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+Independent Submission                                          M. Breen
+Request for Comments: 9226                                    mbreen.com
+Category: Experimental                                      1 April 2022
+ISSN: 2070-1721
+
+
+                        Bioctal: Hexadecimal 2.0
+
+Abstract
+
+   The prevailing hexadecimal system was chosen for congruence with
+   groups of four binary digits, but its design exhibits an indifference
+   to cognitive factors.  An alternative is introduced that is designed
+   to reduce brain cycles in cases where a hexadecimal number should be
+   readily convertible to binary by a human being.
+
+Status of This Memo
+
+   This document is not an Internet Standards Track specification; it is
+   published for examination, experimental implementation, and
+   evaluation.
+
+   This document defines an Experimental Protocol for the Internet
+   community.  This is a contribution to the RFC Series, independently
+   of any other RFC stream.  The RFC Editor has chosen to publish this
+   document at its discretion and makes no statement about its value for
+   implementation or deployment.  Documents approved for publication by
+   the RFC Editor are not candidates for any level of Internet Standard;
+   see Section 2 of RFC 7841.
+
+   Information about the current status of this document, any errata,
+   and how to provide feedback on it may be obtained at
+   https://www.rfc-editor.org/info/rfc9226.
+
+Copyright Notice
+
+   Copyright (c) 2022 IETF Trust and the persons identified as the
+   document authors.  All rights reserved.
+
+   This document is subject to BCP 78 and the IETF Trust's Legal
+   Provisions Relating to IETF Documents
+   (https://trustee.ietf.org/license-info) in effect on the date of
+   publication of this document.  Please review these documents
+   carefully, as they describe your rights and restrictions with respect
+   to this document.
+
+Table of Contents
+
+   1.  Introduction
+     1.1.  The Pernicious Advance of Hexadecimal
+     1.2.  Problems with Hexadecimal
+     1.3.  Other Proposals
+   2.  Bioctal
+   3.  Objections to Be Dismissed
+   4.  Security Considerations
+   5.  IANA Considerations
+   6.  Conclusion
+   7.  Informative References
+   Acknowledgments
+   Author's Address
+
+1.  Introduction
+
+1.1.  The Pernicious Advance of Hexadecimal
+
+   Octal has long been used to represent groups of three binary digits
+   as single characters, and that system has the considerable merit of
+   not requiring any digits other than those already familiar from
+   decimal numbers.  Unfortunately, the increasing use of 16-bit
+   machines and other machines that have word lengths that are evenly
+   divisible by four (but not by three) has led to the widespread
+   adoption of hexadecimal.  Table 1 presents the digits of the
+   hexadecimal alphabet.
+
+                              +=======+=======+
+                              | Value | Digit |
+                              +=======+=======+
+                              |     0 | 0     |
+                              +-------+-------+
+                              |     1 | 1     |
+                              +-------+-------+
+                              |     2 | 2     |
+                              +-------+-------+
+                              |     3 | 3     |
+                              +-------+-------+
+                              |     4 | 4     |
+                              +-------+-------+
+                              |     5 | 5     |
+                              +-------+-------+
+                              |     6 | 6     |
+                              +-------+-------+
+                              |     7 | 7     |
+                              +-------+-------+
+                              |     8 | 8     |
+                              +-------+-------+
+                              |     9 | 9     |
+                              +-------+-------+
+                              |    10 | A     |
+                              +-------+-------+
+                              |    11 | B     |
+                              +-------+-------+
+                              |    12 | C     |
+                              +-------+-------+
+                              |    13 | D     |
+                              +-------+-------+
+                              |    14 | E     |
+                              +-------+-------+
+                              |    15 | F     |
+                              +-------+-------+
+
+                                 Table 1: The
+                             Hexadecimal Alphabet
+
+   The choice of alphabet is clearly arbitrary: On the exhaustion of the
+   decimal digits, the first letters of the Latin alphabet are used in
+   sequence for the remaining hexadecimal digits.  An arbitrary alphabet
+   may be acceptable on an interim or experimental basis.  However,
+   given the diminishing likelihood of a return to 18-bit computing, a
+   review of this choice of alphabet is merited before its use, like
+   that of the QWERTY keyboard, becomes too deeply established to permit
+   the easy adoption of a more logical alternative.
+
+1.2.  Problems with Hexadecimal
+
+   One problem with the hexadecimal alphabet is well known: It contains
+   two vowels, and numbers expressed in hexadecimal have been found to
+   collide with words offensive to vegetarians and other groups.
+
+   Imposing a greater constraint on the solution space, however, is the
+   difficulty of mentally converting a number expressed in hexadecimal
+   to (or from) binary.  Consider the hexadecimal digit 'D', for
+   example.  First, one must remember that 'D' represents a value of 13
+   -- and, while it may be easy to recall that 'F' is 15 with all bits
+   set, for digits in the middle of the non-decimal range, such as 'C'
+   and 'D', one may resort to counting ("A is ten, B is eleven, ...").
+   Next, one must subtract eight from that number to arrive at a number
+   that is in the octal range.  Thus, the benefit of representing one
+   additional bit incurs the cost of two additional mental operations
+   before one arrives at the position where the task that remains
+   reduces to the difficulty of converting the remaining three digits to
+   binary.
+
+   These mental steps are not difficult per se, since a child could do
+   them, but if it is possible to avoid employing children, then it
+   should be avoided.  An appeal to the authority of cognitive
+   psychology is perhaps also due here, in particular to the "seven plus
+   or minus two" principle [Miller] -- either because octal is within
+   the upper end of that range (nine) and hexadecimal is not, or else
+   because the difference in the size of the alphabets is greater than
+   the lower end of that range (five).  Either way, it is almost
+   certainly relevant.
+
+1.3.  Other Proposals
+
+   Various alternatives have already been suggested.  Some of these are
+   equally arbitrary, e.g., in selecting the last six letters of the
+   Latin alphabet rather than the first six letters.
+
+   The scheme that comes closest to solving the main problem to date is
+   described by Bruce A. Martin [Martin] who proposes new characters for
+   the entire octal alphabet.  While his principal motivation is to
+   distinguish hexadecimal numbers from decimals, the design of each
+   character uses horizontal lines to directly represent the "ones" of
+   the corresponding binary number, making mental translation to binary
+   a trivial task.
+
+   Unfortunately for this and other proposals involving new symbols,
+   proposals to change the US-ASCII character set [USASCII] might no
+   longer be accepted.  Also, it seems unrealistic to expect keyboards
+   or printer type elements (whether of the golf ball or daisy wheel
+   kind) to be replaced to accommodate new character designs.
+
+2.  Bioctal
+
+   Table 2 presents the hexadecimal alphabet once again, this time in a
+   sequence of two octaves with values increasing left to right and top
+   to bottom.
+
+                     +---+---+---+---+---+---+---+---+
+                     | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
+                     +---+---+---+---+---+---+---+---+
+                     | 8 | 9 | A | B | C | D | E | F |
+                     +---+---+---+---+---+---+---+---+
+
+                          Table 2: The Hexadecimal
+                           Alphabet in Sequential
+                                  Octaves
+
+   Arranged thus, the binary representation of each digit in the second
+   octave is the same as the digit above it, but with the most
+   significant of the four bits set to '1' instead of '0'.
+
+   The incongruity of two decimal digits in the second octave also
+   suggests that, in blindly aligning with four bits, hexadecimal (six
+   plus ten, neither of which are powers of two) misses an opportunity
+   to align also with three bits.
+
+   Bioctal restores congruence by replacing the second row with
+   characters mnemonically related to the corresponding character in the
+   first octave.
+
+   Table 3 shows the compelling result.
+
+                     +---+---+---+---+---+---+---+---+
+                     | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
+                     +---+---+---+---+---+---+---+---+
+                     | c | j | z | w | f | s | b | v |
+                     +---+---+---+---+---+---+---+---+
+
+                            Table 3: Bioctal in
+                             Sequential Octaves
+
+   The mnemonic basis is the shape of the lowercase character.  This is
+   seen directly for '2', '5', and '6'.  For '3', '4', and '7', the
+   corresponding letters are the result of a quarter-turn clockwise
+   (assuming an "open" '4').  The choice of 'c' and 'j' for '0' and '1'
+   avoids vowels and lowercase 'L', the latter being confusable with '1'
+   in some fonts.
+
+   With this choice of letters, it is immediately evident that both
+   problems with hexadecimal are solved.  Mental conversion is now
+   straightforward: if the digit is a letter, then the most significant
+   of the four binary bits is '1', and the remaining three bits are the
+   same as for the Arabic numeral with the same shape in the first
+   octave.
+
+3.  Objections to Be Dismissed
+
+   Several objections can be anticipated, the first of which concerns
+   the name.  The term "bioctal" is already used to refer to the
+   combination of two octal characters into a single field on, for
+   example, paper tape (e.g., [UNIVAC]).  However, if the word "bioctal"
+   must be disadvantaged relative to words such as "biannual" in the
+   number of meanings it is allowed to have, then it is the paper tapers
+   who must give way: in that context, the "octal" part of "bioctal"
+   refers to the number of distinct values that three bits can have,
+   while the "bi" refers to a doubling of the number of bits, not
+   values.  A meaning depending on such a discordant etymology does not
+   deserve to endure.
+
+   Second, it may be argued that the use of hexadecimal has already
+   become too entrenched to be changed in the short term: Bioctal should
+   be introduced only after those working in the industry who have grown
+   accustomed to hexadecimal have retired.  Such a dilatory contention
+   cannot be allowed to impede the march of progress.  Instead, any data
+   entry technician who claims to have difficulty with bioctal may be
+   reassigned to duties involving only binary numbers.
+
+   A third possible objection is that numbers in bioctal do not sort
+   numerically.  However, this assumes a sort based on the US-ASCII
+   order of symbols; it is quite possible that bioctal numbers sort
+   naturally in some lesser known variety of EBCDIC.  Further,
+   resistance to numeric sorting may be an indicator of virtue, being
+   suggestive of an alphabet with a certain strength of character.
+
+   One difficulty remains: Not all computers support lowercase letters.
+   While this is indeed true, it should be confirmed in any particular
+   instance: the author has observed that in many cases a machine having
+   a keyboard with buttons marked only with uppercase letters also
+   supports lowercase letters.  In any case, it is permissible to use
+   uppercase letters instead of the lowercase ones of Table 3; the
+   morphology mnemonic continues to work for most bioctal digits in
+   uppercase, although an extra mental cycle is required for 'B'.
+
+4.  Security Considerations
+
+   The letters 'b' and 'f' appear in both the bioctal and hexadecimal
+   alphabets, which makes potential misinterpretation a concern.  A case
+   of particular hazard arises where two embedded systems engineers work
+   to develop a miniature lizard detector designed to be worn like a
+   wristwatch.  One engineer works on the lizard proximity sensor and
+   the other on a minimal two-character display.  The interface between
+   the circuits is 14 bits.  To make things easier, the engineer working
+   on the display arranges for these bits to be set in a pattern that
+   allows them to be used directly as two seven-bit US-ASCII characters
+   indicating the most significant lacertilian species detected in the
+   vicinity of the device.  Due to the use of an old US-ASCII table
+   (i.e., one in hex, not bioctal) and human error, some of the values
+   specified as outputs for the detection subsystem are in hexadecimal,
+   not the bioctal the engineer developing that subsystem expects --
+   including, in the case of one type of lizard, "4b 4f".  The result is
+   that the detector displays "NL" (No Lizards) when it should display
+   "KO" (Komodo dragon).  This may be considered prejudicial to the
+   security of the user of the device.
+
+   Extensive research has uncovered no other security-related scenarios
+   to date.
+
+5.  IANA Considerations
+
+   This document has no IANA actions.
+
+6.  Conclusion
+
+   Bioctal is a significant advance over hexadecimal technology and
+   promises to reduce the small (but assuredly non-zero) contribution to
+   anthropogenic global warming of mental hex-to-binary conversions.
+   Since the mnemonic basis of the alphabet is independent of English or
+   any other particular natural language, there is no reason that it
+   should not be adopted immediately around the world, excepting perhaps
+   certain islands of Indonesia to which _Varanus komodoensis_ is
+   native.
+
+7.  Informative References
+
+   [Martin]   Martin, B. A., "Letters to the editor: On binary
+              notation", Communications of the ACM, Vol. 11, No. 10,
+              DOI 10.1145/364096.364107, October 1968,
+              <https://doi.org/10.1145/364096.364107>.
+
+   [Miller]   Miller, G. A., "The Magical Number Seven, Plus or Minus
+              Two: Some Limits on Our Capacity for Processing
+              Information", Psychological Review, Vol. 101, No. 2, 1956.
+
+   [UNIVAC]   Sperry Rand Corporation, "Programmers Reference Manual for
+              UNIVAC 1218 Computer", Revision C, Update 2, November
+              1969, <http:/bitsavers.computerhistory.org/pdf/univac/
+              military/1218/PX2910_Univac1218PgmrRef_Nov69.pdf>.
+
+   [USASCII]  American National Standards Institute, "Coded Character
+              Set -- 7-bit American Standard Code for Information
+              Interchange", ANSI X3.4, 1986.
+
+Acknowledgments
+
+   The author is indebted to R. Goldberg for assistance with Section 4.
+
+Author's Address
+
+   Michael Breen
+   mbreen.com
+   Email: rfc@mbreen.com