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Why does the word "hexadecimal" have the prefix "hexa-" if it has a base of 16, not 6?

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hexa = 6, deci = 10. seems pretty obvious to me. –  tenfour Apr 30 '11 at 11:50
    
I find it odd because en.wikipedia.org/wiki/Senary is the numeral system with a base of 6. –  RyanScottLewis Apr 30 '11 at 11:52
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@c00lryguy, at the top of the wikipedia article you link, the article explains (one reasoning for) the choice of Senary over "heximal", the corollary of hexadecimal and decimal: "The name heximal is also valid for such a numeral system, but is deprecated to avoid confusion with the more often used hexadecimal number base, colloquially known as 'hex'." –  Tao Apr 30 '11 at 12:23
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Awesome site outlining greek and latin numerical prefixes (both of which come into play here): phrontistery.info/numbers.html –  Tao Apr 30 '11 at 12:34
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hexadecimal is a hybrid word, a mixture of Greek and Latin. Perhaps it would better be Greek (dekexial?) or Latin (sedecimal). –  Henry Apr 30 '11 at 12:49

4 Answers 4

up vote 5 down vote accepted

Hexa- is the Greek prefix for the number six, from hex, "six"; cf. hexagon, hexameter, hexad, etc.

Decimus is the Latin ordinal number "tenth"; cf. decimate, decimal.

This hybrid construction hexadecimal is strange but often seen in English to mean "sixteenth" or "pertaining to sixteen". It does not exist in either Latin or Greek, of course.

In Latin, it would be sedecimus, "sixteenth", leading to English sedecimal.

In Greek, in would be hekkaidekatos, "sixteenth", possibly leading to English heccaedecatic; but derivations of such polysyllabic Greek numbers are rarely used in English. The prefix would be heccaedeca-, as in a heccaedeca(h)edron, a polyhedron with sixteen surfaces.

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Back in those times, little importance was given to numbers beyond around 12. For this reason in english, numbers one through twelve are all unique names while a pattern emerges afterds (thir*teen* four*teen* fif*teen* etc.). They came afterwards. Consequently, the typical way to handle such ideas was to sum two such numbers to define a larger number. In fact, "thirteen" "fourteen" "fifteen" essentially only mean "3 10" "4 10" "5 10". –  Neil May 6 '11 at 14:04
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@Neil: True. And 11 and 12 also come from one-ten and two-ten in Latin (un-decim) and Greek (hen-deka). It is just the Germanic languages that use one-left and two-left ("one left if you remove ten", or something like that). –  Cerberus May 6 '11 at 14:18

If decimal is "ten-ly", hexadecimal is "six-ten-ly", or "sixteenly".

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Ahh yes, this makes sense to me. –  RyanScottLewis Apr 30 '11 at 12:35

Because "sexadecimal" would be considered too rude for IBM in the 50s.

Knuth says that it should be "senidenary." (The art of computer programming vol. 2 Seminumerical Algorithms p200.)

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Hmm, but Latin would be “sedecim-”, not “sexadecim-”. So that IBM story is probably apocryphal. –  Gilles Apr 30 '11 at 21:53

The prefix “hexa-” originally means six, it's “hexadecim-” that means sixteen. (Latin and greek had constructions similar to English for numbers between 13 and 19.) In computer-related usage, base 16 is very common, so the prefix for 16 has come to be systematically abbreviated “hex-” or “hexa-”. Since base 6 is never used, there's no ambiguity.

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I've been using base 6 ever since I lost four fingers in a taxidermy accident. –  Malvolio Apr 30 '11 at 18:02
    
It makes sense that the prefix is hexadecim and not hexa. After all, if the root was decimal then we'd say decidecimal for base 10, no? –  Scott Mitchell Apr 30 '11 at 21:44
    
@ScottMitchell: Strictly speaking, this should be “decaxi-” (Greek) or “sedecim-” (Latin). –  Gilles Apr 30 '11 at 21:53
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@Gilles: Where did you get decaxi-? Is that new Greek for tenth, perhaps? Sixteenth would be heccaidecatos in Ancient Greek; hexadecatos might exist in later Greek, though I doubt it. –  Cerberus May 2 '11 at 0:22
    
@Cerberus: Erm, yes, that was modern Greek, oops. I just wanted to nitpick on the Latin-Greek mixture and goofed. –  Gilles May 2 '11 at 7:08

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