Editing Hexadecimal (section)

==Cultural history==
The traditional [[Chinese units of measurement]] were base-16. For example, one jīn&nbsp;(斤) in the old system equals sixteen [[tael]]s. The [[suanpan]] (Chinese [[abacus]]) can be used to perform hexadecimal calculations such as additions and subtractions.<ref>{{Cite web|url=http://totton.idirect.com/soroban/Hex_as/|title=算盤 Hexadecimal Addition & Subtraction on a Chinese Abacus|website=totton.idirect.com|access-date=2019-06-26|archive-date=2019-07-06 |archive-url=https://web.archive.org/web/20190706221609/http://totton.idirect.com/soroban/Hex_as/|url-status=live}}</ref>

As with the [[duodecimal]] system, there have been occasional attempts to promote hexadecimal as the preferred numeral system. These attempts often propose specific pronunciation and symbols for the individual numerals.<ref>{{cite web
 | url = http://www.hauptmech.com/base42
 | title = Base 4^2 Hexadecimal Symbol Proposal
 | website = Hauptmech
 | access-date = 2008-09-04
 | archive-date = 2021-10-20
 | archive-url = https://web.archive.org/web/20211020192525/http://www.hauptmech.com/base42/wiki/index.php?title=Main_Page
 | url-status = live
 }}</ref> Some proposals unify standard measures so that they are multiples of 16.<ref>{{cite web|url=http://www.intuitor.com/hex/|title=Intuitor Hex Headquarters|website=Intuitor|access-date=28 October 2018|archive-date=2010-09-04 |archive-url=https://web.archive.org/web/20100904144850/http://www.intuitor.com/hex/|url-status=live}}</ref><ref>{{cite web|url=https://www.unicode.org/wg2/docs/n2677.pdf |title=A proposal for addition of the six Hexadecimal digits (A-F) to Unicode |last=Niemietz|first=Ricardo Cancho|date=21 October 2003 |publisher=ISO/IEC JTC1/SC2/WG2 |access-date=2024-06-25}}</ref>
An early such proposal was put forward by [[John W. Nystrom]] in ''Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to be called the Tonal System, with Sixteen to the Base'', published in 1862.<ref name="nystrom">{{cite book|url=https://archive.org/details/bub_gb_aNYGAAAAYAAJ|title=Project of a New System of Arithmetic, Weight, Measure and Coins: Proposed to be called the Tonal System, with Sixteen to the Base|last=Nystrom|first=John William|publisher=Lippincott|year=1862|location=Philadelphia}}</ref>
Nystrom among other things suggested [[hexadecimal time]], which subdivides a day by 16,
so that there are 16 "hours" (or "10 ''tims''", pronounced ''tontim'') in a day.<ref>Nystrom (1862), p. 33:
"In expressing time, angle of a circle, or points on the compass, the unit ''tim'' should be noted as integer, and parts thereof as ''tonal fractions'', as 5·86 ''tims'' is five times and ''metonby'' [*"sutim and metonby" John Nystrom  accidentally gives part of the number in decimal names; in Nystrom's pronunciation scheme, 5=su, 8=me, 6=by, c.f. [http://www.unifoundry.com/tonal/index.html unifoundry.com] {{Webarchive|url=https://web.archive.org/web/20210519080658/http://www.unifoundry.com/tonal/index.html |date=2021-05-19  }} ]."</ref>

{{anchor|Etymology}}{{wiktionary|hexadecimal}}
The word ''hexadecimal'' is first recorded in 1952.<ref>C. E. Fröberg, ''Hexadecimal Conversion Tables'', Lund (1952).</ref> It is [[macaronic]] in the sense that it combines [[Greek language|Greek]] ἕξ (hex)  "six" with [[Latin]]ate ''-decimal''.
The  all-Latin alternative ''[[:wikt:sexadecimal|sexadecimal]]'' (compare the word ''[[sexagesimal]]'' for base 60) is older, and sees at least occasional use from the late 19th century.<ref>
''The Century Dictionary'' of 1895 has ''sexadecimal'' in the more general sense of "relating to sixteen".
An early explicit use of ''sexadecimal'' in the sense of "using base 16" is found also in 1895, in  the ''Journal of the American Geographical Society of New York'', vols. 27–28, p. 197.</ref>
It is still in use in the 1950s   in [[Bendix Corporation|Bendix]] documentation.
Schwartzman (1994) argues that use of  ''sexadecimal'' may have been avoided because of its suggestive abbreviation to ''sex''.<ref>{{cite book|first=Steven|last=Schwartzman|title=The Words of Mathematics: An etymological dictionary of mathematical terms used in English|date=1994|publisher=The Mathematical Association of America|page=105|isbn=0-88385-511-9}} s.v. hexadecimal</ref>
Many western languages since the 1960s have adopted terms equivalent in formation to ''hexadecimal'' (e.g. French ''hexadécimal'', Italian ''esadecimale'', Romanian ''hexazecimal'', Serbian ''хексадецимални'', etc.)
but others have introduced terms which substitute native words for "sixteen" (e.g. Greek  δεκαεξαδικός, Icelandic ''sextándakerfi'', Russian ''шестнадцатеричной'' etc.)

Terminology and notation did not become settled until the end of the 1960s.
In 1969, [[Donald Knuth]] argued that the etymologically correct term would be ''senidenary'', or possibly ''sedenary'', a Latinate term intended to convey "grouped by 16" modelled on ''binary'', ''ternary'', ''quaternary'', etc.
According to Knuth's argument, the correct terms for   ''decimal'' and ''octal'' arithmetic would be ''denary'' and ''octonary'', respectively.<ref>Knuth, Donald. (1969). ''[[The Art of Computer Programming]], Volume 2''. {{isbn|0-201-03802-1}}. (Chapter 17.)</ref>
Alfred B. Taylor used ''senidenary'' in his mid-1800s work on alternative number bases, although he rejected base 16 because of its "incommodious number of digits".<ref>Alfred B. Taylor, [https://archive.org/details/reportonweights00taylgoog Report on Weights and Measures], Pharmaceutical Association, 8th Annual Session, Boston, 15 September 1859.  See pages and 33 and 41.</ref><ref>Alfred B. Taylor, "Octonary numeration and its application to a system of weights and measures", [https://books.google.com/books?id=KsAUAAAAYAAJ&pg=PA296 ''Proc Amer. Phil. Soc.'' Vol XXIV] {{Webarchive|url=https://web.archive.org/web/20160624070056/https://books.google.com/books?id=KsAUAAAAYAAJ&pg=PA296 |date=2016-06-24  }}, Philadelphia, 1887; pages 296–366.  See pages 317 and 322.</ref>

The now-current notation using the letters A to F establishes itself as the de facto standard beginning in 1966, in the wake of the
publication of the [[Fortran IV]] manual for [[IBM System/360]], which (unlike earlier variants of Fortran) recognizes a standard for entering hexadecimal constants.<ref>[http://www.bitsavers.org/pdf/ibm/360/fortran/C28-6515-6_FORTRAN_IV_Language_1966.pdf IBM System/360 FORTRAN IV Language] {{Webarchive|url=https://web.archive.org/web/20210519073220/http://www.bitsavers.org/pdf/ibm/360/fortran/C28-6515-6_FORTRAN_IV_Language_1966.pdf |date=2021-05-19  }} (1966), p. 13.</ref>
As noted above, alternative notations were used by [[NEC]]  (1960)  and The Pacific Data Systems&nbsp;1020 (1964). The standard adopted by IBM seems to have become widely adopted by 1968, when Bruce Alan Martin
in his  letter to the editor of the [[Communications of the ACM|CACM]] complains that
{{blockquote|With the ridiculous choice of letters A, B, C, D, E, F as hexadecimal number symbols adding to already troublesome problems of distinguishing octal (or hex) numbers from decimal numbers (or variable names), the time is overripe for reconsideration of our number symbols. This should have been done before poor choices gelled into a de facto standard!}}
Martin's argument was that  use of numerals 0 to 9 in nondecimal numbers  "imply to us a base-ten place-value scheme":
"Why not use entirely new symbols (and names) for the seven or fifteen nonzero digits needed in octal or hex. Even use of the letters A through P would be an improvement, but entirely new symbols could reflect the binary nature of the system".<ref name="Martin_1968"/>
He also argued that "re-using alphabetic letters for numerical digits represents a gigantic backward step from the invention of distinct, non-alphabetic glyphs for numerals sixteen centuries ago" (as [[Brahmi numerals]], and later in a [[Hindu–Arabic numeral system]]),
and that the recent [[ASCII]] standards (ASA X3.4-1963 and USAS X3.4-1968)
"should have preserved six code table positions following the ten decimal digits
-- rather than needlessly filling these with punctuation characters"
(":;<=>?") that might have been placed elsewhere among the 128 available positions.
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