IT Professional, Author / Researcher E. Terrell Internet Draft September 1999 Document: draft-terrell-ip-spec-ipv7-ipv8-addr-cls-00.txt Expires March 17, 2000 Internet Protocol Specifications for IPv7 and IPv8 Address Classes Status of this Memo This document is an Internet-Draft and is in full conformance with all provisions of Section 10 of RFC2026.Internet-Drafts are working documents of the Internet Engineering Task Force (IETF), its areas, and its working groups. Note that other groups may also distribute working documents as Internet-Drafts. Internet-Drafts are draft documents valid for a maximum of six months and may be updated, replaced, or obsoleted by other documents at any time. It is inappropriate to use Internet- Drafts as reference material or to cite them other than as "work in progress." The list of current Internet-Drafts can be accessed at http://www.ietf.org/ietf/1id-abstracts.txt The list of Internet-Draft Shadow Directories can be accessed at http://www.ietf.org/shadow.html. Conventions Please note the font size of the Tables contained in this white paper are smaller than the expected 12 pts. However, if you are using the most current Web Browser, the View Section of the Title bar provides you with the option to either increase or decrease the font size for comfort level of viewing. (Provided that this is the HTML version.) Contents Abstract Overview Chapter I: An Overview of IPv7 the Expansion of Ipv4 Chapter II: An Overview of IPv8 the Enhancement of Ipv7 Chapter III:The Principles of Subnetting in IPv7 & IPv8 Chapter IV: The Structure of the Header of IPv8 Chapter V Conclusion:The Benefits of IPv7 and IPv8 Security Appendix I:Graphical Schematic of the IP Slide Ruler Appendix II: The Mathematical Anomaly Explained References Abstract This paper is a direct result, necessitated by the correction of the mathematical anomaly that plague IPv4. However, the resolution of this problem which sought an end to the disparities resulting from a shortage of available IP Addresses. Did not seem to garner the unfledging support, through the suggestion of an alternate IP system of addressing. As presented in the paper entitled; "The Mathematical Reality of IP Addressing in IPv4 Questions the need for Another IP System of Addressing". Needless to say, it is thought that a greater clarification of the underlining foundation of this subject matter is that which is needed. Notwithstanding my personal beliefs, that the promises made by the IT Industry itself, will not be forth coming if an adequate IP System of Addressing is not employed. Nevertheless, the Overview is an attempt to provide the reader with a succinct introductory foundation of those aspects of the Internet Protocol that will change as a direct result of the implementation of either IPv7 or IPv8. In other words, I shall present only those aspects of IPv4 that deal with its methods of Addressing and its former Class Structure. However, while admitting this would be an over simplification of its functional use or purpose, and a serious reduction of an adequate explanation of a vast majority the foundational information encompassing the IP Specification. It is nevertheless, seen justifiable, because the remaining aspects concerning the IP Specification will not change, and shall retain their functional use regardless of whether or not these systems are employed. However, there will not be any analysis, which would propose a mandate for implementation of either of these IP Addressing Systems, as the suitable replacement of IPv4. That is to say, not unless the foundations as presented by this work, become the Standard chosen after an extensive review and comprehensive analysis by the members of the committee for the IESG and IETF. In short, the analysis providing the support for a further exploitation of IPv4 has been presented, and the information provided in the remaining chapters of this paper shall entertain only the aspects of IPv7 and IPv8 which differ from that of IPv4. This however, does not include the chapter dealing with Subnetting. Especially since, there is a significant difference, and an argument can be made that would warrant not only a comparative analysis, but support for its justification as well. Overview There are only two main aspects of IPv4 addressing in the IP Specification that warrant mention; that being Addressing and Fragmentation. However, since the methods employed in fragmentation and the IP Specifications dealing with the interaction with other Protocols or its Modules, will not change as such, they will not be a subject entertained in this Overview. Where by, the matters that are presented in brief. Which entertains our present concerns, deal only with the subject matters of the IP Specifications that encompass the Class and the Classless Systems, and their functional use as employed in the IP Addressing of the current system. Nevertheless, the current IP Specification methodology for IP addressing in the IPv4 Addressing Scheme is the 'CLASSLESS System'. Needless to say, while the IP Specifications employing the 'CLASS System' in the IPv4 Addressing Scheme are no longer used. There are however, similarities remaining in each of these systems. In which they share a common foundation, and are still used in the IP Specification for IP Addressing. Where by, the shared practices, descriptions, and methodologies of each system is identified as being: 'The IPv4 Class Address Range'; 'The 32 Bit IP Address Format'; 'The Method for Subnetting'; 'The Principle of the Octet'; and 'The Binary and Decimal representations of the IP Address'. However, notwithstanding the treatment which will be rendered to each in this overview. There will also be a section outlining there differences as well. The Binary and Decimal representations in the IP Address The Binary and Decimal representations are two different mathematical systems of enumeration. In which the Binary Representation is a Mathematical System dealing with the operations of Logical Expressions having only two states, which can be translated to represent Integers and Fractions. While the Decimal Representation, is a Mathematical System involving the operations of Integers, and can only represent the Whole Numbers used in Counting. Nevertheless, in spite of the existing differences. These mathematical systems are shared and used by both, the Class and Classless Systems. The difference however, underlies the structure of their respective Mathematical Systems. In other words, only two Binary Representations exist, that being a 1 or a 0. However, the combined use of One's and Zero's in a series, can be used to represent any Integer. That is, for some representative combination of 1's and 0's in a series, there can exist one and only Integer, in which this Series is Equal to. Even then, a Mathematical Equation involving the Integers must exist, which would 'Translate' this Binary Representation into its Decimal (Integer) Equivalent. In which case, the result would be an enumeration representing 'One-to-One' Correspondence that is an Expression of Equality. In which two different systems represent the same quantity. Nonetheless, each would retain an independence from the other, in any quantitative result of their employ, governed by the Mathematical Laws specific to their operation. Nevertheless, the mathematical operation used to perform this Translation between the Binary and Decimal representations is Multiplication. In which the equation is an Exponential Operation involving Integers. Where by, for every Translation of any Decimal (Integer) number is given by Table 1. TABLE 1. 4 3 2 1 X X X X <---------| | | | | | | | | | v 1. | | | |<---> 2^0 = B x 2^0 | | | 2. | | |<---------> 2^1 = B x 2^1 | | 3. | |<---------------> 2^2 = B x 2^2 | 4. |<---------------------> 2^3 = B x 2^3 Where it is given that, the value of B represents the Binary representation of either a 1 or a 0. Which will equal the value of X (the top of the Table). Needless to say, it should be clear that any Decimal (Integer Value) can be represented using this method. Where by, a Binary value of 1, in the B column of equation 1, is a Binary value of 1 for its corresponding X, and the result of the equation is the Decimal (Integer value) value equal to 1. Hence, the Decimal representation is equal to the Sum of the results from the Equations for which the value of X equals 1, and this process proceeds from the Left to the Right. Nonetheless, while the process of Translating a Decimal (Integer value) number to its Binary equivalent is a little more involved, it is nonetheless this process (Noted above) in the reverse. Which is shown in Table 2. TABLE 2. 4 3 2 1 X X X X <-------> | | | | | | | | | | v 1. | | | |<---> 2^0 = D - (B x 2^0) = Y | | | 2. | | |<---------> 2^1 = D - (B x 2^1) = Y | | 3. | |<---------------> 2^2 = D - (B x 2^2) = Y | 4. |<---------------------> 2^3 = D - (B x 2^3) = Y In other words, the Reverse process proceeds from the Right to the Left. Which means, according to the corresponding equations, 'the Binary Representation of any Decimal Number D, is equal to the Decimal number (D) minus the Highest Value of the Exponential Equation yielding a Positive Number, Y. Until the value of their Difference, Y, at some point, is Equal to Zero. (Clearly Y is a Variable Integer) Nevertheless, it is clearly a conclusion, as noted in the Tables above, that the Binary Representation of an extremely large Integer number, would indeed, be a very long series of 1's and 0's. Especially since, 1 and 0 are the only numbers of these mathematical systems in which the equality of a One-to-One correspondence exist without the need for a mathematical Translation. Notwithstanding the fact that the Tables above used examples without any specifics or consideration regarding parameters. Nonetheless, in the IPv4 Addressing System, the Boundary's imposed upon the size of the Binary Series and the Range of the Decimal (Integer Values) Representations, help to define the 32 Bit Address Range of the Internet Protocol. Where by, there can only be 8 Bits (Binary 1's and or 0's) in a Binary Series, which provides, in Translation, a Decimal Range of 1 - 255, inclusive. Furthermore, it can also be concluded that the lack of a direct correlation between the 8 digit and 3 digit displacements that are the foundations of these respective systems, can not be achieved without some form of Translation or multiplication Factor. Which would render these respective displacements Equivalent. However, it should be clearly noted. There is soundness in any argument for logical foundation that would support such a justification. In other words, while it is clear that this Digital Representation is an existing difference between them. It should also be understood, that even without Translation they each can only represent one Integer Value. Needless to say, there abounds the possibility of Error in the Calculations involving either of these systems. Especially when either of these Mathematical Systems, are used to represent or determine some resulting value of the other. That is, errors become impossible to avoid without performing the necessary Translation to achieve the One-to-One correspondence, which maps accurately the Total count of one system to that of other. Saying the very least however, it seems to me, the choice would be to allow either the Machine to manipulate the Binary Numbers, or calculate using only the Decimal numbers, then translate the result to a Binary Representation. The 32 Bit Address Format and the Principle of the Octet The 32 Bit Address Format in use today, comprises 4 sections, each having a Binary Series of 8 Bits which can be any combination of 1's and 0's. Hence the name, Octet, represents the 8 Bit Binary representation, of which there are 4 that make up the 32 Bit Address Format. Nevertheless, its Decimal Translation, yields a Dotted Notation having an Integer Range of 0 - 255 inclusive. The IPv4 Address Class System The IP Class System, while somewhat blurred through the use of the Subnet Mask in the Supernetting methodology of the Classless System, it has not yet, lost the significance of its use. Nevertheless, it is given by the defacto Standard, that the IP Class of a given Network Address is determined by the Decimal value of the First Octet relative to the IP Address Class Range in which it is associated. This method is used in conjunction with the Default Subnet Mask to determine the total number of IP Addresses available for the calculation of the total number of Networks and Hosts, and their distribution counts for every IP Address Range. Where by, the Default Subnet Mask maintains a Decimal value of 255 for every Octet in which it is assigned. This Decimal value translates to a Binary Representation of all 1's, or 8 Binary 1's (11111111) in every Octet in which it is used. However, the mathematical method employed to resolve the Network IP Address in which the Default Subnet Mask is associated, is called BITWISE ANDING. Nonetheless, Bitwise Anding is a mathematical operation involving the Binary System, and is given by Table 3. TABLE 3 1. 1 and 1 = 1 2. 1 and 0 = 0 3. 0 and 0 = 0 Where by, the process of BITWISE ANDING is a Machine calculation that can be performed by anyone. Its functional purpose is the resolution of an IP Address, which can be either a Network or an associated Host. Nevertheless, the IP Class structure while providing a count of the total Networks and Hosts for each IP Class, as shown in Table 4. It additionally provided the IPv4 Addressing System with a structure, methodology, and a small set of rules to govern the distribution, deployment, and management of IP Addresses within any given Internetwork or Network domain. Nonetheless, Table 5 provides the description of its Binary interpretation, which is related to the number of available Binary Digits that can be used, when translated, to determine the Decimal Notation an IP Address, and the total number of addresses available. Table 4. Structure of the IPv4 Representation IP Class System Class A, 1 - 126, Default Subnet Mask 255.y.y.y: 126 Networks and 16,777,216 Hosts: 0 Class B, 128- 191, Default Subnet Mask 255.255.y.y: 16,384 Networks and 32,004 Hosts: 10 Class C, 192 - 223, Default Subnet Mask 255.255.255.y: 2,097,151 Networks and 254 Hosts: 110 Table 5 1. Class A: 1 - 126, with 8 Bit Network Count and 24 Bit Host count ; Where 0 (Zero ) and 127 reserved unknown Network and loopback 2. Class B: 128 - 191, with 14 Bit Network Count and 16 Bit Host count 3. Class C: 192 - 223, with 24 Bit Network Count and 8 Bit Host count 4. Class D: 224 - 239 ; Used for Multicasting, Host count not applicable 5. Class E: 240 - 254 ; Denoting Experimental, Host counts not applicable Note: There is no Division of Classes D or E. In fact, their definitions provide descriptions of their functional use. The Rules that enabled and govern the structure of the IPv4 Addressing System, are indeed laws. Where by, either the Internetwork or Networking Domain could become disabled, if a violation of any one or more of these laws occurred. Nevertheless, the laws as outlined in Table 6, represents a Set of Restrictions and their, regarding the Binary and Decimal values assigned to a given IP Address. However, any further, or more detailed analysis of Table 6 would be superfluous, because the presentation itself, is a definition. Nevertheless, notwithstanding the benefits that the hierarchical organizational structure of the IPv4 Class Addressing Scheme provided the Networking Community as a whole. The treatment rendered, regarding its explanation, while somewhat shallow, shall suffice as the grounding foundation for the overall purposes and objectives of this presentation. TABLE 6 1. The Network Address portion of an IP address cannot be Set to either all Binary Ones or All Binary Zeros 2. The Subnet portion of an IP address cannot be Set to either All Binary Ones or All Binary Zeros 3. The Host portion of an IP address cannot be Set to All Binary Ones or All Binary Zeros 4. The IP address 127.x.x.x can never be assigned as a Network Address The Differences between the Class and the Classless Systems The fall of the IPv4 Class System of Addressing, as such, is viewed as resulting from the lack of IP Addresses available for distribution and servicing the every growing Global Internetworking Community. However, the Internet Draft from which this results, describes an alternate view of the reality of its fall. Nevertheless, the IPv4 Class System has been described as an Organized Hierarchical Class Structure. But, this not a definitive depiction, noting that there are parts yet remaining within the IPv4 Class System, that are indeed wanting of a more conclusive and exacting definition of their functional purpose. This however, becomes even more apparent upon analysis of the use of Default Subnet Mask for the Class B. That is, when compared with the results of Appendix II and the definition of the use and purpose of the Default Subnet Mask. Where by, it is clear from the definition of the Default Subnet Mask. That its purpose defines the location of the Octet, which is assigned some Decimal Value from the IP Address Class Range. While, one of it uses, is the identification or resolution of a Network or Host IP Address. But clearly, this is not sufficient. Because this implies that only the first Octet of any given IP Address, maintains the right relative to the IP Address Range, to define the IP Class to which any given IP Address belongs. In other words, given the Class B as our example. Which has a Default Subnet Mask of 255.255.000.000. Then, given the results, as that given by equation 1a. We could conceivably derive two different Decimal Values, which would be an equally accurate determination of the number of Networks present in Class B. That is, provided there does not exist a more precise definition, and or, functional use of the Default Subnet Mask. 1a. 64 x 254 = 16,256 "OR" 64 x 64 = 4,096 (That is, given that: Class B 128 - 191, Default Subnet Mask 255.255.000.000) Needless to say, regardless of the method employed, they are clearly different numerical values representing the same object, which are indeed less than the Binary value given by 2^14 (16,384). Furthermore, without the indulgence of another example, this conclusion is applicable to the Class C as well. (This problem is eliminated in IPv7.) Nevertheless, the concept of Masking and its inverse,'Un-Masking', deserves some attention. That is, the Subnet Mask, which is the Catalysis for this presentation, is used by both of these Systems, the Class and Classless. However, it is the concept of the Subnet Mask, as it shall be discovered, which maintains a far greater significance when distinguishing the difference between these two Systems. Notwithstanding, the notion, idea, or evolution of the Class System would have been a resulting consequence, predicated by some inseparable component regardless. Where by, the misnomer, 'Classless', is not the existing difference, which mandates the defining distinction that separates these Systems. Needless to say, the doubt, which the underpinning of this conclusion surmounts, is the functional definition and the associated boundaries of the IP Class Addressing System. Which is indeed, the IP Addressing Divisional Methodology employed by each of these Systems. Nonetheless, without any support outlining or defining a Structure, one such component whose defined function, which would have caused the predestine evolution each, is indeed that of the Subnet Mask. (But! What are the losses? Or trade-offs of this implementation?) Nevertheless, the associated problems concerning IP Address availability were resolved through the creation of another Sub-Division of the Subnet Mask. Which indeed, is the 'DEBARKATION LINE', defining the difference between these Systems. However, this was a two-phase progression, involving two divisions of the Subnet Mask, the VLSM and the SUPERNETTING of the Class C, CIDR. Nevertheless, Supernetting maintains the distinction as being the USHER for the Classless. That is, the underlining difference distinguishing these Systems. It does moreover, impose a barrier, which limits the overview's presentation to the relevance pertaining thereto. Nonetheless, it is worthy of mention, noting that Supernetting can be viewed as a refinement of VLSM, Variable Length Subnet Mask. The promises of Supernetting, when viewed from its exploitation of the Class C, as relinquishing the dependence upon the Class Structured System, can be realized only if this application is applied to the remaining Classes. At least, this is the current and accepted outline of the Populist's view of the objectives presented. Notwithstanding, the most discomforting drawback encompassing this objective, is the elimination of the process and use of the Default Subnet Mask. Which ultimately means, the redefining of the functional use of all Binary 1's and 0's within the any given Octet, and the loss of the Logical Structure in IP Addressing as well. Nevertheless, there is indeed a warrant for an analysis of the process of Supernetting, which transcends the obligations of this overview. Needless to say, the foundational support of this argument is the underlining objectives found upon the Internet Draft upon which of this presentation resides. Nonetheless, prior to the analysis and investigation of Supernetting, a brief introduction of some of the foundational principles of Subnetting, from which Supernetting is derived, is required. The Binary Representation of 1's and 0's, and the specific rules for their combination or usage, is the chosen form of communication used in Machine Language. The principles of BITWISE ANDING was presented in the section entitled, "The IPv4 Address Class System", which is the mathematical method used by the Computer when the Subnet Mask or the Default Subnet Mask is used to resolve either a Network or Host IP Address. That is, if you were given a Decimal Network IP Address of 172.16.182.19, the Machine or Computer could not read nor translate these Integers into any usable format. That is to say, there is a Translator for the Input and Output for the Computer, because its language is of the Binary Format. In other words, the Computer would read the Input of the IP Address, 172.16.182.19, as that given by figure 1. Figure 1 Bit Map of the 32 Bit IP Address 10101100 00010000 10110110 00010011 However, through the use of the Default Subnet Mask, 255.255.255.000, and its Binary translation, as given in figure 2. The Computer or Router could, through the use of Bitwise Anding resolve the Network Address for the given IP Address, as shown in figure 3. Whose Decimal translation through the Binary Mathematics of Bitwise Anding would yields the Network IP Address as, 172.16.182.000. Figure 2 Bit Map of the 32 Bit IP Address 11111111 11111111 11111111 00000000 Figure 3 Bit Map of the 32 Bit IP Address 10101100 00010000 10110110 00000000 Nevertheless, there are several advantages that can be ascertained through the use of the Subnet Mask, and even more, if the mathematics of Bitwise Anding remain same. In other words, the problems associated with the difference between the Binary and Decimal methods of enumeration do not exist within the Machine's Mathematical Calculations for the Translation into the Binary format. That is, the Binary Format allows for the manipulation of individual BITS. Where by, the resulting Decimal Translation could be either a Fraction or an Integer. In which case, it is assumed that any resulting Fractional Component produces a Range of possible Subnet numbers in which several Network IP Addresses might belong. (Supernetting) Nonetheless, the Breaking-Up, or the division of any Network into smaller Sub-Networks, is called Subnetting. Which is accomplished through the use of the Subnet Mask. Where the Subnet Mask can be used or mapped onto any Octet, except the first Octet, which is used to identify the Address Class Range to which a particular IP Address might belong. Needless to say, there is a De Facto process by which a Subnet Number is chosen, and these numbers are given in Table 7. TABLE 7 Values of Least Binary Decimal Number Significant Bit: Representation: Equivalent: of Subnets: Host / per 0 00000000 0* 0 0 2^7 10000000 128 1 128 2^6 11000000 192 3 64 2^5 11100000 224 7 32 2^4 11110000 240 15 16 2^3 11111000 248 31 8 2^2 11111100 252 63 4 2^1 11111110 254 127 2 2^0 11111111 255* N/A Note: The 'Asterisk' represents Values that can not be used by the OCTET, which is define by the 'Subnet Mask' Although, this is not a Law. Nonetheless, the first example of the use of the Subnet was that of the Default Subnet Mask, which was used with the Binary Mathematical operation of Bitwise Anding to resolve the Network IP Address. However, from the list summarized by Table 7, the Subnetting concept can be further expanded, and use in an example to demonstrate the division of a Network Address into several smaller Network Addresses. That is, if given the Parent Network IP Address of '172.16.0.0', for which smaller Subdivisions are sought. This being the conclusion based upon an examination of the over all Network performance and needs. Then the appropriate Subnet Mask can be derived from the 7 choices given by Table 7 based upon the conclusions. Wherefore, if '252' is chosen, the IP address of this Decimal Number corresponds to the Subnet Mask given by an IP Address of '225.255.252.0'. In which a total number of 63 available Subnets can be generated from '252'. Which is the result generated by its (252) division by the factor determined as being the value of the Least Significant Bit of its Binary Representation (4). However, the inclusive count would maintain a composite value equal 64, which includes 252 in the total. Nevertheless, the resulting Subnet IP Addresses generated would be determined by sequential additions of the Least Significant Bit (4) to the Parent IP Network Address. Which also determine number of hosts per Subnet, and is summarized in Table 7. Notwithstanding, that the example above was a demonstration of the concepts and underlining the principles of Subnetting. However, its principles and concepts needless to say, is the foundation of which the principles underlining the concept of Supernetting is derived. Moreover, since it is the First Octet that is reserved for the Identification of the IP Address Class to which any IP Address belongs. The example chosen could have been selected from any one of the 3 primary IP Address Classes. Hence, Supernetting is the Subnetting of an IP Address having the Default Skeletal Structure as defined for the Class A. (The depiction rendered by this conclusion, is summarized in Table 8 of the next chapter.) The concepts for the principles and beliefs in the Classless System, in closing, is a derivation from the concepts of CLASSLESS INTERDOMAIN ROUTING (CIDR). In which, the basic strategy is the AGGREGATION of Multiple Divisions of an IP Address Class into One Network. Whose size would exceed that of the initial IP Address Class, and could be Routable using a 'One Route Path' for its thoroughfare. In other words, the only real difference between the CLASS and CLASSLESS Systems is that of the Routing Methodology they employ. Chapter I:An Overview of IPv7 the Expansion of Ipv4 The suitable replacement for IPv4 is IPv7, because it provides a greater adherence to the rules of any logical system having an underlining mathematical foundation. Furthermore, while the differences are small modifications to its foundational structure. It is nonetheless, an exploitation and expansion of IPv4. Which the analysis of Tables 4, 5, and 6, including the concepts of Supernetting, produces the results in Table 8 that provide the justification for the results of Table 9. In other words, the vast majority of the grounding principles and applications of IPv4 would be the same in IPv7. Nonetheless, it should be reasonably clear, that a Logical Foundation is the mandated requirement for any system to maintain longevity as an Organized Hierarchical Class Structure. In which case, the words 'De FACTO' and 'De JURE' would not have any relevant significance. Which would warrant the acceptance or use, of some standard that has no rational or logical foundation of its structure or application. Notwithstanding however, the Naming convention is arbitrary. That is, to avoid the problems associated with encoding '4.2', since IPv6 is being used, IPv7 was the next logical choice. Table 8. " The Reality resulting from Supernetting, the combination of TABLES 4 and 5 yields" Class A, 1 - 126, Default Subnet Mask 255.y.y.y: 126 Networks and 2^24 Hosts: 0 Total Number of IP Addresses Available: 126 x 16,777,216 = 2,113,929,216 Class B, 128- 191, Default Subnet Mask 255.y.y.y: 2^6 Networks and 2^24 Hosts: 10 Total Number of IP Addresses Available: 64 x 16,777,216 = 1,073,741,824 Class C, 192 - 223, Default Subnet Mask 255.y.y.y: 2^5 Networks and 2^24 Hosts: 110 Total Number of IP Addresses Available: 32 x 16,777,216 = 536,870,912 Class D, 224 - 239, Default Subnet Mask 255.y.y.y: 2^4 Networks and 2^24 Hosts: 1110 Total Number of IP Addresses Available: 16 x 16,777,216 = 268,435,456 Class E, 240 - 254, Default Subnet Mask 255.y.y.y: 15 Networks and 2^24 Hosts: 1111 Total Number of IP Addresses Available: 15 x 16,777,216 = 251,658,240 Note: Without having the Default Subnet Masking Define as limiting the values of the Octet to the Address Range of the Class in which it is mapped. Then, only the Value of the First Octet in any IP Address can Determine the IP Address Class of which, the resulting IP Address might belong. This means that, the Total number of IP Addresses available is equal to the Binary Bit Count of the Address Range multiplied by the Host Bit Count, 2^24. That is, every Class can maintain the Default IP Address as given for the Class A, which justifies the Expansion as given in Table 7. Table 9. "Structure of the 'IDEAL' Decimal Representation of the IP Class System" 1. Class A-1, 1 - 126, Subnet Identifier 255.000.000.000: 126 Networks and 254^3 Hosts: 0 Class A-2, 1- 126, Subnet Identifier 255.255.000.000: 126^2 Networks and 254^2 Hosts: 0 Class A-3, 1 - 126, Subnet Identifier 255.255.255.000: 126^3 Networks and 254 Hosts: 0 2. Class B-1, 128 - 191, Sublet Identifier 255.000.000.000: 64 Networks and 254^3 Hosts: 10 Class B-2, 128 - 191, Subnet Identifier 255.255.000.000: 64^2 Networks and 254^2 Hosts: 10 Class B-3, 128 -191, Subnet Identifier 255.255.255.000: 64^3 Networks and 254 Hosts: 10 3. Class C-1, 192 - 223, Subnet Identifier 255.000.000.000: 32 Networks and 254^3 Hosts: 110 Class C-2, 192 - 223, Subnet Identifier 255.255.000.000: 32^2 Networks and 254^2 Hosts: 110 Class C-3, 192 - 223, Subnet Identifier 255.255.255.000: 32^3 Networks and 254 Hosts: 110 4. Class D-1, 224 - 239, Subnet Identifier 255.000.000.000: 16 Networks and 254^3 Hosts: 1110 Class D-1, 224 - 239, Subnet Identifier 255.255.000.000: 16^2 Networks and 254^2 Hosts: 1110 Class D-3, 224 - 239, Subnet Identifier 255.255.255.000: 16^3 Networks and 254 Hosts: 1110 5. Class E-1, 240 - 254, Subnet Identifier 255.000.000.000: 15 Networks and 254^3 Hosts: 1111 Class E-2, 240 - 254, Subnet Identifier 255.255.000.000: 15^2 Networks and 254^2 Hosts: 1111 Class E-3, 240 - 254, Subnet Identifier 255.255.255.000: 15^3 Networks and 254 Hosts: 1111 Note: The Equation for Determining the IP Address Range for any IP Class is; (REN - RBN) + 1 = Total of Available IP Addresses for the given Class. (Where R = Range, E = End, B = Beginning, N = Number) However, the resulting expansion, that is IPv7, as summarized in Table 9 raises an issue, while not a major problem. It does indeed, represent a Mathematical Conflict within the of IPv7 Class Addressing Scheme, as depicted in Table 9. Where by, the Mathematics Analysis reveals that the Second Octet of the Primary Section of Each Class maintains a Set of Values within each of their respective IP Address Ranges. Which can not be employed or used as part of the count resulting in the total number of available IP Addresses. This is because they are not available as a valid IP Address, and if they were, then there would exist a mathematical conflict with the calculation of the total number of available IP Addresses of the Secondary Section for each IP Address Class. In other words, there would arise an error in reporting the results of the calculated totals. This can easily visualized when compared with the results of the second Octet of the Secondary Section for each of the IPv7 Class Address Ranges. That is, there exist a barrier imposed by the use of the Subnet Identifier of the second Octet from the Secondary Section of each IPv7 Class Address Schemes, with bars the use of any of the numbers given by the IP Address Range for that given IP Address Class. This is seen true, because the 1 - 254 total Host Count, does indeed contain all of the numbers available to be used as IP Addresses. However, this does not cripple the IPv7 Class Addressing System. Where by, the calculation of the mathematical difference between IP Address Range for each Class and the total Host count would yield the valid Address Range that can be use to calculate that total number of available IP Addresses. This however, is provided that there exist a distinction between, and definitions for the 'Default Subnet Mask', the 'Subnet Mask', and the 'Subnet Identifier', which are given below. Definitions 1. The Subnet Identifier defines the Default Subnet Mask and the Octet, which can only be assigned the values specified by in the IP Class Address Range within boundaries of IP Address Class in which it is used. 2. The Default Subnet Mask has a Binary value of 11111111 and a Decimal value of 255, it is used calculate the IP Network Address and to map the location of the Network portion of the IP Address defined by the Subnet Identifier. 3. The Subnet Mask is used to divide any Parent Network IP Address into several smaller and Logical Sub-Networks. When used in conjunction with the Default Subnet Mask, it identifies the resulting Sub-Network IP Address it was used to create. Nonetheless, the analysis of mathematical procedures for the elimination of this discrepancy is achieved by definitions resulting from the Laws of the Octet, which are summarized in Table 10. TABLE 10 {" The Laws of the Octet "} 1. By definition, there exist 3 distinct Sections or Divisions for every IP Address Class. However, the number of Sections or Divisions is dependent upon IP Bit Address Range defined for the IP Address. 2. The Sections or Divisions of the IP Address Class are defined as: Primary, Secondary, Ternary, etcàAnd are labeled according to their respective Class Location (e.g.: Class A would be Class A-1, Class A-2, Class A-3, and continued as would be necessary to distinguish the remaining Classes, B - E.) 3. The Subnet Identifier assigns to any Octet it defines in any Section or Division of every IP Class, when not use as the Default Subnet Mask, only the value of the numbers available in the IP Address Range assigned to that IP Class. 4. For every OCTET in any Section or Division of any IP Class that the Subnet Identifier does not define, can be assigned any value in the range of 1 - 254. That is, provided that there is no succeeding Section or Division, or if, there is an OCTET in a succeeding Section or Division, whose reference is the same, then it can not be defined by the Subnet Identifier. {This is seen true, because the Octet of this Section or Division, could not be in a Succeeding Section or Division which the Subnet Identifier can define.} 5. For every OCTET within any Section or Division of any IP Class, that is defined by the Subnet Identifier and is preceded by a Section or Division whose reference is the same Octet. Where the case is such that, the Octet of the preceding Section or Division is not defined by the Subnet Identifier. Then the Octet of the preceding Section, or Division, can not be assigned any value as given by the IP Address Range assigned to that IP Class. Needless to say, this situation can be further explored, through mathematical calculations. Where in the given example in this case would be Class A-1 and Class A-2. 1. Class A-1, 1 - 126, Subnet Identifier 255.000.000.000: 126 Networks and 254^3 Hosts: 0 2. Class A-2, 1- 126, Subnet Identifier 255.255.000.000: 126^2 Networks and 254^2 Hosts: 10 Nevertheless, the examination of these classes yields the conclusion. That if Class A-1's second Octet were to maintain any of the values in the IP Address Range, 1 - 126, then it would be reporting IP Address of Class A-2 because the second Octet of this Class is defined by the Subnet Identifier. However, the easiest mathematical method for the determination of the total number of available IP Addresses from Class A-1 would be to calculate the total number of IP Addresses available from its original configuration. Then subtract the value as would be determined from the calculation of the Class A-1 IP Address configuration that can not be used. In which case, we have: 3. Class A-1, 1 - 126, Subnet Identifier 255.126.000.000: 126 Networks and 254^2 Hosts: 0 4. 126 * (254)^2 = 8,129,016 Where the total, would be that given as: 5. 126 * (254)^3 = 2,064,770,064 In other words, the total number of available IP Addresses in Class A-1, that could be assigned as a Global (Parent) Network IP Address for connection to the Internetwork (That is, other than for use in a Private Domain Network), would be the difference between these equations. As given by: 6. 2,064,770,064 - 8,128,016 = 2,056,641,048 This method is summarized in Table 11. Where the results of equation 6 equals the total number of IP Addresses available for assignment as a Parent Network in a Global Internetworking Environment, and the results of equation 4 yield the number of Hosts that can be repeatedly assigned and used as private Domain Network IP Addresses. In which case, one would need to access the Parent Network to have access to any of these internal private Networks and Hosts identified by these IP Addresses. Thus, there would be no conflict from there continued use, which is the process now employed. Table 11. "Reality of the Structure of the Decimal Representation for the IP Class System."(Where the Value for the variable 'X' is given by the Rules in Table 6.) 1. Class A-1, 1 - 126, Subnet Identifier 255.x.x.y: 2,073,026,844 Networks and 8,033,256 Hosts: 0 Class A-2, 1- 126, Subnet Identifier 255.255.x.y: 1,028,256,768 Networks and 31,752 Hosts Class A-3, 1 - 126, Subnet Identifier 255.255.255.y: 472,660,218 Networks and 252, or X = 0, 253 Hosts 2. Class B-1, 128 - 191, Subnet Identifier 255.x.x.y: 1,052,966,016 Networks and 4,080,384 Hosts: 10 Class B-2, 128 - 191, Subnet Identifier 255.255.x.y: 265,281,792 Networks and 16,128 Hosts Class B-3, 128 -191, Subnet Identifier 255.255.255.y: 66,584,576 Networks and 252, or X = 0, 253 Hosts 3. Class C-1, 192 - 223, Subnet Identifier 255.x.x.y: 526,483,008 Networks and 2,040,192 Hosts: 110 Class C-2, 192 - 223, Subnet Identifier 255.255.x.y: 66,316,416 Networks and 8,064 Hosts Class C-3, 192 - 223, Subnet Identifier 255.255.255.y: 8,323,072 Networks and 252, or X = 0, 253 Hosts 4. Class D-1, 224 - 239, Subnet Identifier 255.x.x.y: 263,241,504 Networks and 1,020,096 Hosts: 1110 Class D-1, 224 - 239, Subnet Identifier 255.255.x.y: 16,577,088 Networks and 4,032 Hosts Class D-3, 224 - 239, Subnet Identifier 255.255.255.y: 1,040,384 Networks and 252, or X = 0, 253 Hosts 5. Class E-1, 240 - 254, Subnet Identifier 255.x.x.y: 246,788,910 Networks and 956,340 Hosts: 1111 Class E-2, 240 - 254, Subnet Identifier 255.255.x.y: 14,569,974 Networks and 3,276 Hosts Class E-3, 240 - 254, Subnet Identifier 255.255.255.y: 857,250 Networks and 252, or X = 0, 253 Hosts Note: The Rules given in Table 6 and Table 10 (Laws of the Octet) Limits the Range for the Value of the Variable 'X'. That is, when 'X' represents the HOST, then the Range of Values that 'X' can be assigned is given by the Equation: {X | If X = Y, then X = ([256 - 4] + 1)}. (X can never be Equal to the Numbers; 256, 255, 111, or 000) That is, if and only if, there exist no condition where 'X = N = Y', and N = the Octet defined by the Network IP Address, where when true, then {X | X = ([256 - 5] + 1)} However, when 'X' represents the Network, then the Range of Values that 'X' can be assigned is governed by the Laws of the Octet (Table ??) and given by the Equations: {X | If X = Y, then X = ([256 - 3] + 1)}, where 'X' can never be assigned the values, 256, 255, or 111. Or {X = X | If X = N, then ([256 - 2] + 1)}, where 'X' can Never be assigned the values, 256, or 255. The Subnetting features of Supernetting did not eliminate the IP Address Classes it just changed the format of the structure of their IP Address, which made the Class C become more appealing to the businesses seeking Global Internetworking Connections. However, the benefit was indeed significant to distribution and the availability of IP Addresses. This fact is evinced as a result of the Class restructuring its use ultimately produced. Which caused an increase in the number of IP Addresses available of Class B to twice its original value, and about 12 million for Class C. However, IPv7 doubles even this amount from its expansion of the IPv4 32 Bit Addressing Scheme. In other words, IPv4 offered approximately 3.12 * 10^9 IP Addresses, and Supernetting increased the number of available IP Addresses to approximate 3.6 * 10^9. While IPv7, its expansion given by Table 11, renders the number of available IP Addresses as being approximately 5.6 * 10^9. Which, to say the very least, is nearly double the original value, and the IP Address Bit Range remains '32'. The Binary Representation resulting from the use of Supernetting and IPv7, is summarized in Table 12 and 13 respectively. Table 12. "The Reality resulting from Supernetting, the Binary Representation" Class A, 1 - 126, Default Subnet Mask 255.y.y.y: 126 Networks and 2^24 Hosts: 0 Class B, 128- 191, Default Subnet Mask 255.y.y.y: 2^6 Networks and 2^24 Hosts: 10 Class C, 192 - 223, Default Subnet Mask 255.y.y.y: 2^5 Networks and 2^24 Hosts: 110 Class D, 224 - 239, Default Subnet Mask 255.y.y.y: 2^4 Networks and 2^24 Hosts: 1110 Class E, 240 - 254, Default Subnet Mask 255.y.y.y: 15 Networks and 2^24 Hosts: 1111 Table 13 Structure of the Binary Representation IPv7 Class System 1. Class A-1, 1 - 126, Subnet Identifier 255.000.000.000: 126 Networks and 2^24 Hosts: 0 Class A-2, 1- 126, Subnet Identifier 255.255.000.000: 2^15 Networks and 2^16 Hosts: 0 Class A-3, 1 - 126, Subnet Identifier 255.255.255.000: 2^23 Networks and 2^8 Hosts: 0 2. Class B-1, 128 - 191, Subnet Identifier 255.000.000.000: 2^6 Networks and 2^24 Hosts: 10 Class B-2, 128 - 191, Subnet Identifier 255.255.000.000: 2^14 Networks and 2^16 Hosts: 10 Class B-3, 128 -191, Subnet Identifier 255.255.255.000: 2^22 Networks and 2^8 Hosts: 10 3. Class C-1, 192 - 223, Subnet Identifier 255.000.000.000: 2^5 Networks and 2^24 Hosts: 110 Class C-2, 192 - 223, Subnet Identifier 255.255.000.000: 2^13 Networks and 2^16 Hosts: 110 Class C-3, 192 - 223, Subnet Identifier 255.255.255.000: 2^21 Networks and 2^8 Hosts: 110 4. Class D-1, 224 - 239, Subnet Identifier 255.000.000.000: 2^4 Networks and 2^24 Hosts: 1110 Class D-21, 224 - 239, Subnet Identifier 255.255.000.000: 2^12 Networks and 2^16 Hosts: 1110 Class D-3, 224 - 239, Subnet Identifier 255.255.255.000: 2^20 Networks and 2^8 Hosts: 1110 5. Class E-1, 240 - 254, Subnet Identifier 255.000.000.000: 15 Networks and 2^24 Hosts: 1111 Class E-2, 240 - 254, Subnet Identifier 255.255.000.000: 2^12 Networks and 2^16 Hosts: 1111 Class E-3, 240 - 254, Subnet Identifier 255.255.255.000: 2^20 Networks and 2^8 Hosts: 1111 Note: The number of Networks in the Primary Division of each Class, is the Quantified difference between the IP Address Range Plus 1, for each respective Class Boundary's. [(REN - RBN) + 1)]. Moreover, the Sublet Identifier, 255, has a Binary Representation of; 11111111. Nevertheless, by exploiting the Default Subnet Mask, that is, understanding its real purpose as used in BITWISE ANDING. Which is IP Network Address Resolution by determining the value of the defining Octet. Then anyone could easily visualize that, the former IPv4 Class Addressing Scheme, as summarized in Tables 4 and 5, warrants the expansion to that given by Table 11. Where the Default Subnet Mask, now the Subnet Identifier, assumes the duties of its actual definition. That is, it remains the Default Subnet Mask, which when used in Bitwise Anding serves to resolve the Network IP Address. This working definition provides further justification for the acceptance of IPv7. Especially since, IPv7 can now be viewed as the expansion of the IP Classes from the change in the Default Structure defining each division of the IP Class, which resulted from the use of Supernetting. This produced a change in all of the Structures of the IP Classes to the Default Structure as depicted for the Class A. In other words, IPv7's evolution is founded upon changes made in IPv4, that were used to compensate for the shortages in the number of available IP Addresses. However, the changes became the foundational premises of deductive reasoning, for the logical conclusion, which necessitates IPv7, and offers a cost free solution for the shortages in the number of available IP Addresses. Note: Other than the clarification of the functional purpose, enhanced specification for the definitions of a few terms, and the expansion the of the of IP Classes reduced by the use of Supernetting, IPv7 only provides a greater logical Structure, because nothing else changes as a result of its implementation. Chapter II: An Overview of IPv8 the Enhancement of Ipv7 The over all structure and organization regarding the overview of IPv8 offers no change to the foundation, as rendering a major distinction from that underlining IPv7. In other words, it is viewed as an enhancement of IPv7. Where by, IPv8 offers separate copies of the IP Addressing Scheme, as summarized in Table 11. Thus, providing a broader distribution and use of an unlimited number of available IP Addresses for the population of the entire World. Nevertheless, this is evinced by IPv7's IP Address Totals is nearly equal to the present World Population, which is approximately one IP Address assignment per person. In other words, the enhancement offered by IPv8 is characterized by the use and implementation of PREFIXES to the IP Address, such as, 'Country Codes', 'Zone Codes', and 'Area Codes'. The employment of these measures not only guarantees the promises of the IT Industry, while reducing the cost of Long Distance Telephone Calls, but offers a significant boost over the use of 'CIDR' in Router performance, as shall be discussed in the next chapter. In other words, the promises of the IT Industry encompassing the Interactive Television, Live Video Telephone Systems, Video Teleconferencing, and the evolution of a Global Telecommunication Community which encompassed everyone having a telephone today, becomes the Reality of its Dreamers. That is to say, with the implementation of IPv8, all of the promises of the IT Industry would now depend only on the development of the technology to produce these systems. Chapter III 'The Header Structure in IPv7 & IPv8' The IP Addressing Scheme of IPv7 can serve the Global Internetworking Community now. Its implementation offers some significant improvements over any system presently in use. However, while there is a learning curve, it would actually impose no challenge for the seasoned professional. In fact, there are two reasons that support the its implementation and the reality of it being the suitable replacement for IPv4. 1. It provides over 2 Billion additional IP Addresses. 2. Its Header does not change from that used in IPv4. In other words, IPv7 is a system that can be used now, which provides the ease of use and implementation of IPv4. While at the same time, providing an almost seamless transition for its enhancement, IPv8. Nevertheless, while IPv7 is called the "Global Internetworking Community", IPv8 is called the "Global Telecommunication Community". The difference however, distinguishing these systems, are two fold. Where by, the former is a shared IP Addressing System, which utilizes the Network medium for limited communication. However, the latter represents a Global Standardization for all Telecommunications Systems in use today. The advantages of IPv8 however, surmount far beyond any 32 Bit IP Addressing System now employed, or ever conceived. Nevertheless, while retaining the ease of use and implementation of IPv7, IPv8 provides an available number of IP Addresses that's staggering, to say the very least. In other words, the comparable analogy would be, IPv7 can provide an IP Address to every individual in the world today. While IPv8, can provide the same number of people with an individual IP Address on over 4 Billion worlds. That is to say, the people of planet Earth can colonize 4 Billion planets with a population equal to the existing count, and still have reserve IP Addresses. Nevertheless, while the foundations underlining IPv8 is the same as those of IPv7. There is indeed a distinction between these two systems, which accounts for the staggering number of available IP Addresses. The difference, while similar to IPv6, is the change in the structure of the IP Header associated with IPv8, and their depiction is given in Figure 5. Figure 5 IP Header for IPv4 and IPv7 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 | VER | IHL | TYPE OF SERVICE | TOTAL LENGHT | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | IDENTIFICATION |FLA| FRAGMENT OFFSET | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | TIME TO LIVE | PROTOCOL | CHECK SUM HEADER | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | SOURCE ADDRESS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | DESTINATION ADDRESS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | OPTIONS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | DATA | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| |-------------------------------------------------------------| IP Header for IPv8 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 | VER | IHL | TYPE OF SERVICE | TOTAL LENGHT | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | IDENTIFICATION |FLA| FRAGMENT OFFSET | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | TIME TO LIVE | PROTOCOL | CHECK SUM HEADER | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | RESERVED S | S RESERVED | IP S ZONE CODE | IP AREA CODE | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | SOURCE ADDRESS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | RESERVED D | D RESERVED | IP D ZONE CODE | IP AREA CODE | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | DESTINATION ADDRESS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | OPTIONS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | DATA | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| |-------------------------------------------------------------| IP Header for IPv6 0 1 2 3 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 | VER | PRIO. | FLOW LABEL | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| | PAYLOAD LENGTH | NEXT HEADER | HOP LIMIT | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| |-------------------------------------------------------------| | | | | | | | SOURCE ADDRESS | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| |-------------------------------------------------------------| | | | DESTINATION ADDRESS | | | | | |+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +| |-------------------------------------------------------------| |+ + + + + + + + + + + + + DATA + + + + + + + + + + + + + + + | |-------------------------------------------------------------| Nevertheless, the obvious lack of a detailed analysis of the Headers reduces the IPv8 Header to one being that of a suggestion. However, it is clear that IPv4 and IPv7 can share the same Header. But, from the structure as offered as choice for the Header of IPv8, an explanation is indeed warranted. Where by, the over all structure of the IPv8 Header of figure 5 is similar to that of IPv6, except that it 'Divides' the Source and Destination Sections of IPv6's Header Structure. However, its defining purpose is the same as that given for IPv7. The distinction however, is the addition of two additional sections, one for the Source and the other for the Destination. These additions make provisions for a greater individual use and deployment of this IP Addressing Scheme. Where by, above the Source Address Section exist another 32 Bit Section, which is divided into 4 distinct and separately defined Octets. There are 2 Octets reserved for growth and expansion, and another is defined as the Source Address Zone, while the last is defined as the Source IP Address Area Code. The Destination Address Section also has an additional 32 Bit section, which has comparable assignments, excepting that, they are defined for the Destination Address Section. Nevertheless, the numbering system employed for use in these sections is defined as the same as that governing the IP System of Address. While the Structure of this addressing system is given by Figure 6. FIGURE 6 1. Source Addressing Structure: 255:255:255.000.000.000 2. Source Addressing Structure: 255:255:255.255.000.000 3. Source Addressing Structure: 255:255:255.255.255.000 4. Destination Addressing Structure: 255:255:255.000.000.000 5. Destination Addressing Structure: 255:255:255.255.000.000 6. Destination Addressing Structure: 255:255:255.255.255.000 Notice that the Primary, Secondary, and Ternary IP Address Classes are also shown in addition to that of the Zone and IP Address Area Codes for the Source and Destination Addresses. Furthermore, it should be clear that each Octet preceding the IP Address is separated by a Colon, which not only indicates their distinction but an order of precedence as well. In other words, the establishment of a sequential order is another boon for IPv8. Especially when considering the Routing and networking implications. Where by, CIDR attempts to improve Router performance through the use of the Subnet Mask by looking at the Back End of an Aggregation the IP Address. Thus, allowing a reduction in the size of the Router's Table, and increasing the thoroughfare by permitting the assignment of several IP Addresses to this Back End Address. However, the implementation of IPv8 suggests just the opposite. Where by, Router's become more specialized Address Forwarding Computers, consisting of three divisions, the Global, the Internetwork, and the Network. These three divisions serve to reduce the Router's Table, reduce Traffic, and enhance System Management. These benefits are accomplished by programming the Routers to Route using the Front End of the IP Addresses. Thus, achieving a significant Router performance, which is a far superior improvement over that which can be achieved using the CIDR technique. The reality of these benefits becomes even clearer when an understanding of Front End Addressing achieved. That is, the Network Router checks first the Zone Address, then the IP AREA CODE Address. This allows the Router to determine if the communication is an Intercom or an Outercom. In which case, if it is Outercom, the Router needs only to know the location, and or Hop Count, of the nearest Internetworking or Global Router. Which need only be 2 or 3 connecting Routes beyond the single Point of Failure. However, while all Intercom communications are Routed as belonging somewhere within the Domain of its Network. The only the communications destine to either the Global or the Internetworking Telecommunication Community would need to access the Global or Internetworking Routers, which are located outside the Domain of the Network. Furthermore, while the Global and Internetworking Routers employ similar, but the reverse techniques of CIDR, the One Route Thoroughfare for Multi IP Address Access. The Back End of the IP Address is not considered until the IP Packet reaches the Gateway Router of its intended Destination. This clearly offers a boon for the Telecommunications Internetworking Industry, because the Router's in place now, only need an up grade of the IOS to perform these tasks. Notwithstanding the obvious benefits, if IPv8 is implemented as the Standard for the Global Telecommunication System Interface. A simple IP Address can become, as planned, the replacement for the Telephone Numbers in use today, because software could be used to eliminate the need for anyone to maintain the obligation of having to remember any number beyond 15 digits. That is, their IP Address and its associated IP Address Area Code Prefix. Nevertheless, it should be very clear, by now, that there can exist 254 Zones, which could result in the independent implementation of the entire IPv8 Addressing Scheme that could have 254 IP Address Area Codes for each IP Address Class and their associated Divisions. Needless to say, while the implementation of IPv8 does noting in the elimination of Subnetting. It does however question, because of the staggering number of IP Addresses available, the need for Supernetting. Especially since, only the IP Addresses assigned to the individual, which is accompanied by its Zone and IP Address Area Code, could have or maintained access to the Global Telecommunications System. Chapter IV The Principles of Subnetting in IPv7 & IPv8 The concepts and principles which underline the methods of Subnetting and its derivative, Supernetting, will not change. However, there some additional definitions and laws regarding their usage in IPv7 and IPv8. Nevertheless, these Laws and Definitions is a direct consequence of the information provided in the Overview, Table 10, and the definitions derived in Chapter I. Definitions 1. By Definition, every IP BIT Address is divided into sections called OCTETS. Where the first OCTET of any IP Bit Address must be Defined by the Subnet Identifier, and each Octet equals 8 Binary representations of either One's or Zero's that can collectively be Translated into one Decimal (Integer) Number. 2. Every Octet not defined by the Subnet Identifier, may be Defined by the Subnet Mask. Where the value of the Subnet Mask is defined as being equal to the resulting Difference Of Success Subtractions of the Binary number 1 = 2^0 = X and is given by the Equation: [SM = 2^7 - X]. Where by, the Subnet Mask = SM, and given by the Difference of each successive Subtraction of 2^0. 3. Every Network IP Address may contain at least one Subnet Mask. Where the Total Number of Subnet Mask that it can have, depend on the IP Bit Address Range Minus the first Octet in of the IP Address. 4. For every IP Address, having one or more Octets defined by the Subnet Identifier, also defines any IP Network Address which can be Subnetted. Where, if any Logical Division of an IP Network Address, creates multiple IP Addresses derived from the original. Then the derived IP Addresses are called Sub-Networks of the initial IP Address, which is said to be Subnetted. This is provided that every OCTET in the IP Bit Address Range is not defined by the Subnet Identifier. (Where the Subnet Identifier is equal to: 11111111 = 255; The Binary and Decimal Equivalents.). 5. Every Network IP Address having an Octet defined by a Subnet Mask, can be subdivided into only 1 Sub-Network. In which, there are a total of 7 possible logical Sub-Networks that may be defined. 6. For every Octet defined by the Subnet Mask for any Sub-Network IP Address. The Octet referenced as being the IP Network Address from which it was derived, can not be assigned any value in the IP Address Range of the derived Sub-Network IP Addresses. 7. The Laws of the OCTET are applied to every Octet defined by the Subnet Mask. That is, it can not be used in IP Address that would result in a conflict with any IP Address, whose Octet is defined by the Subnet Identifier. Where DE = the Decimal Equivalent that is also equal to the (BR) Binary Representation. That is, the Subnet Mask, can only be assigned the IP Address values summarized in the Table 7. Nonetheless, an example of this Binary Difference is given in Figure 4. Where by, given 2^7 = 11111111 = 255, is the Minuend, then successive Subtractions of 2^0 = 00000001 = the Subtrahend from the resulting Difference is equal to the Summary in Table 7. Figure 4 1. 11111111 - 00000001 = 11111110 = 254 2. 11111110 - 00000001 = 11111100 = 252 3. 11111100 - 00000001 = 11111000 = 248 4. 11111000 - 00000001 = 11110000 = 240 5. 11110000 - 00000001 = 11100000 = 224 6. 11100000 - 00000001 = 11000000 = 192 7. 11000000 - 00000001 = 10000000 = 128 8. 10000000 - 00000001 = 00000000 = 0 9. 11111111 - 11111111 = 00000000 = 0 Note: It should be clear that the Binary method of Subtraction is quite different from the Bitwise Anding method used by the Default Subnet Mask to resolve an IP Address. Nonetheless, there is a logical rationalization for the choice of the values of the Subnet Mask. Where by, the Binary Equations of Subtraction yields functional results, which has a 'Least Significant Digit', that is also the Factor use for the Translation of the Binary representation to its Decimal (Integer) Equivalent. TABLE 7 (Modification of Table 7 noted above) Least Significant Bit: Binary: Decimal: # of Subnets: Host / per | | | | | 0 00000000 0* 0 0 2^7 10000000 128 1 128 - 1 = 127 2^6 11000000 192 3 64 - 1 = 63 2^5 11100000 224 7 32 - 1 = 31 2^4 11110000 240 15 16 - 1 = 15 2^3 11111000 248 31 8 - 1 = 7 2^2 11111100 252 63 4 - 1 = 3 2^1 11111110 254 127 2 - 1 = 1 2^0 11111111 255* N/A N/A Note: The 'Asterisk' represents Values that can not be used by the OCTET, which is define by the 'Subnet Mask'. Nevertheless, since there exist a Total Count of 256 Decimal (Integers) representations expressing the total Number of available IP Addresses. That is, since this is an inclusive count of the given Range 0 - 255. Where by, equation 1, which enumerates this inclusive count, establish the Total number of IP Addresses in the Range '0 - 255'. 1. [(255 - 0) + 1] = 256. Moreover, this is also the Binary Representation, which equal of the inclusive count for the total addresses in the 0 - 255 Range. It can be concluded, that the Minuend 256, is some Multiple of the Number of Total Number of Hosts Bits. That is, given that calculation of this total, is also the inclusive count of the range comprising the Octets. In which case, the Binary Number of Hosts Available would be represented as 2^24, 2^16, and 2^8. Where by, these numbers represent a count relative to the Total Number IP Bit Mapped Host Addresses. However, if the case is such that, the total number of Host Bit available were, '65,536', and the Least Significant Digit given as '128'. Then, the Total of IP Host Bit Addresses available would be given by the equation 2. 2. [65,536 / 128 = 512] Furthermore, if the concept of Supernetting, was the Subnetting of the only Host Octet available in the Class C. Then, the total of IP Host Bit Addresses available, given a Least Significant Digit of 128, is equal to the equation 3. 3. [256 / 128 = 2] Nevertheless, the procedures involving Supernetting, as outlined in the Classless System, did not eliminate the Structure or concepts of the Class System. Especially since, it did not render any provisions to Subnet the only Host Octet available in the Class C. Needless to say, these conclusion clearly justifiable. Nonetheless, the change to the IP Address Skeleton of each Class as summarized in Table 8, and represents the structure of Class A. Notwithstanding, the Definitions and Laws defining the Internet Protocol Specifications for IPv7 and IPv8, which regarding their implementation, would change the concepts of Subnetting and Supernetting. That is to say, the definition of the Subnet Identifier imposes restrictions upon the availability of the Octets, which can be Subnetted or Supernetted. Given that, only the Host Octets are available, and those that can be Subnetted, are the last two within the IP Address. While Supernetting, is now defined as the process of Subentting the last Octet of an IP Address. In other words, the definitions and laws of IPv7 and IPv8 describe an outline for Supernetting and Subnetting, which can not violate the restrictions imposed. However, these changes do not usher any significant change, which would be a major departure from the foundational concepts of IPv4. In other words, except for the laws, definitions, and the resulting constraints imposed, the information provided herein, is the same as that which governed IPv4. Nevertheless, the Tables below summarize the logical format, which outlines the results of the concepts of Subnetting and Supernetting in IPv7 and IPv8. TABLE 14 Decimal & Subnets: Binary Result: Difference Factor: LSD: / ^ \ / ^ \ / ^ \ ^ / | \ / | \ / | \ | / v \ / v \ / v \ /v\ 1.(256 - 128) = 128 = 10000000, 256/128 - 128/128 = 1 2^7 2. 256 - 192 = 64 = 01000000, 256/64 - 192/64 = 1 2^6 3. 256 - 224 = 32 = 00100000, 256/32 - 224/32 = 1 2^5 4. 256 - 240 = 16 = 00010000, 256/16 - 240/16 = 1 2^4 5. 256 - 248 = 8 = 00001000, 256/8 - 248/8 = 1 2^3 6. 256 - 252 = 4 = 00000100, 256/4 - 252/4 = 1 2^2 7. 256 - 254 = 2 = 00000010, 256/2 - 254/2 = 1 2^1 TABLE 15 Subnetting Results in IPv7 and IPv8 Number: Binary Equation to Determine Available Bit Hosts: Equivalent: Subnet Bit Mask Hosts / | \ /|\ / | \ | 1. 512 = 2^9 (16 - 9 = 7) + 16 = 23 508 2. 1024 = 2^10 (16 - 10 = 6) + 16 = 22 1016 3. 2048 = 2^11 (16 - 11 = 5) + 16 = 21 2032 4. 4096 = 2^12 (16 - 12 = 4) + 16 = 20 4064 5. 8192 = 2^13 (16 - 13 = 3) + 16 = 19 8128 6. 16,384 = 2^14 (16 - 14 = 2) + 16 = 18 16,256 7. 32,768 = 2^15 (16 - 15 = 1) + 16 = 17 32,508 TABLE 15 Supernetting Results in IPv7 and IPv8 Number: Binary Equation to Determine Available Bit Hosts: Equivalent: Subnet Bit Mask Hosts / | \ /|\ / | \ / | \ 1. 2 = 2^1 (8 - 1 = 7) + 24 = 31 2 2. 4 = 2^2 (8 - 2 = 6) + 24 = 30 4 + 2 3. 8 = 2^3 (8 - 3 = 5) + 24 = 29 8 + 6 4. 16 = 2^4 (8 - 4 = 4) + 24 = 28 16 + 14 5. 32 = 2^5 (8 - 5 = 3) + 24 = 27 36 + 2 6. 64 = 2^6 (8 - 6 = 2) + 24 = 26 84 + 2 7. 128 = 2^7 (8 - 7 = 1) + 24 = 25 127 Note: The "+" after the Available Hosts Column reveals the number of Hosts remaining. However, this count can be adjusted, because its actual purpose is the determination of the number Hosts in relation to the number of BITS in the Subnet Mask for the Supernet. This situation becomes even more pronounced when the values assigned to the Last Octet of the Host must exclude, '111', '000', '255', and the number of the Supernet Mask (Which would also be a number included in the Network IP Address as well. For example; "255.255.255.Supernet Number".) Chapter V Conclusion: The Benefits of IPv7 and IPv8 The benefits from the implementation of IPV7 could be a reality now. This is because there are absolutely no changes in its Header, or any of the other specifications outlined in other RFC's pertaining to datagrams or its relation to other protocols. However, the addition of a more stringent adherence to the rules of Logic will, to most, seem beneficial. While, the growth in the number of available IP Addresses that are available for assignment and distribution, will usher a more stable growth of the Global Telecommunications Community. Moreover, while mistakes are unavoidable, they will not be an inherent part of the structure of this Addressing System. Furthermore, the benefits from the implementation of IPv8 will seem to overshadow the number of available IP Addresses it provides. That is, its implementation will foster the reality of dreams that were once thought the fantasy found in the pages of a Science fiction novel. This includes the simple problems as those experienced by the Telephone Companies, and the shortages in the supply of telephone numbers. Where by, the adoption of this system would change the count in the number of digits from the present 11, to a maximum of 15. Nonetheless, while this eliminates problems associated with growth and the constantly changing prefix. Its adoption could also change every concept in the Structure, Use, and Underlining Foundations of the Entire Telecommunication Industry. I mean, just think for a moment. Where, something as simple as the 'Junction Box', that now serves as the connecting and distribution point, for homes, business, and apartment complexes. It could quite conceivably, be replaced by a Network Server and a Router, which would lessen the burden associated with the cost of the present arrangement. In short, the existing Private Telephone System would be replaced with a Private Computerized Telecommunication System, and the Public Telephone System would become the Computerized Information Telecommunication Systems. These new systems could service the population of the entire World with any information available from some assigned Resource Distribution Center. While at the same time, IPv8 continues to open many other avenues of exploitation for the Industries of the Entire World. For example, the Television Industry, Cable Television Industry, the Video Telephoning and Video Teleconferencing Industry, are only a few of the many corporations that could benefit from its implementation. However, while this says nothing about the changes and benefits that its implementation offers the producer's of Networking equipment, or any of its associated Hardware and Software. It does nonetheless, bespeaks clearly about the promises and benefits of IPv8, which are indeed an endless reality bound only by the limits of our imagination. Security There are no security considerations rendered in this document. Appendix I: 'Graphical Schematic of the IP Slide Ruler' ====================================================================== = Octets 2st 3nd 4rd Figure 1 = | | ....... = | | . . = ----- v | . 001 . The IP Addressing Slide Ruler clearly = ^ ....... | ....... establishes the Differences between = | . ** . | . . Decimal and Binary Calculations. = | . 001 . v . 160 . Where, in this case, the Number of = | ................... Rulers or Slides, represents the = | ................... Maximum number of Hosts available in = | . . . . an IP Address Range having an = . 160 . 001 . 188 . Exponental Power of 3. That is, if = IP ................... the First Octet is Defined by the =Address ................... "Subnet Identifier", as providing =Range . . . . a Network within the IP Address = . 188 . 160 . 223 . Range assigned to this Class. That is, =1 - 254 ................... the individual Ruler or Slide, has a = | ................... one-to-one correspondence with the = | . . . . OCTET it represents, and is equal to = | . 223 . 188 . 239 . an Exponental Power of 1. Which also = | ................... maintains this one-to-one = | ................... relationship. In any case, it should = | . . . . be understood that the Decimal is an = | . 239 . 223 . 254 . Integer representing the IP Address, = | ................... and has only 1 value that occupies = | ................... the given Octet. However, the Binary = | . . . representation for the IP Address, is = | . 254 . 239 . an 8 digit Logical Expression = v ............. occuping one Octet. Where each digit = ----- ....... has a 2 state representation of either = . . a 1 or a 0. The distinction is that, = . 254 . this is a Logical expression, that has = ....... no Equivalence. However, there is a = Mathematical Method which resolves =The ( ** ) indicates this distinction, and allows for the =the Reference point Translation of each into the other. =of the IP Side Ruler. In other words, one System can never = be used to interpret any given value = of the other, at least, not without = the Mathematical Method used for = Translation. But each, can separately = be mapped to the structure of the 'IP = Slide Ruler ', rendering a translation = for one of the two representations. = (Noting that the Binary Translation of = its Decimal equivalent must be known = first.) ====================================================================== Appendix II : The Mathematical Anomaly Explained Nonetheless, this mathematical issue is an argument concerning, whether or not there exist a 'One-to-One' Correspondence between the Mathematical Calculations involving the Decimals (represented as Intehers) and those concerning the Binary Operators (Logical Expressions; the Truth Table values of 1's and 0's). Needless to say, this Mathematical Anomaly becomes even more apparent when one observes the Class B situation. Where by: 1. Class B; 128 -191, IP Address Range Default Subnet Mask; 255.255.000.000 (Which yields: 2^14 Networks and 2^16 Hosts; that is, 16,384 Networks and 65,536 Hosts.) However, this total is not the correct method of enumeration, and it is not the actual number (Integer Number) of available networks. And this FACT becomes even more apparent when the Binary Translation of the Decimal (Integers) Numbers is completed. That is, the result would yield 64 Binary Numerical Representations, ONE for each of the Decimal numbers (Integers) that are available in the IP Address for the Class B. Where Class B should maintain the representation (Which provides the actual Integer enumeration for the calculation of the total IP Addresses available. In other words, their independent count, of their respective totals for the Actual Number of Available IP Addresses in the Class B should Equal 64.) given by: 2. Class B: 128 -191, (Which equal the total of 64 possible IP Addresses for the given Address Range) Default Subnet Mask: 255.255.000.000 9Which results in 64^2 Networks and 254^2 Hosts; that is, 4,096 Networks and 64,516 Hosts.) Nevertheless, an enumeration or break down count association, of each representation, that is, Binary and Decimal. Would indeed, provide a greater support for the conclusion presented thus far. Where by, given the Classes noted in 1 & 2 above. We have: 1a. (128 + 128 + 128 + 128 + ...+ 128) = 128 x 128 = 2^14 1 2 3 4 ... - 128 = Total Count Which equal the Total number of Networks for the Given Address Range. and 1b. (255 + 255 + 255 + 255 +...+ 255) = 255 x 255 = 2^16 1 2 3 4 ... - 255 = Total Count Which equals the Total Number of Hosts for the Given Address Range. While noting that these equations represent the Binary Method for determining the number of Networks and Hosts for the given Address Range of Class B. However, keeping this in mind, notice the difference that exist when this same calculation is used for the Decimal (Integer) representation. 2a. (64 + 64 + 64 + 64 +...+ 64) = 64 x 64 = 64^2 1 2 3 4 ... - 64 = Total Count Where this number equals the number of Networks for the Given Address Range assigned to Class B. And 2b. (254 + 254 + 254 + 254 +...+ 254) = 254 x 254 = 254^2 1 2 3 4 ... - 254 = Total Count Where this equation represent the Total Number of Hosts for the Given Address Range of Class B. In other words, given the equation (191 -128) + 1 = 64. We are then presented with the Total Number of Addresses available for the given Address Range, 128 - 191, for the Class B. Where it can be seen that, any One-to-One mapping of the Numbers in the Address Range and the Counting Numbers (Integers), beginning with 1. Should yield the Total Number of Addresses available in any Count, for the Determination of the Total Number of Networks. And this same line of reasoning applies to the Host count, as well. ['Where the Subscript Number equals the Value of the Total Number of Availabe IP Addresses (a One-to-One Correspondence between the Enumeration of, and the Address Ranges given) for the Network and Host Ranges in Class B. Where both Binary and Decimal Number representations are the given examples.'] Nevertheless, when the Decimal and Binary conversion is completed. That is, when you establish a One-to-One relationship between the Binary and Decimal Numbers. You would discover that the their respective totals would be the same. That is, there can only be 64 Binary numbers and 64 Decimal numbers for the calculation of the Total Number of Networks. And there can only be 254 Binary Numbers and 254 Decimal Numbers for the calculation of the Total Number of Hosts. The difference is that, the former method reveals the Binary calculation, while the latter is the Integer (called the Decimal) Calculation. Needless to say, it should be very clear that the Binary method is a Logical Expression, and does see the Integer Count, that is the 'Difference between the Range Boundaries Plus 1'. Which yields the total number of available IP Addresses to be used to determine the actual number of Hosts within a given IP Address Class Range. Clearly, the Decimal method is indeed a Mathematical Expression representing the operations involving the Integers. Needless to say, if you are confused or are in doubt of these conclusions. Then my suggestion, would be to present my findings to a Professor of Mathematics at some well established university. References 1. E. Terrell ( not published notarized, 1979 ) " The Proof of Fermat's Last Theorem: The Revolution in Mathematical Thought " Outlines the significance of the need for a thorough understanding of the Concept of Quantification and the Concept of the Common Coefficient. These principles, as well many others, were found to maintain an unyielding importance in the Logical Analysis of Exponential Equations in Number Theory. 2. E. Terrell ( not published notarized, 1983 ) " The Rudiments of Finite Algebra: The Results of Quantification " Demonstrates the use of the Exponent in Logical Analysis, not only of the Pure Arithmetic Functions of Number Theory, but Pure Logic as well. Where the Exponent was utilized in the Logical Expansion of the underlining concepts of Set Theory and the Field Postulates. The results yield; another Distributive Property ( i.e. Distributive Law ) and emphasized the possibility of an Alternate View of the Entire Mathematical field. 3. G Boole ( Dover publication, 1958 ) "An Investigation of The Laws of Thought" On which is founded The Mathematical Theories of Logic and Probabilities; and the Logic of Computer Mathematics. 4. R Carnap ( University of Chicago Press, 1947 / 1958 ) "Meaning and Necessity" A study in Semantics and Modal Logic. 5. R Carnap ( Dover Publications, 1958 ) " Introduction to Symbolic Logic and its Applications" 6. Authors: Arnett, Dulaney, Harper, Hill, Krochmal, Kuo, LeValley, McGarvey, Mellor, Miller, Orr, Ray, Rimbey, Wang, ( New Riders Publishing, 1994 ) " Inside TCP/IP " 7. B Graham ( AP Professional, 1996 ) " TCP/IP Addressing " Lectures on the design and optimizing IP addressing. 8. Postel, J. (ed.), "Internet Protocol - DARPA Internet Program Protocol Specification," RFC 791, USC/Information Sciences Institute, September 1981. 9. Cisco Systems, Inc. ( Copyright 1989 - 1999 ) " Internetworking Technology Overview " 10. S. Bradner, A. Mankin, Network Working Group of Harvard University ( December 1993 ) " RFC 1550: IP: Next Generation (IPng) White Paper Solicitation " 11. RFC 791 12. E. Terrell (August 1999) Internet-Draft: "The Mathematical Reality of IP Addressing in IPv4 Questions the need for another IP System of Addressing". Author (Please comment to:) Eugene Terrell 24409 Soto Road Apt. 7 Hayward, CA. 94544-1438 Voice: 510-537-2390 E-Mail: eterrell00@netzero.net ["Copyright (C) [ The Internet Society (1999). All Rights Reserved. This document and translations of it may be copied and furnished to others, and derivative works that comment on or otherwise explain it or assist in its implementation may be prepared, copied, published and distributed, in whole or in part, without restriction of any kind, provided that the above copyright notice and this paragraph are included on all such copies and derivative works. However, this document itself may not be modified in any way, such as by removing the copyright notice or references to the Internet Society or other Internet organizations, except as needed for the purpose of developing Internet standards in which case the procedures for copyrights defined in the Internet Standards process must be followed, or as required to translate it into."]