zebibit Zibit 2^70
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IEEE 1541 is a standard issued by the Institute of Electrical and
Electronics Engineers (IEEE) concerning the use of prefixes for
binary multiples of units of measurement related to digital
electronics and computing.
While the International System of Units (SI) defines multiples
(and submultiples) based on powers of ten (like 10^3, 10^6, etc.),
in computing multiples based on powers of two (like 2^10, 2^20,
etc.) have been usually preferred. In the early times, this choice
was made due to the intrinsic binary nature of computers, and
often of computer equipment (such as RAM chips), considering that
the error between 2^10 = 1024 and 10^3 = 1000 was small enough to
favor binary multiples. Thus, SI prefixes, such as kilo- (k,
usually misspelled as K), mega- (M) and so on, have been used to
indicate binary multiples in computer-related quantities, that
are not SI quantities. Moreover, there is not a consistent use of
the symbols to indicate quantities such as bits and bytes. IEEE
1541 sets new recommendations to represent those quantities and
units unambiguously.
After a trial period of two years, in 2005 IEEE 1541-2002 has been
elevated to a full-use standard by the IEEE Standards Association,
and it is now scheduled for maintenance in 2007.
Special Note: Clearly, the profound interpretation underpinning
the foundational theory for the IPtX Protocol
Specification, which transcends the prescribed
purpose defining its application, redefines the:
- Electromagnetic Scale - providing Precision Tuning
- Quantum Scale Theory - Changing the Propagation Frequency
- Quantum Scale Theory - Changing the Radiation Frequency
- Quantum Scale Theory - Changing the Energy Mass Relationship
- Electromagnetic Scale - New Physics - Quantum Scale Theory
- Quantum Scale Theory - Work Energy Relationship Redefined
- Electromagnetic Scale - Resolving Frequency of an IP Address
- Quantum Scale Theory - Resolving Radiation Exposure Issues
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- Quantum Scale Theory - A New Energy Cache Defined
- Quantum Scale Theory - Defining the Electron Bit Relationship
- Quantum Scale Theory - Mathematics of the Electromagnetic Spectrum
Furthermore, it is of special importance to mention that IEEE,
specification 1541-2002, did not make any reference to the
possibility of a Bit-Map association with an Electron - And this
it can be said, is probably due, in part(s); to the inability to
resolve a mathematical relationship associating the Unit Bit with
the measurement of the Frequencies defined by the Electromagnetic
Spectrum; the failure to understand the Electronic States of
Matter; or the failure to understand the mathematics of
Exponential (Binary Base 2) Enumeration and the respective
Logarithmic Translations resolving an Irrational Exponent. And
Tables XVIII and XIX, which Obsoletes IEEE Specification 1541-2002,
substantiates the realization of this fact, by rendering the Binary
Equivalent Conversion for the " SI Units " and the 'Electron Bit
Association' - given by;
TABLE XVIII
Well - How should the " SI Units " be Defined...?
[Especially since, when using the Binary System, I have
to define the Count of the Number of Digits the actual
Number contains... just to Define the Number having a
Binary Translation, which is equal to the Bit-Mapped
Length!]
2^F = 1,000 = 10^3 = 10E3 = 2EF = Kilobit
2^F = 1,000,000 = 10^6 = 10E6 = 2EF = Megabit
2^F = 1,000,000,000 = 10^9 = 10E9 = 2EF = Gigabit
2^F = 1,000,000,000,000 = 10^12 = 10E12 = 2EF = Terabit
2^F = 1,000,000,000,000,000 = 10^15 = 10E15 = 2EF = Petabit
2^F = 1,000,000,000,000,000,000 = 10^18 = 10E18 = 2EF = Exabit
[Given that: E = Exponential Operator; F = Variable Irrational
Number; and X = Any Variable defined as a Member of the Real
Number Set - And Look... ! IPv6 = 2^128 ~ 3.40282367 x 10^38]
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TABLE XIX - The 'Electron Bit Association'
The Binary Translation/Interpretation of the Electromagnetic Spectrum
+-------------------------------------------------------------------+
Note: And now, the Binary Translation, as defined by the Logic from
the Mathematics of Quantification, maintains that:
"If 2 Electrons or 2eV = 1 Byte, then;
2 Bits = 1 Byte
2 Electrons = 2eV = 1 Byte
2^X = Analog Signal Frequency
2^X[eV] = One Electromagnetic Spectral Frequency
{1eV = 1 Electron Volt}"
- IANA/FCC/IEEE Specifications -
And this is a valid conclusion, especially since using
the Logarithmic Translations to resolve the respective
Irrational Exponent; if the value of the Unit Measurement
of any Frequency is equal to '1 eV', and 2^X = 2^0 = 1 is
true, then ' 2^X[eV] ' defines {equals the Bit Count} a
Neutral result, which does not change or effect the current
value for the measurement of any Frequency defined by the
Electromagnetic Spectrum. (as defined by the Substitution
Law for Equality)
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CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
And more importantly, the greatest advantage of the IPtX-MX
Protocol is that, it redefines the Internet Backbone for the
IPtX Address Space, which uses the Addressing Overlay from the
IPv4 Specification to Map and Connect the Front-End-Nodes
distributed throughout the Address Space of the Backbone
Environment- Thus allowing for;
1) Creating a Free Public Internet Access Address Space -
a) 32 Bit - Intelligent Quantum Tunneling Worm Protocol
b) 256 Copies of the 2^128 Bit Address Pool in IPt1
- Free Access to e911 and emergency eTelephony
- Free Access to Local eTelephony and Basic
Internet Services {The entire World Population)
- No 32/64 Bit Information Exchange Control
2) Universally Shared '32 and 64' Bit Internet Backbone
a) Distinguishing the Commercial, Public, and Private
Sectors Users
b) Defined by the Configuration of the "CIDR Network
Descriptor" for either the 32 or 64 Bit Specification
for the Network Card (NIC)
c) Specifying the IPtX-MX Protocol for either a 32 or 64
Bit Environment
d) Specifying any one of the IPtX-MX 'Polymorph' Protocol
designs for Exclusive, Commercial, and Private Address
Space Access, and the Non-Polymorph Specification for
Free Public 32 Bit Access Services
3) 'Exclusive' Public Address Space - 64-Bit
a) 64 Bit - Intelligent Quantum Tunneling Worm Protocol
b) 256 Copies of the 2^2,147,483,648 Bit Address Pool in IPt2
- Unlimited Access to eTelephony and Internet Services
c) 64 Bit - 'Semi-Private' Network Backbone Address Space
[ A 32/64 Bit Information Exchange Backbone Environment ]
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4) Commercial Address Space - 64-Bit
a) 64 Bit - Intelligent Quantum Tunneling Worm Protocol
b) 256 Copies of the 2^2,147,483,648 Bit Address Pool in IPt2
- Unlimited Access to eTelephony and Internet Services
c) 64 Bit - 'Semi-Private' Network Backbone Address Space
[The Contact Point for Customers and/or Clients; 32/64 Bit
Xchg]
5) "Non-Commercial and Non-Public" - Private Address Space
a) 32 Bit - 'Secure Exclusive' Private Address Space
- Controlled 32 and Limited-64 Bit Information
Exchange with a 32/64 Bit Network
- the continuous change or rotation of the
Masking and UN-Masking Equation(s) use with
the Polymorph Intelligent Quantum Tunneling
Worm Protocol
- Unlimited eTelephony and Internet Access
b) 64 Bit - 'Secure Exclusive' Private Address Space
- Controlled 32/64 Bit Information
Exchange with any 32/64 Bit Network
- the continuous change or rotation of the
Masking and UN-Masking Equation(s) use with
the Polymorph Intelligent Quantum Tunneling
Worm Protocol
- Unlimited eTelephony and Internet Access
Note: The OCTET, or 8 Bit Binary Numbering Sequence that defines
the Numbering Format for an IP Address, actually, never has
to Change from the current pattern - given by;
32 Bit-Mapped Displacement = 0000:00E0000.0000...
0000:00E0000.0000... = 256:00E0000.0000...
256:00E0000.0000... = 256:2E128.0000...
[ Where 2E128 = XXX : XXX : XXX . XXX . XXX . XXX ]
256:2E128.0000... = 256:{XXX:XXX:XXX.XXX.XXX.XXX}.0000...
XXX:XXX:XXX.XXX.XXX.XXX = Any IP Address = XXXXXXXXXXXXXXXXXX
Any Number (IP Addressing Scheme Range) = ' XXXXXXXXXXXXXXXXXX '
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- OR -
64 Bit-Mapped Displacement = 0000:00E0000.0000...
0000:00E0000.0000... = 256:00E0000.0000...
256:00E0000.0000... = 256:2E2,147,483,648.0000...
256:00E0000.0000... = 256:2^2,147,483,648.0000...
[ Where 2E2,147,483,648 = XXX : XXX : XXX . XXX . XXX . XXX ]
256:2E2,147,483,648.0000... = 256:{XXX:XXX:XXX.XXX.XXX.XXX}.0000...
2E2,147,483,648 = 2^2,147,483,648 = ' XXXXXXXXXXXXXXXXXX '
XXXXXXXXXXXXXXXXXX = Any IP Address = 123123123123123123 (e.g.)
Any Number (IP Addressing Scheme Range) = ' XXXXXXXXXXXXXXXXXX '
- AND (See References; [5], [10]) -
[Example: IPtX IP Address - 64 thru 86 Bits ~ 24 or 30 Digit Number]
3 State CIDR Network Descriptor
8 Bit - Switch {'0','+','-', '/'}
[Where '0' means "No Sign" or '/']
\ /
\ /
THE END-NODE OR FRONT-END | Network ID
| Network IP | | 8 Bits
| Address | | | Network
8 Bit | 38 Bits Or | | | Octet ID
ZONE IP ADDRESS | 4-8 Bit Octets | | | 5 or 8 Bits
\ |/ \ / \| | | /
'2EX' = [ XXX : XXX : XXX . XXX . XXX . XXX '?' /0000:00 ]
\ / | \
8 Bit - IP AREA CODE ADDRESS / | \
/ / \ \
16 thru 32 Bits - 'CIDR Network Descriptor'
("AS-RIP" Protocol: 8 Bits = '/'; 16 Bits = '+/'; 16 Bits = '-/':
"IANA/EMGNCY" IP Address Pool Total = 0000:00E0000.0000... =
256:2EX.0000... ~ 256(1.1038234 x 10E12) ~ 256(2^40 + 2^32 + 2^24)
- Where [Figure 4] 'X' equals any variable defined by the Range
of an 8 Bit Octet.)
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[So... What would the IPt4/IPt4-MX Protocol look Like...? Well-?]
78 Bit = 2^78
2^8 = 8 Bit Prefix Exponent
\ /
\ 2^2 = 2 Bit Base /
\ | /
0000 : 00 E 0000 . 0000...
| \
2^8 = 8 Bit Exponential Operator \
\
2^32 = 32 Bit Decimal String Accuracy
[Note: The accuracy of the Decimal String does not have to
change until the displacement between any '2' Consecutive
'Integral Values' for the Exponent becomes greater; i.e.
more Irrational Exponents between any '2' Consecutive
'Integral Values' than the Bit-Mapped Accuracy of the
Decimal String. However, using the pattern for the "Class
System", which is a technique defined by the 'CIDR Network
Descriptor', minimizes this growth by Enhancing the
Uniqueness of every Number representing an IP Address -
And this prevents the Any LOSS in the Bit-Mapped Accuracy
of the Decimal String [FIGURE 5 : 'IPt1']. Furthermore,
to maintain a mathematically consistent growth pattern
throughout the IPtX Specification, use the IPt1 [5]
Specification [page 74] as the Baseline Guide. Where by,
the 8 Bit Prefix, the 2 Bit Base, and the 8 Bit Exponential
Operator, are the values that are consistently maintained
throughout the IPtX Specification - Given that, for every
Sequential change in the IPtX IP Addressing Specification;
(e.g. IPt2, IPt3, ..., IPt50, etc.) an additional 24 Bits
is added to the Exponent, and an additional 8 Bits is added
to enhance the accuracy of the Exponential Decimal String.]
IPt4/IPt4-MX Protocol - 128 Bit-Mapped Displacement Length
128 Bit = 0000:00E0000.0000...
= 256: 4 E 302,231,454,903,657,293,676,544
= 256: 2 E 604,462,909,807,314,587,353,088.0000...
= 604,462,909,807,314,587,353,088 Bit-Mapped Length
= 75,557,863,725,914,323,419,136 Octets
= 226,673,591,177,742,970,257,408 Digit Number!
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- And with the 8 Bit Prefix -
0000:00E0000.0000... = 256(226,673,591,177,742,970,257,408)
= 58,028,439,341,502,200,385,896,448 Digit Number!
['The IPt4/IPt4-MX IP Address Bit-Mapped Displacement is greater
than the Bit Length of 100,000,000,000,000,000,000 Bit-Mapped
(One Hundred Million Billion BITs; 1.00 x 10^20: [Figure 3]) IP
Address.']
[Special Note: The IPv4 Overlay IP Addressing Scheme (Defining the
"Front-End 'Only' Protocol Format), when using the
appropriate Mathematical Factor for 'Masking and
UnMasking' an IP Address, works quite well when
using any one of the 'Polymorph Protocols' defined
by the IPtX / IPtX-MX Protocol Specification.
However, applying the Octet Rules, which does not
include the 'Prefix', allows only the Manipulation
(Rearrangement) of the '4' Positions defining; the
Base, 'E' (the Exponential Operator), the Exponent,
and the Exponential Decimal String - limiting the
Number of 'Polymorph Protocols' for every Member of
the IPtX-MX IP Addressing Protocol Family.]
NOTE: Notwithstanding the comparable difficulty in trying to
imagine the Size of a Set, which requires a 1 Billion
Digit Number to represent the Count of the Members it
Contains, as compared to the Number representing 1
Billion, which defines a 10 Digit Number (1,000,000,000).
However, to imagine, or garner a realistic perspective of
the Size representing the Displacement of only One
IPt4/IPt4-MX Bit-Mapped IP Address. Use the Current Hard
Drive Capacity Specification (e.g. Seagate's 750GB Hard
Drive) to determine how many 'Hard Drives' would be
required to 'Write', or 'Store', 'Only One IP Address'
defined by IPt4/IPt4-MX Protocol, when the IP Address
Length is '604,462,909,807,314,587,353,088' Bits. In
which case, 'IF you Cannot' use the "Intelligent Quantum
Tunneling Worm Protocol", you'll need the 'Storage
Capacity' of about 100,743,818,301 '750GB' Hard Drives
just to 'Write' the Bit-Mapped Displacement, or the Bit
Length of one Un-Masked IPt4/IPt4-MX Protocol IP Address.
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[Closing Note: It is important to mention that since every
Octet represents a (maximum of) 3 Digit Number;
where, for example, a 32 Bit IP Address contains
12 Digits. The actual number representing this 12
Digit string exceeds the value of the 'DCE' Unit
(2E32, or 2^32) in the IPtX/IPtX-MX Specification.
In other words, the IP Address must be Converted
to the Number equaling the Bit-Mapped String
representing the IP Address: where the SUM or
Joining of the individual Octets, is equal to
the IP Address's Bit-Map Length:
256.256.256.256 = 256^4 = 4,294,967,296 = 32 Bit Length
= ( 11111111 + 11111111 + 11111111 + 11111111 ) = 2^32 = 2E32
= "DCE" Unit: Multiplication is the Quantified Sum of Addition [11]
Note: Joining the Bit-Mapped String of an IP Address
requires computing the Number equaling the Bit Count defining
the IP Address, which also equals the Exponent, 'X', in
2EX. And this procedure sustains uniqueness and prevents
duplicating the Octet 'SUM', which represents an IP Address.
Given that, when Sequential Counting represents
an IP Address having Leading Zero(s); e.g.:
000.000.000.001 thru 000.256.256.256, or
000.000.000.00X thru 000.XXX.XXX.XXX
the CIDR Network Descriptor equals;
/0000:00, or "/E"; An all Zero representation
having No Identifying Network ID, or Octet ID.
And when the IP Address is represented by:
256.256.256.256 or XXX.XXX.XXX.XXX,
the CIDR Network Descriptor equals; /XXXX:XX; and if
it is a Transmitted Electronic Signal, then;
/0000:XX = /E:XX - when, 0000 = 00 = 1, and if
':XX' = 00 = 1, then 'Octet ID = ClassID' = A = /E:XX
= /E:A - 'Routed or Routing Protocol Specification'
In this case, as shown, the Network ID and the Octet
ID are Identified.
In Both Cases, noted above - Giving the Right to Left,
8 Bit, Bit-Mapped Displacement of the IP Address, which
can easily be defined by the Masking/Unmasking Software.
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Note: Sequential Counting does not exceed the value
of the 'DCE' Unit specified by the IPtX Specification.
However, since defining the Bit-Map of an IP Address is
Required, Bit Counting produces the Decimal String in
the Exponent; given that "0E0 = 0^0 = 0 = E": i.e. when
'0E0 = E', then 'E' = 'Empty'; and "2E0 = 1 = 2^0 = 2E":
where by, 'E' has 3 Definitions and Uses; the Binary Set,
{0,1}, (Non Zero) 'Prefix' Signal Transmission, or
'E:' = 00 = 1; the 'Exponential Operator' in the "DCE"
Unit, or E = 0E0 = 'Empty'; and the CIDR Network Descriptor,
or /0000:00 = '/E'. {The IP Address Pool Total, as defined
by the 'DCE Unit' in the IPtX-MX Specification, Excludes
the Prefix and the Exponential Decimal String from the
Calculation of the Address Pool Total.}]
- Example: Masking and Un-Masking Procedure -
( 'ONLY' Network IP Address used )
1) End-Node - Node Location / Front-End - Network IP Address
= 211:002 : " 256.256.256.256 " -/1111:32
2) Bit-Map Base 2 Exponential Conversion -
= 256.256.256.256 = 256^4 = 2^32
= 4 , 294 , 967 , 296
= 11111111 . 11111111 . 11111111 . 11111111
3) IPtX-MX 'DCE' Unit Conversion - 'DCE' Unit = 2E128
= 11111111 . 11111111 . 11111111 . 11111111 = 2E32
- Optional 'Zone IP' and 'IP Area Code' Bit-Mapped Sum = 2E48
- Additional; 'CIDR Network Descriptor' Bit-Mapped Sum ~ 2E80
4) IPtX-MX IP Address - IPt1-MX Protocol
= 0000: 00 E 0000 . 0000... = 32 Bit-Mapped Length
= 0001: 2 E 32 . ( Exponential Decimal String and/or + Pad )
5) Bit-Mapped IPt1-MX IP Address -
= 0001 : 2 E 32 . ( + Pad )
= 0000 : 01 01000101 11111 . ++++...
6) Binary Transmission Signal (Prefix) Conversion -
= 0000 : 01 01000101 11111 . ++++...
= E : 2 E 32 . ( + Pad )
7) Bit-Map Binary Transmission Signal -
= E : 2 E 32 . ( + Pad )
= 01000101 : 01 01000101 11111 . ++++...
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- Where; 2 = 01, E = 01000101, 32 = 2^5 = 11111, ++++... = Pad
- Masking Steps; 1) thru 7) - Un-Masking Steps; 7) thru 1)
- Noting that the "Mask/UnMask" Software can distinguish the;
- Prefix; 0000: = 00 = 'E:'
- DCE Unit; 0E0 = 0^0 = 0 = 'E' = 'Empty';
where 0EX = Emergency Broadcast = BEX; 'EBoIP' See 'GWEBS' [8]
e.g., the IPt1 / IPt1-MX Emergency Broadcast Protocol,
'BEX' = DCE Unit: 0000:BE0000.0000... = 32 Bit, is given by;
2^4 = 4 Bit Integer
2^8 = 8 Bit Prefix /
\ 2^8 = 8 Bit Broadcast
\ | /
0000 : B E 0000 . 0000...
| \
2^8 = 8 Bit Emergency Operator \
\
2^4 = 4 Bit Decimal String
Emergency Broadcast Protocol = e911 = 256:BE9.11 = 32 Bits;
and - 2E0 = 2^0 = 1 = '2E': where AM/FM Radio, and Television;
- AM/FM Radio Broadcast = BRoIP = 0000:BR0000.0000... = 32 Bit
- AM/FM Radio Broadcast = BRoIP = 0000:BR0000.0000... = 64 Bit
- Television Broadcast = BToIP = 0000:BT0000.0000... 32/64 Bit
Note: The Broadcast Protocol(s) discussed above are Channels
that can be Transmitted, or 'Pushed' by any 'Carrier
Wave' Frequency defined by the Electromagnetic Spectrum;
within any given Hertz Range Specification.
- CIDR Network Descriptor; /0000:00 = '/E'
- Separating their Individual "Mask and UnMask" Procedures
- While the 'DCE' MUST Bit-Map the Octet Distribution, Joining
the Bit String equaling the IP Address. The 'Exponential
Decimal String' however, the 'Fraction or Decimal' part of
the Exponent defined by the 'DCE' Unit, DOES NOT Follow the
Octet Rules (Per se)- It Bit-Maps the Number(s) Sequentially;
the ENTIRE Bit-Mapped Displacement Length that represents
the Exponential Decimal String. For example: IPt1-MX - 8 Bit
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Exponential Decimal (where Significant Figures includes the
'Zeros' to the Right, after the 'Decimal Point'; defining an
Accuracy for the Numeral representing the Decimal that depends
upon the Bit Length of the Exponential Decimal String.);
'0.11111111', '0.00000001', e.g.;
'0.00001000' (Binary) = '0.000090' (Decimal Equivalent); or
'0.1000' (Binary) = '0.90' (Decimal Equivalent)
Where; '0.0' = '0' = 'Empty' - Hence; 2E'0.0' = 2E0 = '2E'
2^0.0 = 2E0.0 = 2^0 = 2E = 1
Given that;
'0.00000000' (Binary) = '0.00000001' (Decimal Equivalent) -
Then;
Binary Transmission Equivalent
Bit-Map Conversion Decimal
/ | \ / | \ |
'0.0' = ' . ' = '0.E' = '.E' = 'E' = '0.00000000'
Hence, the Bit-Mapped Displacement of the Decimal portion of
the Result from a Base 2 Exponential Operation equals the
Decimal String of the Decimal portion of the Numeral Equaling
the Exponent in the Exponential Equation. Given that;
IF 'Z.Z.Z.Z = 2^N.XXXX' , then the Bit-Mapped Displacement
of 'N.XXXX' is Equal to 'Z.Z.Z.Z' = Z^4 = XXX,XXX,XXX,XXX.
e.g.: Resolving the Bit-Mapped Displacement of the IP Address,
'123.123.123.123', is given by;
= 123.123.123.123 = (123)^4
= (123)^4 = 2EQ = 228,886,641
= 2EQ = 228,886,641 = 2^Q
Q = 1101.10100100.10001000.01110000 ~ 28 Bits
= Bit-Mapped Displacement Length = 28 Bits
Log v2 228,886,641 = Q
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Q ~ 27.770058024... ~ 27.77 (2 Digit Accuracy)
2EQ = 2^27.770058024... - Octet ID = ' :28 '
2 E 27.770058024... ~ 228,886,641.4193240053 ~ 228,886,641.42
- Or -
2 E 27.77 ~ 228,886,641.42 ~ 228,886,641
However, if the Decimal String is the Result from a Base 2
Exponential Operation, then the Exponent, Q, is Negative:
as given by;
2E-Q = 2E'Q (READ: Two Bar E Q) = '.xxxx' (Decimal Result).
[Hence; 2E'Q = 2E-Q = 2^(-Q) = 2E'Q (READ: Two Bar E Q;
'Bar E' is used to Denote a Negative Exponent)]
Then the Logarithm of any Decimal Fraction, '.XXXX', to the
Base 2, is given by;
Log v2 '.XXXX' = - Q, since Log v2 0.5 = -1 and 2^-1 = 0.5
And recall, that if 2^0 = 1 and 2^1 = 2, then any value
assigned to the Exponent that is 'Less Than' 1, yields a
Result defining the Base 2 Exponential Equation, which is
said to Approach the Value of '1', as the value of the
Exponent approaches Zero.
( Hence, Polymorphing the Basic IPtX-MX Protocol; is the
Rearranging of the Components defining the 'DCE Unit':
'iff, DCE Not Equal 0E0' - IPtX-MX Protocol Specification. )
- See [page 86 - Example: IPtX IP Address], [Page 74]
Additional Note: To Sustain the Users 32 Bit IP Addressing
format definition when the Bit-Mapped Displacement for the
actual IP Address defining the 'DCE Unit', exceeds 80 Bits,
or Any Numbering Pattern of Choice; 'Think Binary 'DCE Unit'
Conversion'. (See [Page 86]; e.g.:
DCE Unit = 2E500 = 2^500
2^500 = 3.2733906078961418700131896968276 x 10E150.
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In other words, while there might be several logically viable
mathematical formulations which can be used to Convert, or
resolve the User's Network IP Address. The easiest method
however, which follows the Octet Rule(s), requires performing
the Operation of Addition and Subtraction in an Equation
involving the Converted IP Address's Respective 'DCE Unit'
configurations. That is, when the Total Number of Available IP
Addresses is Greater, to Exhaust the Entire IP Address Pool
Range defined by the 'DCE Unit' of the IPtX / IPtX-MX
Specification. It only requires performing the Operation of
of Addition and the Operation of Subtraction on the respective
DCE Units; the order of the Operation(s) is determined not only
by the Result, which Cannot exceed the DCE Unit's Address Pool
Total*, but the Transmission Direction as well. e.g.:
11111111 . 11111111 . 11111111 . 11111111
= 32 Bit-Mapped Displacement Length = DCE Unit = 2E32
11111111111111111111111111111111 . 11111111111111111111111111111111
.11111111111111111111111111111111 . 11111111111111111111111111111111
= 128 Bit-Mapped Displacement Length = DCE Unit = 2E128
Where each Octet has 4 Times the Number of Bits, yields;
4 x ( 11111111 ) = 11111111 + 11111111 + 11111111 + 11111111
= 11111111111111111111111111111111 = 32 Bits
The Masking / UnMasking Bit-Mapped relationship - given by;
1) Masking; 2EX (DCE Unit) + 2E32 (DCE Unit) = 2E128; Union Octets
2) UnMasking; 2E128 (DCE Unit) - 2EX = 2E32; Dis-Union Octets
where; 2^32 = IPv4 Overlay assigned Users Network IP Address
and; 2^128 = 2E128 = DCE Unit's IP Address Pool Total*;
in which the IP Address specified by the Range of the IPv4
Overlay, or the 48 Bit, 18 Digit specified by the IPtX IP
Address Specification Cannot exceed the Address Range Limits
imposed by the 'DCE Unit' Bit-Mapped Specification.
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Note: Given that; "Multiplication is the Quantified Sum of
Addition" [2.] The Rudiments of Finite Algebra, [11]
- we have:
1) Joining the Octet String of an IP Address represents
Multiplication - the Product of the Numerical values
defining every Octet in the IP Address - where by;
128.002.128.002 = 128 x 2 x 128 x 2 = 2E16 = 2^16
2) Sum of the Octet String of an IP Address represents
Addition - the Sum of the Bit-Mapped Lengths defining
every Octet in the IP Address - where by;
01111111.00000001.01111111.00000001 =
01111111 + 00000001 + 01111111 + 00000001 =
1111111111111111 = 2E16 = 2^16 = 65,536
3) Hence; 128.002.128.002 = 1111111111111111 = 65,536
Even still, the foregoing conclusions, while true (The
Commutative Law), clearly demonstrates the reality of
a Mathematical Anomaly. That is, it emphases that which
is clearly evident: "if the Numerical Representation for
an IP Address is Unique [page 33] - dialing a IP Telephone
Number), then every Digit in the IP Address Must Be
Significant (Closure Law(s))" -
128.002.128.002 - Is Not Equal To - 128 x 2 x 128 x 2
128.002.128.002 = 128.002.128.002
Especially since, the Equations below must also be True;
128 x 2 x 128 x 2 = 128.002.128.002 = 1111111111111111 = 2E16
2 x 128 x 2 x 128 = 002.128.002.128 = 1111111111111111 = 2E16
128 x 2 x 2 x 128 = 128.002.002.128 = 1111111111111111 = 2E16
128 x 128 x 2 x 2 = 128.128.002.002 = 1111111111111111 = 2E16
2 x 128 x 128 x 2 = 002.128.128.002 = 1111111111111111 = 2E16
2 x 2 x 128 x 128 = 002.002.128.128 = 1111111111111111 = 2E16
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In other words, the procedures noted above could Not serve
as a viable means for resolving the Conversion for the
'IP Address - Bit-Map' Translation. However, since the
'DCE Unit" in the IPtX Specification, counts sequentially,
beginning with '1'; and given that in IPt1-MX, the -
'DCE Unit' = 2E128 = 2^128 ~ 3.403 x 10^38
= 2^128 = 3.4028236692093846346337460743177e+38
= 2^128 ~ 340,282,366,920,938,463,463,374,607,431,768,211,456
(Representing More Than 300 Million Trillion Trillion IP
Addresses - when Sequentially Counted)
The "Preferred Method", which is the easiest way to resolve
the 'IP Address - Bit-Map' Translation, given that
Sequential Counting used in the IPtX Specification complies
with the "Octet Rules", equates the Numeral representing
the IP Address to the value of the Result from a Base 2
Exponential Operation. Especially since [TABLE 1.a1];
128.002.128.002 = 128,002,128,002 = 2EF
002.128.002.128 = 2,128,002,128 = 2EF
128.002.002.128 = 128,002,002,128 = 2EF
128.128.002.002 = 128,128,002,002 = 2EF
002.128.128.002 = 2,128,128,002 = 2EF
002.002.128.128 = 2,002,128,128 = 2EF
- Noting specifically that the Numeral representing the IP
Address, hence it's Bit-Mapped Configuration, never
changes; because this procedure emphasizes using the IP
Address Numeral, with the "Dots" in the 'Dotted Notation'
Removed. ([Page 49 & 67] - IP Address = 2EX;
as in Exponential Counting - e.g. 2E0 = 1, 2E1 = 2)
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- Clearly, this is an Important Step concluding the process
that provides a 100% Backward Compatibility with the
IPv4 Specification. In other words, because the current
Computer Specification, hence Computer Programming,
Bit-Maps using the Only the 'Binary Pair (Set)', {0,1},
100% Compatibility could only be achieved if all the
Procedures involving the current IP Address's associated
Applications, Conventions, and Connection (i.e. OSI and
TCP/IP Models) remained unchanged at the Operating System
level - and this was in fact achieved, because everything
can be Converted into the Base 2 Exponential Expression
for Transmission on the Backbone (Support CHIPs / Firmware
EEprom / NIC Driver Updates, e.g. / etc.) - e.g.;
256.256.256.256 = 2EX ;
End-Node Location
Bit-Mapped Translation
11111111.11111111.11111111.11111111 = 256.256.256.256
Backbone
Bit-Mapped Translation
256.256.256.256 = 00002EX0000...; 2EX = 2^37.90010...
01000101 : 01 01000101 100110 . 1000 00 ...++++
Bit-Mapped IPt1-MX IP Address -
= 0001 : 2 E 37 . 9 00 1 0...+ Pad
= 0000 : 01 01000101 100110 . 1000 00 ...++++
Bit-Map Binary Transmission Signal -
= E : 2 E 37 . 9 00 1 0...+ Pad
= 01000101 : 01 01000101 100110 . 1000 00 ...++++
Or -
254.254.254.254 = 2EX ; (Could also be used in the Example)
The above conclusions are valid, because in both cases,
when using the IPtX/IPtX-MX Protocol Specification;
256.256.256.256 = 2EX < 2E128 = IPt1/IPt1-MX Protocol
Or -
E Terrell Internet Draft [Page 98]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
The IPt1-MX Protocol could, if the Current Computer
Specification used the Base 2 Exponential Representation,
increase the Number of available IP Addresses in the
Overlay for the IPv4 Specification - to;
256.256.256.256 = 2EX =
256 Billion, 256 Million, 256 Thousand, 256 (Hundred)
IP Addresses
More than 256 Billion IP Addresses, compared to the 4
Billion IP Addresses in the IPv4 Specification
- and using the Logarithm to Resolve the Exponent for the
Equation's Result (the IP Address) completes the process,
which requires Minor Back-End Changes to implement, and
'Major' Back-End and Front-End Changes to fully exploit
the Addressing capacity of the IPtX/IPtX-MX Specification.
- For Example; IPv4 cannot use the IP Address:
256.999.999.999 = 11101111010110011001001100101000000000 > 32 Bits
Or -
254.999.999.999 = 11101101011111001011110011011000000000 > 32 Bits
the Bit-Mapped Length is Greater Than 32 Bits, which
demonstrates the difference between Bit-Mapping the
Numeral and Bit-Mapping the Exponent equaling the Binary
conversion representing the Numeral. In other words,
these are Addressing Formats defining an IPtX-MX IP
Address, which are defined as the Result from a Base 2
Exponential Mathematical Operation that uses (works
with) the actual Number equaling the value of the
Numeral representing an IP Address.
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CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
Also - given that, in Reality;
ftp://256.256.256.256 = 'Is Just a Binary Numeral'
8 Bits 8 Bits 8 Bits : 8 Bits 8 Bits 8 Bits. 8 Bits. 8 Bits. 8 Bits
ftp://256.256.256.256 = 2EX ~ 72 Bits
And in;
http://www.name.com, where (for example)
' www ' = Zone IP + IP Area Code = '256 : 256' = 16 Bits
In other words, since every IP, URL, or FTP Address must
have a Binary Representation, which represents the
Equivalent Binary Conversion of the Bit-Mapped Length
for the Exponent in the Base 2 Equation defining the
Numeral equaling the Address. Then every IP, URL, or FTP
Address must have an Equivalent Numerical Representation,
which can be Expressed as the Result from a Binary Base 2
Exponential Operation. Clearly, changing only the Method
of Masking, before Bit-Mapping the Data String for
Transmission - The 'DCE Unit' carries a 'Payload' of
compressed, or Encoded Data, which can be Un-compressed
and used without Change - which is to say; Only the
Method(s) for Data 'Handling' of the Data String has
to change, and it must occur before Transmission -
Note: The '2' in '0000:2EX.0000' represents 2 Binary Bits, which
defines a 2 Bit Binary Sequence having a Variable Range
equal to the Numbers; '1', '2', '3', or '4'. However, the
the significance of this relationship demonstrates that
in most cases, the use of the Decimal String defining the
'DCE Unit' can be eliminated. That is, take the number '3'
for example, because the Base for the Exponential
Expression '2EX', has a 2 Bit Binary Range, the need for a
Decimal String can be eliminated. i.e. if;
2EX = 2EF = 3 = 0000:2EF.0000...
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CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
Changing the 'Base' value for the 'DCE Unit' changes the
'Intelligent Quantum Tunneling Worm' to;
3EX = 3E1 = 3 = 0000:3E1(Plus Pad +++) = 32 Bits
However, it should be clearly noted, while 100% Backward
Compatibility is factual, it also means inheriting all of the
Flaws and Errors, which plagued the IPv4 Specification (See;
Work(s) in Progress [11.]) - Inherent Foundational Flaws
involving the 'Misinterpretation of Zero - Even still, if All of
the Masking and Un-Masking Procedures were Preformed in the 'OSI
and TCP/IP Layers', which is the Preferred Method (the Temporary
Patch until Base 2 Binary System Conversion is Completed), as
given below (See; [page 94 and 95] and [The TCP/IP Model for the
'IPtX Specification']); then the entire Address Range would be
Available. The resulting exploitation would make it possible to
use the entire IP Address Range defined by the 'DCE Unit'; the
Hallmark of the IPtX Specification. And more importantly, this
process would also provide IP Address and Bit-Mapped Length
Control, effectively Hiding all Additional Bits beyond the
assigned Network IP Address Space; while preventing User Access
and Control. An important functional usage for vendors such as
AT&T, and other Telephone Companies, which typically use a
Telephone "Account" Numbering System for Billing purposes: A
Numbering System Format that includes the User's Assigned
Telephone Number in a Digital count that exceeds the Number of
Digits assigned to the User's Telephone Number.
Furthermore, it should also be added; this is a benefit that can
be adopted throughout the business community. That is, any
Business seeking to enhance Control and Security of the User's
Billing Account; e.g. the Cable TV and Satellite Broadcast
Communication Companies, could use the same, or similar Numbering
format to Enhance Security using this type of 'Account
Personalization' - Clearly, enhancing the Security Protocols for
the identification of the User and End-Node Location, could also
provide Users with additional benefits - such as:
Enhanced Personalized Controls -
Enhanced Security -
Enhanced Data Transfer Rates over existing Lines,
without Expensive Equipment, and / or Upgrade Cost,
because this procedure does not impact, or affect any
of the current standards involving Data Transfer -
Enhanced Interactive Personalized Entertainment
(i.e., 'Broadcast Entertainment Internet Protocol':
the 'BEoIP' Protocol) -
E Terrell Internet Draft [Page 101]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
TABLE 1.a1
The TCP/IP Model for the 'IPtX Specification'
100% Backward Compatibility with the IPv4 Specification
OSI Model TCP / IP Stack
|---------------+ +-----------------------+
| Application | | |
|---------------+ | |
| Presentation | | APPLICATION |
|---------------+ | |
| Session | | |
|---------------+ +-----------------------+
| Transport | | TRANSPORT |
|---------------+ +-----------------------+
| Network | | INTERNET |
|---------------+ +-----------------------+
| Data Link | | |
|---------------+ | - INTERFACE - |
| - Physical - | | |
| Binary | | 'Binary Base 2 |
| Base 2 | | Exponential Conversion|
| Conversion | | See; Example: Masking |
| See; | | and Un-masking |
| 'Example: | | Procedure'* |
| Masking } | |
| and | | [ Pages 91 thur 95 ] |
| Un-Masking | | |
| Procedure* | | |
| [ Pages 91 | | |
| thur 95 ] | | |
+---------------+ +-----------------------+
Cost Effectiveness - Well? Weighting the Benefits of IPtX...
It's Less Than IPv6!
Only the 'Physical Layer' in the "OSI Model', and the
'Interface Layer' in the TCP/IP Stack are required to
Change - Minor when compared to Changing every Program
associated with every Communications 'Layer' - Major
Change is required to make everything Mathematically
Compatible with Binary Exponential Base 2 System -
Eliminating the 'HEX' System and Replacing it with
'The Binary Base 2 Exponential System of Counting'.
E Terrell Internet Draft [Page 102]
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Note: Currently the 'Data Link' and 'Transport layers converts
the Bits into Frames or Packets, moving the Frames between
Connected Hosts;
Minimum packet size - 64 Octets
Maximum packet size - 1518 Octets
Gigabit Ethernet Jumbo Frames - 9018 Bytes ~ 9018 Octets
However, this Size limitation can be Eliminated, if the
Data Stream used the Binary Base 2 Exponential System
before the Bit-Mapped conversion is sent to the 'Data
Link' and 'Transport layers -
And modification of the 'Session' and 'Transport' Layers
would allow the 'Simulcast' of a 'Frame by Frame
Transmission and Reception of a Voice, Data, and Video
Communication(s) Broadcast' - creating a World-Wide
'VVoIP' Network.
-- Using the 'Data Compression' Ratio; '2EX : 1', or 2^X --
Example of Encoding the Bit-Map of the Equation for the 'Data Stream'
Text to encode...
'I went to the store today.'
I = 01001001 = 73 = 2EX ~ 2E8
went = 01110111011001010110111001110100 = 2,003,136,116 = 2EX
~ 2E32
to = 0111010001101111 = 29,807 = 2EX ~ 2E16
the = 011101000110100001100101 = 7,628,901 = 2EX ~ 2E24
store = 0111001101110100011011110111001001100101 = 495,874,699,877
= 2EX ~ 2E40
E Terrell Internet Draft [Page 103]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
today = 0111010001101111011001000110000101111001 = 500,085,055,865
= 2EX ~ 2E40
' . ' = 00101110 = 46 = 2EX ~ 2E8
The Equivalent Binary Numerical Conversion to be Transmitted;
'I went to the store today.' 'Iwenttothestoretoday.'
010010010010000001110111011001 010010010111011101100101011011
010110111001110100001000000111 100111010001110100011011110111
010001101111001000000111010001 010001101000011001010111001101
101000011001010010000001110011 110100011011110111001001100101
011101000110111101110010011001 011101000110111101100100011000
010010000001110100011011110110 010111100100101110
0100011000010111100100101110
208 Bits 168 Bits
In other words, everything is counted, which includes the Blank
SPACES Separating every word the sentence contains -
168 Bit Sentence '6 Words' = 'I went to the store today.'
Blank Space ' ' separating Words
00100000
8 Bits
E Terrell Internet Draft [Page 104]
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Now... 'Taking it Away' yields;
'I went to the store today.'
I = 01001001 ~ 2E8 = 73
Blank Space ' ' = 00100000 ~ 2E8 = 32
went = 011101110110010101101110011101000
~ 2E32 = 2,003,136,116
Blank Space ' ' = 00100000 ~ 2E8 = 32
to = 01110100011011110 ~ 2E16 = 29,807
Blank Space ' ' = 00100000 ~ 2E8 = 32
the = 0111010001101000011001010 ~ 2E24 = 7,628,901
Blank Space ' ' = 00100000 ~ 2E8 = 32
store = 01110011011101000110111101110010011001010
~ 2E40 = 495,874,699,877
Blank Space ' ' = 00100000 ~ 2E8 = 32
today = 01110100011011110110010001100001011110010
~ 2E40 = 500,085,055,865
- No Blank Space Separating the 'WORD' and the 'Period' -
' . ' = 00101110 ~ 2E8 = 46 (No Blank Space or 'Carriage Return'
after the Period.)
E Terrell Internet Draft [Page 105]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
And... 'Putting it Together' yields;
'I + went + to + the + store + today + .'
I = 01001001 = 73 +
Blank Space = 00100000 = 32 +
went = 01110111011001010110111001110100 = 2,003,136,116 +
Blank Space = 00100000 = 32 +
to = 01110100011011110 = 29,807 +
Blank Space = 00100000 = 32 +
the = 0111010001101000011001010 = 7,628,901 +
Blank Space = 00100000 = 32 +
store = 01110011011101000110111101110010011001010 = 495,874,699,877 +
Blank Space = 00100000 = 32 +
today = 01110100011011110110010001100001011110010 = 500,085,055,865 +
No Blank Space = Zero
' . ' = 00101110 = 46
Assembling (Joining) the Data Stream yields;
I(73) + Blank(32) + went(2,003,136,116) + Blank(32) + to(29,807) +
Blank(32) + the(7,628,901) + Blank(32) + store(495,874,699,877) +
Blank(32) + today(500,085,055,865) + Period(46)
= 73 + 32 + 2003136116 + 32 + 29807 + 32 + 7628901 + 32 +
495874699877 + 32 + 500085055865 + 46 = 60 Digit Number
= 733,220,031,361,163,229,807,327,628,901,324,958,746,
998,773,250,008,505,586,546 = 2E198.868003799...
= 2 E 198 . 868003799 ...
= 11 01000101 11000110 . 110011101111001010111111010111
= 2E198.868003799... = 48 Bit-Mapped Displacement
[ ' . ' = 8 Bits = 00101110 = 46 ]
48 - 56 Bits vs 208 Bits - 6 - 7 Octets vs 26 Octets
E Terrell Internet Draft [Page 106]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
- Or -
= 60 Digit Number = 'I went to the store today.' = 2E198.868003799...
And this is equivalent to 26 Bytes, or approximately 208 Bits.
- Or -
2E198.868003799... ~ 2E208 = an approximate Bit-Mapped Displacement
of 20 Bits (4 + 8 + 8). Or 20 Bits vs 208 Bits;
represents the difference between Bit-Mapping
the 'Data Stream', as compared to Bit-Mapping
the Equation of the 'Data Stream'.
Note: The Bit Mapped example used above follows from the Current
Binary Translation, which includes the Askew Error!
And more importantly, the Compression Ratio becomes even greater, by
some Exponential factor, as the amount of Data, which is to be
Compressed, increases. - e.g. 100Mbyte (800 MBit ~ 100,000,000 Octets)
Document is compressed to '2E800,000,000', or (4 + 8 + 30) 42 Bits
(~ 6 Octets)[Approximating a '20,000,000 to 1' Bit-Mapped Compression
Ratio].
Furthermore, it should be readily concluded, since the Transmission
Frames [e.g. the 'Packet Range Size' of 64 Octets, 1518 Octets, or
Jumbo Frames ~ 9018 Octets] represent a Bit-Mapped 'Data Stream', the
Size or Number of Transmission Frames can be reduced dramatically.
Especially since, using the 'DCE Unit' a Greater amount of Data can
be transmitted in an Extremely Small, 'Quanta Sized', Packet. Hence,
overall, the Transmission Rate, by comparison to today's standards,
would increase by an 'Astronomically Exponential' amount. [e.g. if
today's Transmission Rate is 1MB to 10GB per Second, then this would,
when using the IPtX-MX Specification, be comparable to the
Transmission Rate of 1MB to 10GB in the Micro to Nano Second Range.]
The real benefits however, is that the Structure of the 'IPtX Ethernet
Frame' provides for the ability of having a 'Diverse Colony Population'
of "Intelligent Quantum Tunneling Worm Protocol" Specifications
populating the Backbone - i.e. any one or more IPtX IP Addressing
Specification can populate the Backbone {e.g. IPt1, IPt2, IPt3, and
IPt4 IP Addressing Formats can be used simultaneously. In other
words, the "Destination and Source Address Segments", when using the
IPtX-MX IP Addressing Specification, can contain the MAC Address and
the IPtX-MX IP Address, and this includes the simultaneous Use of
Multiple IP addressing Formats. Noting more specifically that, the
accuracy of the 'Exponential Decimal String' provides another Level
of Uniqueness to every IPtX 'IP and MAC' Address - as given below;
E Terrell Internet Draft [Page 107]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
-+- Structure of an IPtX Ethernet Frame -+-
Approximating a Ethernet Data Segment Data Stream
'Payload Capacity' for (1);
19,807,040,628,566,084,398,385,987,584 Bits
2,475,880,078,570,760,549,798,248,448 Octets
7,427,640,235,712,281,649,394,745,344 Digit Number
" - IPtX Ethernet Frame (802.3iptx) Octet Distribution - "
_____________________________________________________________________
Preamble|SFD|Dest. Address|Sourc. Address|VLan T|Length| Data* |FCS
1) 7 | 1 | 6 - 16 | 6 - 16 | 4 | 2 | 18 - 14 | 4
2) 7 | 1 | 6 - 32 | 6 - 32 | 4 | 2 | 98 - 174 | 4
3) 7 | 1 | 6 - 64 | 6 - 64 | 4 | 2 |482 - 878 | 4
---------------------------------------------------------------------
- 1 - IPt1 - IPt2 Minimum Packet Size Range - 48 to 64 Octets *
'Destination & Source' Address Segmemts, and Data Segmemt Expansion
- 2 - IPt1 - IPt6 Average Packet Size Range - 128 to 256 Octets
'Destination & Source' Address Segmemts, and Data Segmemt Expansion
- 3 - IPt1 - IPt14 Maximum Packet Size Range - 512 to 1024 Octets
'Destination & Source' Address Segmemts, and Data Segmemt Expansion
+++++ Anatomy of the Data Segment Equation - 'Payload Capacity' +++++
102 Bit = 2^102
Exponent
/
2^2 = 2 Bit Base /
| /
00 E 0000 . 0000...
| \
2^8 = 8 Bit Exponential Operator \
\
2^40 = 40 Bit Decimal String Accuracy
Representing the 'Baseline' Mimimum of 40 Bits for the Accuracy of
the Exponential Decimal String for the Data* Field Equation - A
Compression Ratio of 2^X:1 for the 64 Octet IPtX-MX Ethernet Frame;
2EX.0000... = 00E0000.0000...
= 2E5,070,602,400,912,917,605,986,812,821,504
E Terrell Internet Draft [Page 108]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
Note: While the Preferred design for Ethernet Frame provides for the
simultaneous use of the IPtX-MX MAC and the Users IP Address(s),
increasing the Number of available IPtX / IPtX-MX IP Addresses
Handled by the IPtX 802.3iptx Ethernet Frame. However, Backwards
Compatibility, the Desired 'Data Field' Minimum Payload Capacity,
and IP Address Range Access of IPt1 - IPt16777216, would be lost
when the Length of the Ethernet Frame equals 64 Octets - Hence,
the design of an Ethernet Frame using Partial and Complete IP
Address, as given by;
IPtX/IPtX-MX 'Partial IP' and 'MAC' SOURCE/DESTINATION Address Fields
| IPtX Version = 2E24 = 24 Bits |
| | + + + + + + + + + + + + + |
|IPtX Version = 24 Bits(Continued)|Parity Notify Bit* |Prefix |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX/IPtX-MX SOURCE MAC Address = 2EX.0000... = 64 Bits |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX Version = 2E24 = 24 Bits |
| | + + + + + + + + + + + + + |
|IPtX Version = 24 Bits(Continued)|Parity Notify Bit* |Prefix |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX/IPtX-MX DESTINATION MAC Address = 2EX.0000... = 64 Bits|
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
IPtX/IPtX-MX 'Complete IP' and 'MAC' SOURCE/DESTINATION Address Fields
| IPtX Version = 2E24 = 24 Bits | Parity Notify Bit* |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| Prefix = 8 Bits |SOURCE ADDRESS Exponent = 2E 14 / 46 Bits |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| SOURCE ADDRESS Exponential Decimal String = 2E 22 / 54 Bits |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX/IPtX-MX MAC Address = 2EX.0000... = 64 Bits |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX Version = 2E24 = 24 Bits | Parity Notify Bit* |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|Prefix = 8 Bits|DESTINATION ADDRESS Exponent = 2E14 / 46 Bits|
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
|DESTINATION ADDRESS Exponential Decimal String = 2E22/54 Bits|
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
| IPtX/IPtX-MX MAC Address = 2EX.0000... = 64 Bits |
|+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +|
Note*: The 'Parity Notificication' Bit defines the 'PREFIX'
as either a Character (1 Bit), or an Integer (0 Bit).
E Terrell Internet Draft [Page 109]
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" - IPtX Ethernet Frame (802.3iptx) Octet Distribution - "
_____________________________________________________________________
Preamble|SFD|Dest. Address|Sourc. Address|VLan T|Length| Data* |FCS
1) 8 | 1 | 13 | 13 | 4 | 2 | 19 | 4
2) 8 | 1 | 24/32 | 24/32 | 4 | 2 | 189/173 | 4
3) 8 | 1 | 24/32 | 24/32 | 4 | 2 | 957/941 | 4
4) 8 | 1 | 24/32 | 24/32 | 4 | 2 |1451/1435| 4
---------------------------------------------------------------------
Note: '1' and '4' match the current Etnernet Frame size specification
1) IPtX '32/64 Bit Header' = IPt1 - IPt840 / IPt1 - IPt16777216
IPtX Ethernet Frame - Packet Size = 64 Octets
Data Field Size = 19 Octets
Address Field Size = 104 Bits - 13 Octets
Note: IPtX MAC Address and Partial User IP Address
2) IPtX '32/64 Bit Header' = IPt1 - IPt840 / IPt1 - IPt16777216
IPtX Ethernet Frame - Packet Size = 256 Octets
IPtX Ethernet Frame - Data Field Size = 189 / 173 Octets
IPtX Ethernet Frame - Address Field Size = 24/32 Octets
Note: IPtX MAC Address and Complete User IP Address
3) IPtX '32/64 Bit Header' = IPt1 - IPt840 / IPt1 - IPt16777216
IPtX Ethernet Frame - Packet Size = 1024 Octets
IPtX Ethernet Frame - Data Field Size = 957 / 941 Octets
IPtX Ethernet Frame - Address Field Size = 24/32 Octets
Note: IPtX MAC Address and Complete User IP Address
4) IPtX '32/64 Bit Header' = IPt1 - IPt840 / IPt1 - IPt16777216
IPtX Ethernet Frame - Packet Size = 1518 Octets
IPtX Ethernet Frame - Data Field Size = 1451 / 1435 Octets
IPtX Ethernet Frame - Address Field Size = 24/32 Octets
Note: IPtX MAC Address and Complete User IP Address
E Terrell Internet Draft [Page 110]
CIDR Network Descriptor expands IPtX Add Space October 27th, 2006
Note*: Octet distribution between the Exponent 'X' and the Exponential
Decimal String (" .0000... ") is ' 3 to 1 ' for every 32 Bits.
++++ IPtX Ethernet - 802.3iptx - Frame Specification ++++
+---------------+
| | The Preamble consists of 62 bits of alternating
| Preamble | ones and zeros that allows the Ethernet card to
| | synchronize with the beginning of a frame.
| 8 Bytes |
| |
| |
+---------------+ The Start Frame Delimiter is the sequence
| SFD - 1 Byte | 10101011, and indicates the start of a frame.
+---------------+
| Destination | The Destination address is a 8 Byte Media
| 3 Levels IPtX | Access Control (MAC) address, identifying the
| IP Bytes Spec | Ethernet card, and the Computer's IPtX IP Address.
+---------------+
| Source | The Source address is a 8 byte MAC address,
| 3 Levels IPtX | identifying the Ethernet card, and the IPtX IP
| IP Bytes Spec | Address identifying the Computer.
+---------------+
| Type | The Frame Type; 802.3iptx Specification.
| 2 Bytes |
+---------------+
| | Any higher layer information is placed in the
| Data * | Data Segment, which could contain additional
| 3 Levels IPtX | Protocol Information and / or User Data.
| ' DSE ' | [Note: The 'Dot' and 'Colon' Notation in the
| Bytes Spec | Destination and Source Fields, could reduce
| | the 'Data Field' Segment Size by 2 Octets,
+---------------+ unless the IP Address is Divided into Segments.]
| FCS |
| 4 Bytes | The Frame Check Sequence is a Cyclic Redundancy
+---------------+ Check used by the sending and receiving
stations to verify a successful transmission.
The FCS is based on the contents of the
destination address, source address, type,
and data.
Note: 'Data Field' Size Reduction occurs only at the High End
of the IPtX Ethernet Frame Range Size - e.g.
- 1 - IPt1 - IPt2 Minimum Packet Size Range - 64 Octets *
'Data Stream Equation' (DSE) = 2E62 . 40 Bits
DSE - 16 Bits (2 Octets) = 2E46 . 40 Bits
E Terrell Internet Draft [Page 111]
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Given that the Equation's Transmission Pattern defined by;
'0000:00E0000.0000...' = 000000E0000 . 0000...
- The Colon ' : ' is eliminated -
Note: The gist of 'The Rudiments of Finite Quantum Computing and
Finite Quantum Computer Programming' maintains: A 'Quanta Size'
Packet, or Sub-Atomic Particle Size Communications 'Data Stream'
having an equal 'Payload Capacity', as defined for the
Bit-Mapped Displacement of any Addressing Format for the IPtX
Specification. At the Quantum Level, could only be realized when
using the Electromagnetic Spectral Frequency that defines the
Binary Signal ["The Mathematics of Quantification and the Theory
of the 'Gravitonic and Quantum' Scale(s)]. In other words, only
a matching "Quantum Scaled" Electromagnetic Spectral Frequency
that represents the signature identifying the Binary Numeral,
could be utilized to 'Stimulate' or 'Change the State' of the
Particle; which could then 'Read and Interpret' the Decoded
Signal as a Set of Instructions. In which case, it should be
realized, the current techniques and procedures governing all
Programming Languages can remain unchanged. That is, in Theory,
having a 'Payload Capacity' Mathematically defines the
"Intelligent Quantum Tunneling Worm" Protocol as a 'Binary
Carrier Wave'. In other words, other than creating a 'Program
Specific' "Intelligent Quantum Tunneling Worm", only the
techniques defining the Masking and Un-Masking procedures for
'Data Stream' Transmission are different.
- This procedure represents the 'First Stage', defining
the Minimum Requirements, which must be Encoded prior
to the implementation and / or use of the 'IPtX/IPtX-MX'
Protocol Specification - which Complies with the
requirement of 'RFC 1550' - "IP: Next Generation (IPng)
White Paper Solicitation"; 100% Backward Compatibility
with the 'IPv4 IP Addressing Specification'. Noting
specifically that, all of the IP Addresses in the 'IPtX
Specification' are Now Available. And incrementing using
the Addition of "1's", to every IPv4 IP Address, following
the Masking / Un-Masking procedures discussed above, yields
approximately;
a. IPt1 = 256 x 2^96 (Copies of 2^32); the IPv4 Specification
b. IPt1 = 256 x 2^32 (Copies of 2^96); the IPt1 Specification
c. IPt1 = 256 Copies of 2^128; the IPv6 Specification
E Terrell Internet Draft [Page 112]
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Note: It is behooving that consideration is given to Re-defining
the Relationship between the 'Bit' and the 'Byte', as
presented in; [TABLE XIX] - The 'Electron Bit Association'.
Especially since, this would sustain the logical validity
and the Mathematical continuity as defined by the 'Binary
Base 2 Exponential Mathematical System'.
Especially since [page 97 thru 100];
IPv4 IP Address = 'FFF.FFF.FFF.FFF' = 2EX
'FFF.FFF.FFF.FFF' = 'FFF,FFF,FFF,FFF' = 2EX;
and IPt1 = IPv4 = 32 Bit-Mapped Length -
Hence, without using the '3 State CIDR Network Descriptor';
IPt1 a. = IPt1 b. = IPt1 c. = 256 x 2^128 IP Addresses
256 x 2^128 = 2^8 x 2^128 = 2^136 IP Addresses
IP Address Pool Total for the IPt1/IPt1-MX Specification
= 2^136 = 8.7112285931760246646623899502533 x 10E40 IP Addresses
However, when using the 3 State Logic of the CIDR Network
Descriptor (While just a Number; there is a Difference);
a. /0000:00 = 8.7112285931760246646623899502533 x 10E40 Addresses
b. +/0000:00 = 8.7112285931760246646623899502533 x 10E40 Addresses
c. -/0000:00 = 8.7112285931760246646623899502533 x 10E40 Addresses
E Terrell Internet Draft [Page 113]
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Note: 'Every Numeral in the Prefix', 256 - (1 thru 256); where
'256' = '0000:', defines All 3 State(s), representing the
3 Types Switches defining the 'CIDR Network Descriptor'.
Therefore, the IP Address Pool Total for the IPt1/IPt1-MX
Specification increases by a factor of 3 - where by;
'a.' + 'b.' + 'c.' = 2.613368577952807399398716985076 x 10E41
= 3 x 2^136 = 3 x 8.7112285931760246646623899502533 x 10E40
= 2.613368577952807399398716985076 x 10E41 IP Addresses
Note: When the IP Address, instead of the Exponent, Equals the
Result from a Base 2 Exponential Operation, the Bit length
increases by a factor of 2E4; or approximately 16 Bits.
[page 87] - [Example: IPtX IP Address - 64 thru 80 Bits
~ 24 or 30 Digit Number] Furthermore, when the IP Address
is used in this 'way', the Bit-Mapped Length defining the
IP Address, Bit-Maps to the Length corresponding to the
value of the Exponent, which defines the actual, or "Numeric
Face Value' of the Number equaling the Result from a Base 2
Exponential Operation. (i.e., it increases from '2E80' Bits
to approximately '2E96' by representing the actual Number,
and not the Bit-Mapped Length of the Octets equaling the
Exponent. And this yields an Address Pool Total
approximating '2^37...' = '2E37...' IP Addresses) - e.g.;
IPt1 / IPt1-MX = 256.256.256.256 ~ 2^37...
= 256,256,256,256 ~ 2^37... IP Addresses
38 Bit Length = 11101110101010000100000010100100000001
Where the Exponent in '2^37...' ~ 38 Bits
E Terrell Internet Draft [Page 114]
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While in the IPv4 Specification - See [page 99];
256.256.256.256 = 1111111111111111111111111111111111111111
32 Bit Length = 1111111111111111111111111111111111111111
256.256.256.256 = 4,294,967,296 = 2^32 IP Addresses
And more importantly, with Subtraction defined ['Work(s) in
Progress' [11], Set Theory does suggest the possibility for
existence of the 'Decimal Fraction'. Yet, neither the Binary
nor the Unary Systems can represent a 'Decimal Fraction'. That
is, because the Binary Set ({0,1}) can only be used to
represent or define an Integer, a 'Decimal Fraction' cannot be
defined using the current Binary Conversion methods. In other
words, as with the use of the 'Whole Numbers' for the Unary
Set ({1}), only the Base 2 Exponential System of Counting can
accurately represent a 'Decimal Fraction' defined by the
Binary Set ({0,1}). In which case, since every digit in a
Decimal Fraction defines the result from a Base 2 Exponential
Operation, as an Integer, or a series of Integers positioned
behind a 'Decimal Point' (Including Zero). The resulting
Numeral this Integer defines can be easily converted, because
only the Base 2 Exponential equation, which defines the
Result, is Bit-Mapped. (i.e. if the Binary Set can only
convert Integers, then the Decimal Point, for Conversion
Purposes, becomes irrelevant.) Noting more specifically, this
is the procedure for Bit-Mapping any 'Decimal Fraction'
representing the result from a Base 2 Exponential Operation,
which can be Transmitted and later used in the mathematical
calculations involving a Masking or Un-Masking Procedure.
In other words, there is a far greater growth potential, which
expands the IPtX IP Addressing Protocol Family Specification,
well beyond the latter results from the foregoing analysis.
That is, when adding the use of the 'Bar E' notation to the
'DCE Unit' {2E'Q} (given that the Members of the 'Real Number
Set' represents every Numeral possible), the IP Address Pool
Total defined by the IPtX Specification increases to an amount
equal to 'Bit-Mapping' every Element, or Member defined by the
'Set of Real' Numbers.
E Terrell Internet Draft [Page 115]
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- Hence, the IPt1/IPt1-MX, DCE Unit = 2E'128, Address Pool Total
for defines the equivalent 'Negative' Exponent in 2^128; yields
an IP Address Pool Total, as given by;
0000:2E'Q.0000...
' a. /0000:00 ' = ' b. +/0000:00 ' = ' c. -/0000:00 '
= 8.7112285931760246646623899502533 x 10E40 Addresses
'a.' + 'b.' + 'c.' = 2.613368577952807399398716985076 x 10E41
Nevertheless, to mention just a few of the functional purposes,
or the benefits immediately derived from this New Address Pool
Total, suggests the possibility for;
1) Creation of a Dedicated Mobile & Telephony IP Address Pool
a) Providing greater Mobile Technological Reliability
b) Enhanced User's Interactive Personalized Mobile Controls
c) Enhanced Mobile Location and Mobile Tracking Reliability
d) Seamless Integration of All Telephony Services
e) All Telephony Services 'Share' IP Address Space (Pool)
f) Mobile Frequency Distinction from Stationary Connections
g) IPtX Masking and Un-Masking Procedures provides Seamless
Integration of the current Telephone Numbering Systems,
or the implementation of a New Numbering System.
e.g. Using the appropriate factor converts the Telephone
Number for the 'DCE Unit' and Binary Transmission;
1-510-838-9885 = 15,108,389,885
15 + 108 + 389 + 885 = 15,108,389,885
X(15,108,389,885) = 1 / 15,108,389,885
1 / 15,108,389,885 = 2E'Q = 'DCE Unit'
6.6188389868918186181690531611536 x 10E'11 = 2E'Q
E Terrell Internet Draft [Page 116]
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2) Creation of 2 New IPtX 'MAC Address' Specification
a) Stationary Connections - 2EX = Stationary 'DCE Unit'
b) Mobile Connections - 2E'Q = Mobile 'DCE Unit'
Mobile Permanent - IP Address = 0000:2E'Q.0000...
Static - MAC ADDRESS = 2E'Q = 'DCE Unit'
- And -
Stationary Permanent - IP Address = 0000:2EX.0000...
Static - MAC ADDRESS = 2EX = 'DCE Unit'
--+-- IPtX MAC Address Design Specification --+--
64 Bit / 8 Octet IPtX MAC Address
2EX.0000... = 2E4,194,304 - 2E'Q.0000... = 2E'4,194,304
Product ID or Production Code Number
| |
| 48 to 896 Bits |
| |
| Or |
8 Bit Location | |
ZONE IP ADDRESS | 4-8 Bit Octets |
\ |/ \ / \|
'2E1024' = [ XXX : XXX : XXX . XXX . XXX . XXX - 0000:00 ] ~ 1024 Bits
\ / \
8 Bit Location - IP AREA CODE ADDRESS / \
/ \
32 thru 112 Bits - 'Manufacturer's Designation ID'
22 Bit = 2^22
Exponent
/
2^2 = 2 Bit Base /
| /
00 E 0000 . 0000...
| \
2^8 = 8 Bit Exponential Operator \
\
2^32 = 32 Bit Decimal String Accuracy
E Terrell Internet Draft [Page 117]
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- Where, e.g., Bit-Mapping '2^-1' is given by [page [94], [97];
2E'Q = 2E'1
2E'1 = 2^-1
2^-1 = 0.05
2E'1 = 01 11001010 00
2^-1 = 01 11001010 00
01 11001010 00 = 0.5
- Hence, using the 'Octet Rules' for Transmission, ' 2E'1 ', by
definition, is 'Just another Binary Number';
01 11001010 00 = 01 + 11001010 + 00
01 + 11001010 + 00 = 002 + 203 + 001
2 , 203 , 001 = 002 + 203 + 001
002 + 203 + 001 = 002.203.001 = ' 2E'1 '
- Given the Binary Conversions; E' = 11001010 ; 2 = 01 ; 1 = 00 ;
and; 203 = E' = 11001010
E Terrell Internet Draft [Page 118]
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Even still, while the IP Address Pool Total for the 32 Bit IPt1
Specification concludes a far greater number of available IP
Addresses, by Rearranging the Components defining the 'DCE Unit'
(See [page 94]), it raises the question; 'Are these additional IP
Addresses Necessary?' Especially since, the Address Pool Total for
the IPt1 Specification greater than the IPv6 Specification, with or
without the 'Polymorphed Protocol(s)'. Note the comparison table,
given by;
- IPt1 vs IPv6 -
IPv6 IP Addressing Specification
IPv6 = 2001:0db8:85a3:08d3:1319:8a2e:0370:7334
IPv6 = 2^128 IP Address Pool Total
2^128 = 3.4028236692093846346337460743177 x 10E38
IPt1 / IPt1-MX IP Addressing Specification
IPt1 = 0000:2E'X.0000... = 3(2^136)
IPt1 = 0000:2EX.0000... = 3(2^136)
IPt1 = 3(2^136) + 3(2^136)
= 1536(2^128) IP Address Pool Total
IPt1 = 5.226737155905614798797433970152 x 10E41
IPt1p = One Polymorphed Protocol in IPt1
= 3(2^136) IP Addresses
- The Polymorphed Protocol IP Address Pool Total (Is it Needed?);
- There are about 5 Polymorphed Protocols Approximating;
a) 0000:2E'X.0000... = 5(3(2^136))
b) 0000:2EX.0000... = 5(3(2^136))
E Terrell Internet Draft [Page 119]
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- Or -
IPt1p = [15(2^136)) + 15(2^136))] IP Address Pool Total
IPt1p = 5.226737155905614798797433970152 x 10E42
IPt1 + IPt1p = 5.7494108714961762786771773671672 x 10E42
Note: Complying with the "Octet Rules" changes the results,
as presented in FIGURE 7... Where by, the "IPtX-MX
Protocol", at Infinity, as given by FIGURE 7a, becomes;
IPtX / IPtX-MX IPtX / IPtX-MX Protocol
Infinite Bit-Mapped Displacement = 0000:00E0000.0000...
[ eq-f. 'Infinity' = (Infinity + Infinity) = Infinities ]
Infinite Bit
8 Bit Prefix Exponent
\ /
\ 2 Bit Base /
\ | /
0000 : 00 E 0000 . 0000...
| \
8 Bit Exponential Operator \
\
Infinite Bit Exponential
Decimal String Accuracy
FIGURE 7a
Note: While Character Transmission maybe substituted for an Integer,
when the 'Prefix' equals Binary '00', the Integer '1'. However,
when establishing the Communications Connection, the negotiating
Transmission, or 'Awk', must also define the 'Prefix' as either
an 'Integer' or an 'Alpha Character' to the Receiving Station.
And more importantly, if you'll note, this procedure requires
'ONLY the addition of a One-Bit FLAG' - where the '1' signifies
the used of a Character defining the 'Prefix', and the '0' Bit
is used to defined the 'Prefix' when it represents an 'Integer'.
E Terrell Internet Draft [Page 120]
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Nevertheless, while providing IANA, FCC, and all other noted
Regulatory Agencies [defined with FCC responsibilities within
their respective ZONE IP location(s); e.g. IEEE], with an
extremely broad range of decision options, concluding the
overall general design and operational procedures for the
IPtX Addressing Protocol Family Specification. [The Internet
Protocol telecommunications Xchange Specification; IPtX,
represents a design specification that can contain a 'Diverse
Colony Population' of "Intelligent Quantum Tunneling Worm
Protocol" Specifications - i.e. any one or more members
from the IPtX Addressing Protocol Family Specification can
populate the Backbone Environment approaching an unlimited size
'Bit-Map' Address Space.] However, embedded within the context of
this document are the Preferred, or Recommended Operational
Procedures that mandates the continued existence of the
mathematical continuity ascribed by the Hierarchy of the IPtX
Specification, which assigns the controlling position of
Addressing in the Address Space (containing the "Front-End" and
the "Back-End") to the "Front-End".
E Terrell Internet Draft [Page 121]
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Work(s) in Progress;
Computer Science / Internet Technology:
These drafts represent the twelve chapters of the Networking Bible,
designing a Network IP Addressing Specification that maintains a 100
Percent backward compatibility with the IPv4 Specification. In other
words, this is a design specification developed from the Theory of
the Expansion of the IPv4 IP Addressing Specification, which allowed
the representation of the Network for the entire World on paper, and
the possibility of an Infinite IP Address Pool. Nevertheless, the
Internet-Drafts listed below, 'Cited as Work(s) in Progress',
explain the design Specification for the development of the IPtX
(IP Telecommunications Specification) Protocol Addressing System and
the correction of the Mathematical Error in the Binary System.
1. http://www.ietf.org/internet-drafts/draft-terrell-logic-analy-
bin-ip-spec-ipv7-ipv8-10.txt - 'Work(s) in Progress'
(Foundational Theory for the New IPtX family IP Addressing
Specification, and the Binary Enumeration correction)
2. http://www.ietf.org/internet-drafts/draft-terrell-simple-proof-
support-logic-analy-bin-02.txt - 'Work(s) in Progress'
(The completion of the 2nd Proof correcting the error in Binary
Enumeration)
3. http://www.ietf.org/internet-drafts/draft-terrell-visual-change
-redefining-role-ipv6-01.pdf - 'Work(s) in Progress'
(Argument against the deployment of IPv6)
4. http://www.ietf.org/internet-drafts/draft-terrell-schem-desgn-
ipt1-ipt2-cmput-tel-numb-02.pdf - 'Work(s) in Progress'
(The foundation of the New IPtX IP Addressing Spec now similar
to the Telephone Numbering System)
5. http://www.ietf.org/internet-drafts/draft-terrell-internet-
protocol-t1-t2-ad-sp-06.pdf - 'Work(s) in Progress'
(The IPtX IP Addressing Specification Address Space/IP Address
Allocation Table; establishes the visual perspective that
actually represents Networking Schematic of the entire World.)
6. http://www.ietf.org/internet-drafts/draft-terrell-iptx-spec-def
-cidr-ach-net-descrip-01.pdf - 'Work(s) in Progress'
(Re-Defining 'CIDR' {Classless Inter-Domain Routing
Architecture} for the IPtX Addressing Standard)
E Terrell Internet Draft [Page 122]
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7. http://www.ietf.org/internet-drafts/draft-terrell-math-quant
-new-para-redefi-bin-math-04.pdf - 'Work(s) in Progress'
(The completion of the 3rd Proof correcting the error in Binary
Enumeration)
8. http://www.ietf.org/internet-drafts/draft-terrell-gwebs-vs-ieps
-00.pdf
(Global Wide Emergency Broadcast System) 'Work(s) in Progress'
9. http://www.ietf.org/internet-drafts/draft-terrell-iptx-dhcp-req
-iptx-ip-add-spec-00.pdf - 'Work(s) in Progress'
(The development of DHCP {Dynamic Host Configuration Protocol}
for the IPTX IP Addressing Spec)
10. http://www.ietf.org/internet-drafts/draft-terrell-iptx-dns-req
-iptx-ip-add-spec-03.pdf - 'Work(s) in Progress'
(The development of DNS {Domain Naming Specification} for IPTX
IP Addressing Spec)
11. http://www.ietf.org/internet-drafts/draft-terrell-math-quant
-ternary-logic-of-binary-sys-10.pdf(Derived the Binary System
from the proof of "Fermat's Last Theorem", and Developed the
Ternary Logic for the Binary System) 'Work(s) in Progress'
12. http://www.ietf.org/internet-drafts/draft-terrell-cidr-net
-descrpt-expands-iptx-add-spc-20.pdf 'Work(s) in Progress'
(An application of Quantum Scale Theory, the 2^X : 1
Compression Ratio, the Expansion derived from the 'CIDR
Network Descriptor, and the Mathematics of Quantification
provided the foundation for the development of the
"Intelligent Quantum Tunneling Worm Protocol"; A Routable
Mathematical Exponential Expression, BackEnd IP Addressing
Space using the Compression Ratio 2^X : 1.)
13. http://www.ietf.org/internet-drafts/draft-terrell-iptx-mx-dns-
specification-04.pdf (The development of the IPtX / IPtX-MX DNS
{Domain Name Service} for IPTX IP Addressing Spec)
'Work(s) in Progress'
14. http://www.ietf.org/internet-drafts/draft-terrell-iptx-mx-dhcp-
specification-00.pdf (The development of the IPtX / IPtX-MX DHCP
{Dynamic Host Configuration Protocol } for IPTX IP Addressing
Spec) 'Work(s) in Progress'
NOTE: These Drafts has Expired at www.ietf.org Web Site. However, you
can still find copies of these Manuscripts posted at Web Sites
all over the World. Suggestion; Perform Internet Search using
either 'Yahoo' or 'Google' - Keyword: 'ETT-R&D Publications'}.
E Terrell Internet Draft [Page 123]
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7. Normative References
Pure Mathematics:
1. The Proof of Fermat's Last Theorem; The Revolution in
Mathematical Thought {Nov 1979} E. Terrell
2. The Rudiments of Finite Algebra; The Results of
Quantification {July 1983} E. Terrell
3. The Rudiments of Finite Geometry; The Results of Quantification
{June 2003} E. Terrell
4. The Rudiments of Finite Trigonometry; The Results of
Quantification {July 2004} E. Terrell
5. The Mathematics of Quantification and the Metamorphosis of Pi:Tau
{October 200} E. Terrell
6. The Mathematics of Quantification & The Rudiments of Finite
Physics The Analysis of Newton's Laws of Motion...the Graviton'
{December 2004) E. Terrell
7. Squaring the Circle? First! What is the Circle's Area?
{January 2005}
The Rhind Papyrus Tale, and the 10,000 year old quest involving
"Squaring the Circle"; derivation of the equation resolving the
Area of the Circle. An illusion perplexing the Sight and Mind
of the greatest mathematicians for about 10,000 years, which
maintains an elementary algebraic solution:
(Pi(r)/2)^2 = Area of Circle.
E Terrell Internet Draft [Page 124]
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Informative References
1. 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.
2. R Carnap ( University of Chicago Press, 1947 / 1958 )
"Meaning and Necessity" A study in Semantics and
Modal Logic.
3. R Carnap ( Dover Publications, 1958 ) " Introduction to
Symbolic Logic and its Applications"
4. Regis Desmeules ( Cisco Press, April 24, 2003 ) " Cisco
Self-Study: Implementing Cisco IPv6 Networks "
5. Gary C. Kessler ( Auerbach Press, August 1997 )
" Handbook on Local Area Networks "
6. R. Hinden (Nokia) and S. Deering (Cisco Systems)
RFC 2373 - " IP Version 6 Addressing Architecture "
7. Authors: Scott Bradner, and Allison Mankin;
RFC 1550 - " IP: NextGeneration (IPng) White Paper
Solicitation "
E Terrell Internet Draft [Page 125]
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Author:
Eugene Terrell
Principle Director
Research & Development
Engineering Theoretical Technologies
Research & Development Publications
(ETT-R&D Publications)
3312 64th Avenue Place
Oakland, CA. 94605
Voice: 510-636-9885
E-Mail: eterrell00@netzero.net
"This work is Dedicated to my first and only child, 'Princess
Yahnay', because she is the gift of Dreams, the true treasure
of my reality, and the 'Princess of the Universe'. (E.T. 2007)"
E Terrell Internet Draft [Page 126]
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Copyright (C) The IETF Trust (2007).
This document is subject to the rights, licenses and restrictions
contained in BCP 78, and except as set forth therein, the authors
retain all their rights.
This document and the information contained herein are provided on an
"AS IS" basis and THE CONTRIBUTOR, THE ORGANIZATION HE/SHE REPRESENTS
OR IS SPONSORED BY (IF ANY), THE INTERNET SOCIETY, THE IETF TRUST,
AND THE INTERNET ENGINEERING TASK FORCE DISCLAIM ALL WARRANTIES,
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on the procedures with respect to rights in RFC documents can be
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Copies of IPR disclosures made to the IETF Secretariat and any
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The IETF invites any interested party to bring to its attention any
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this standard. Please address the information to the IETF at
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Acknowledgement
Funding for the RFC Editor function is provided by the IETF
Administrative Support Activity (IASA).
E Terrell Internet Draft [Page 127]
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