Talk:Hexadecimal

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The word "hexadecimal" is strange in that "hexa" is derived from Greek six and "decimal" is derived from Latin ten. The original term was the fully-Latin "sexidecimal", but that was changed because some people thought it to be too racy. The correct Greek would be hexagesimal, which some purists use.

The first sentence is OK. The second sentence is true, but "sexidecimal" seems to be used to mean "base 60" more often than "base 16". The third sentence is untrue, because "hexagesimal" (if it exists in English) is composed of a Greek prefix hexa- and a Latinate suffix -gesimal, as in sexagesimus, meaning "sixtieth". A Google search shows that "hexagesimal" is used in Spanish but hardly ever in English, and even then its meaning is divided between "base 16" and "base 60". My conclusion is that there is no word with a pure pedigree that is copper-bottom guaranteed to mean "base 16". -- Heron

Contents

[edit] Sexidecimal is Correct! (not Literally but Historically)

It is true that engineers at IBM first used the bastardized Latin form Sexidecimal to describe a base 16 numbering system. It is not, and should not be the primary question here whether the form is correct grammatically. Instead, what is much more important is that the term was accurate historically -- it was used at a certain place and time. Language is less concerned with Accuracy than with Consensus. As such, it is always subject to change as soon as enough people agree that it should.

Google returns 374 results on "sexidecimal". Sounds like consensus to me.

[edit] Is it really strange to combine Greek & Latin in an English word ?

I have been told that Greek/Latin hybrids are actually not so uncommon in English. Off-hand the only one that I can recall, however, is automobile--which in modern Greek is aftokeenito, not using the Latin backend :)

The most well known one to me is television -- User:Karl Palmen.

[edit] Alternative Digit Representations

Raul654 has said "In some representations, the characters ~, !, @, #, $ and % are used instead of ABCDEF (respectively). " I'd like to know where?

Is % an acceptable digit?

-- User:Karl Palmen 3 June 2004

An anon contributor added that much. I rewrote it to make it blend into the article better. I'm not 100% sure if the statement is true, though. →Raul654 13:19, Jun 3, 2004 (UTC)
I was wondering that, too. Marnanel 17:19, 23 Jun 2004 (UTC)
I deleted the obscure figures (~ to %) introduced by User:206.80.111.48 on June 3.
Before reintroducing them, please give sources of their use. Paul Martin 18:48, 7 Dec 2004 (UTC)

[edit] True or false??

True or false: this word is common because people fail to take notes on whether a prefix is Greek or Latin. The correct sequence from 11-19 is:

  • 11. undecimal
  • 12. duodecimal
  • 13. tredecimal
  • 14. quattuordecimal
  • 15. quindecimal
  • 16. sexdecimal
  • 17. septendecimal
  • 18. octodecimal
  • 19. novemdecimal

66.245.104.133 17:40, 2 Aug 2004 (UTC)

There are many hybrid words like this, such as homosexual. Hyacinth 05:19, 9 Apr 2005 (UTC)

[edit] X'5A3' representation

A discussion at Talk:Newline has reminded me that I run into the notation X'5A3' every so often, in documents such as protocol specifications. (At least, I believe it's a representation of hex literals.)

Does anyone know where it comes from? Is it tied to a particular programming language or culture?

JTN 21:57, 2004 Oct 4 (UTC)

Update: when Googling it seems to come up in IBM-ish contexts more often than not, and PL/I appears to have this or similar notation [1]. Don't know if it was around before that.

JTN 23:01, 2004 Oct 4 (UTC)

[edit] Table in article - Opera rendering

Isn't the table on the right a little wrong? After 9 in dec, the table seems to be mirrored, and decimal values are listed under binary and vice versa. --Spug 13:03, 3 Nov 2004 (UTC)

Looks fine to me. What's your browser? --JTN 14:00, 2004 Nov 3 (UTC)

I use Opera, and indeed, it looks fine in both IE and FF while Opera flips the table after dec 9. How strange. --Spug 10:17, 4 Nov 2004 (UTC)

But it's preformatted text! (At least the version served to my Firefox, and also the Wiki source.) How bizarre. --JTN 15:16, 2004 Nov 4 (UTC)

I know! Here's a screenshot. I have no idea why that's happening, but at least it's not the article's fault, so nevermind :) --Spug 22:21, 4 Nov 2004 (UTC)

That looks almost like it might be bidirectional script support misfiring. --JTN 10:55, 2004 Nov 5 (UTC)

Yeah... What could be triggering that, though? I've posted a topic about it in the Opera forums. --Spug 11:21, 5 Nov 2004 (UTC)

any chance of a link to the forum post? Plugwash 23:59, 9 Apr 2005 (UTC)

[edit] Fractions

Why exactly is hexadecimal "quite good" for forming fractions? I don't see how it's particularly better than any other numeral system. -- Wapcaplet 04:14, 6 Nov 2004 (UTC)

To me, it even seems "quite bad" for forming fractions, since it only has one prime factor, almost as bad as base 10... Κσυπ Cyp   2004年11月6日 (土) 14:30 (UTC)
It is good because not only does 16 have many divisors, but also 16 is one more than 15, which divides into the next two prime numbers after 2 (3 and 5), so one also gets a good set of repeating fractions. For that reason is much better than either Octal (base 8) or base 32. It may possibly be considered better than Duodecimal (base 12) because 11 is prime. Karl Palmen, 8 December 2004
If you wan't to represent as many fractions as possible without reccurance then lots of prime factors are good (so base 10 is better than base 16 in this respect). I can't really say anything about the niceness of recurring fractions as i don't know that sort of maths.

[edit] Hexadecimal notation using ABCDEF and IBM?

The article currently has two mentions of IBM as associated with the use of alphabetic characters A to F to represent numbers in hexadecimal representation. Does anyone have a link for a reference that would describe this as a notation first used by IBM? - [[User:Bevo|Bevo]] 05:34, 10 Dec 2004 (UTC)

Neither Gauss (1777-1855) nor Legendre (1752-1833) used this digits. I ignore if John W. Nystrom – the real inventor of hexadecimal time format (and not Mark V. Rogers of intuitor.com) – already used them. (The same as...)
Before the 20th century, hexadecimal digits are very seldom used and that's why no standard existed. Since IBM adopted this format, it is universally recognised. That's a fact. But surely IBM not used them first. As yet, it's not clearly established who used them first and since when. (1930th?).
Anyone knows more on this interesting topic? 81.57.112.41 15:10, 10 Dec 2004 (UTC)

[edit] "SHOL"

Since several years the International Bureau for the hexadecimal metric system (SMH) proposes a so-called "omni-literal hexadecimal system" (SHOL).

Could someone provide a reference for this? A Google search for "omni-literal hexadecimal system" turned up precisely one link: this article. A search for SHOL hexadecimal turned up this article first, followed by a lot of unrelated things. I also fail to see how the use of arbitrary consonants for the hex digits is "remarkable, logical and consistent"; the paragraph in question ends "See also the external link below", though none of the external links pertains to this representation.

The paragraph was an anonymous contribution, and I am thinking of removing it unless some supporting evidence appears. I'm open to the possibility that these facts are translated from another language, which would explain the lack of Google hits, but if that is the case then we should remove the claim that this system is receiving "growing worldwide attention" and try to put it in proper perspective. If it is an extremely niche-oriented system, as I suspect, it probably shouldn't be mentioned at all, and certainly shouldn't be included in the table of hex representations as though it were widely accepted. -- Wapcaplet 00:38, 12 Dec 2004 (UTC)

  • Edit: Should have looked at the French site. Indeed, the anonymous contributor also provided a link to this rather poorly-designed site, in French (with English also available). It appears to me as though this sytem appears in one publication, by one person (or organization). If it has been accepted elsewhere, perhaps we could leave it in the article. If not, it should go. -- Wapcaplet 00:42, 12 Dec 2004 (UTC)
  • It's my feeling also that it should go or at least be made much less prominent, but I wasn't feeling energetic enough to research its notability. I note that despite its apparently French origin, fr:Système hexadécimal doesn't appear to mention it. -- JTN 11:42, 2004 Dec 12 (UTC)

I think I'll go ahead and remove the SHOL references. If SHOL turns out to be significant, anyone who cares to can pillage the article history and restore it. -- Wapcaplet 17:19, 12 Dec 2004 (UTC)

[edit] SHOL proposal & Fractions removal

I think, Wapcaplet, you've acts a little quick. You start a discussion and a few hours later, you erase this very interesting insertion relative to the SHOL. Only one person had time to answer you.

I visited the site of which you deleted the external link. You are right, this is a "rather poorly-designed site". But it's charming and first of all its contents are highly interesting. Unfortunately my French is not perfect, but good enough to understand, that it exposes new things clearly and without blinders. Whoever made it, he should be a great and independent thinker. (Googel ranks this site 5/10, rather good for a young site.)

I think, we should leave the "omni-literal digits" therein. The announcement of this proposal is judicious. This is a "remarkable, logical and consistent proposal". There are many proposals stated on Wikipedia, but this one is up-and-coming. Does someone other want to express his opinion to this topic?

Also your removal of the octal and hexadecimal fractions was as quick as not justified ! At the Octal talk-page you give to understand, that you do not like binary bases and that you prefer the base 12, because "that would be nice considering how common 1/3 is". It's your right to think so! But a page treating the "Base 8" and "Base 16 system" must mention in a few lines its fractions.

-- Paul Martin 03:30, 13 Dec 2004 (UTC)


SHOL doesn't appear to pass the Google test for notability. The added content made a number of unsupported assertions ("growing worldwide attention", "logical and consistent", "official" this and that) and the evidence for even its existence appears to be only one website (other than Wikipedia). It looks an awful lot like a one-person crusade; Wikipedia is not the place to drum up support. Maybe it could come back if evidence were to be found that someone other than "Michael Florencetime" does anything with it. -- JTN 11:30, 2004 Dec 13 (UTC)


  • The English version of the SHOL site does not appear to me to reveal anything particularly interesting, aside from a few numerological relationships. I am very skeptical of any publication (web or otherwise) that purports to describe some new "universal" measurement that is somehow better than our other measurement systems and should replace them. That the system is hexadecimal in nature doesn't justify extended inclusion in this article; an existing external link is a site campaigning to use hexadecimal timekeeping, but it would be inappropriate to talk about the merits and flaws of that system in this article also. We can't include comments on every oddball interpretation of the hexadecimal system here; the article should primarily cover the dominant usage, with perhaps a small section on these alternative interpretations.
  • On the fraction issue: I believe you mis-read the discussion on Talk:Octal; I did not express any disdain for binary (on the contrary, I quite like it). Another user noted the commonplace nature of 1/3. My reason for removing the fractions is that their inclusion seems rather arbitrary and incomplete (why only consider fractions with a numerator "1"? Why include division without including addition, subtraction, and multiplication?) and, for the most part, unrelated to understanding why octal and hexadecimal are useful. The inclusion seems especially odd considering that neither system is very well-suited to working with them.
  • You say that we must mention fractions in a few lines for these systems. Why fractions, and not, say, square roots, powers, or primes? I think we should concentrate on the techniques that are actually useful in these systems, particularly the ways they are useful in computer science (and in their relationship to the binary numeral system). I would not be opposed to having discussion of fractions, as long as it's part of a more thorough mathematical treatment. -- Wapcaplet 20:37, 14 Dec 2004 (UTC)


It is obvious that this article "hexadecimal" is not the place to explain hexadecimal timekeeping and its differences (16 H/d or 2×16 H/d?). Concerning the SHOL proposal, let's deepen later.

On the fraction issue: "Why include division without including addition, subtraction, and multiplication?" Because all these operations are delivering integer results (sometimes perhaps negative integers). A basic multiplication table might be interesting, but at present is not top-urgent.

The binary system and the hexadecimal system is quite the same. (Octal is an obsolete system with several disadvantages, whereon – here – I'll not dwell on.) You know as me, that in informatics, values always have "data types": signed byte, unsigned word, signed doubleword etc. That's the raison why many pocket calculators parse integers in hexadecimal divisions and neglect the fraction part. Therefore many persons – even some computer scientists think – hexadecimal fractions don't exist. They are at fault! Understanding the binary (or hexadecimal) floating point format helps to comprehend why. For abolishing implicitly this misapprehension, the presence of hexadecimal fractions in this article is essential.

Recurring fraction parts are not a problem, quite the contrary, are an advantage. (Short and finite fraction parts are certainly still better.) But the advantage of an identified recurring rule is, that your number is a number exact and not a rounded one. 1/3 showed as 0.3, where is the problem? As we know 1/6 = 0.16 in decimal, we will learn that's also 0x0.2A. It's easy to memorise. 1/3 = 0x0.5 since 5×3 = 0xF. Surely, even in decimal, not many individuals know that 1/7 is 0.142857. But for 1/0x5 and 1/0xA, no problems: Equal 0x0.3 and 0x0.19 respectively. You see, hexadecimal system is as "well-suited" as the decimal one. (Excepting the ugly mixed-digits and the need of the prefix "0x".)

"Why only consider fractions with a numerator "1"?" You are right. Perhaps someone makes another pretty table, not too large, including values like 2/3, 3/4 or 4/5. But this are only additions of the existing fractions.

"Square, roots, powers, or primes?". I don't like long useless listings. Hexadecimal calculators exist. Prime numbers are independent of bases! But some constants (pi or e) and often used values like square root of two, perhaps one day, can be mention.

"...as long as it's part of a more thorough mathematical treatment." Except the "bitwise logical operations" in limited "data types", there is no difference between hexadecimal and decimal arithmetic. Simply we forgot to swot our hexadecimal multiplication tables.

What do you think of?

Finally, it's true, I "mis-read". Another user wrote it. I wonder: You, contributing to "programming languages" etc. preferring "Base 12"? (Though, it's not a "bad base", but future belongs to hexadecimal. Also ancient weights and measures are often multiplied or divided by 8 or 16.) Excuse me for the mistake.

-- Paul Martin 14:26, 15 Dec 2004 (UTC)


"If at first, an idea doesn't seem crazy, then there is no hope for it." Albert Einstein.

Hi, it's me the "oddball". (I take it with humour.) Paul Martin informed me by email with a link up to here. I studied the history... and nice to find you here discussing my SHOL proposal.

But stop! – Before we can begin any discussion, it's absolutely necessary, that either you support your term "numerological" by any quotation you want or'But stop! – Before we can begin any discussion, it's absolutely necessary, that either you support your term "numerological" by any quotation you want or you will retake it very formally.

-- Michael Florencetime 16:40, 17 Dec 2004 (UTC)


Before I respond, keep in mind that I am basing my reaction on the English-translated portion of your site only, since I do not know French. I used the term "numerological" because of the way in which the hexadecimal system of length is derived. If I understand correctly, these measurements (league, stade, chain, aune, etc.) are wholly derived from Earth's circumference, using various divisions by four or powers of 16. It appears that the reader is expected to perceive some cosmic order in these measurements, when their only real relationship is to the Earth's circumference (a figure that can only really be measured to within several kilometers, and which is rather fuzzy by virtue of the fact that the polar circumference is some 70 km less than the equatorial circumference). That the hexadecimal length system has an internally logical organization of units has little bearing on whether the system could be useful or practical. The metric system may appear equally arbitrary, but at least some of its units are based on natural phenomena.

However, those issues are beside the point; the contention here is whether SHOL should be included at any length in this article. Has this proposal been adopted by any standards organization, or is it being used in a practical way by a significant number of people (say, more than 10)? Is there any publication, aside from your website, that describes the system and its applications? If not, I'm sorry, but I just don't see a place for it here. -- Wapcaplet 07:27, 18 Dec 2004 (UTC)


Thanks Wapcaplet for replying. I will soon answer you. -- Michael Florencetime 11:48, 20 Dec 2004 (UTC)


Nice edit by Plugwash; that old definition is certainly better than mine was. Sorry, I didn't dig enough into the history to find it. Poweroid 18:33, 21 September 2005 (UTC)


[edit] Errors in the multiplication table

Error in the hexadecimal multiplication table. D x 7 does not equal 4B, it should read 5B. Also 5 x 6 = 1E, not 2E - M.S. 7th March 2006

Yes, it was wrong, so I uploaded a screenshot of one of my own pages to replace it. MathsIsFun 23:23, 21 May 2006 (UTC)

[edit] Counting hexidecimal on the fingers.

I've noticed that it is possible to count hex on the fingers. You can use the thumb to count the fingertips and joints of the other four fingers of one hand. With two hands you could count base 32 or even 256. Linguofreak 02:13, 19 March 2006 (UTC)

Is this what you mean?

Image:Hex-Hand.JPG

-- Sasuke Sarutobi 13:05, 21 May 2006 (UTC)


[edit] Humour

In the humour section is the sentence: "With that last H it becomes possible to write new words and sentences, such as for example 1517ADEADB17CH." As it clearly implies "bitch" i feel this is inappropriate for wikipedia. Any thoughts?

[edit] Conversion vs. Representation

Hexadecimal is just a way to represent a number. This article seems to have a significant bias toward indicating that a number is somehow different in different representations and needs to be converted.

I think it should be made extremely obvious that hexadecimal is one way to represent a number, and the representation can be converted to other representations. I've removed the section that describes computer converting a number to binary and hexadecimal.

-- Lakin 23:15, 3 June 2006 (UTC)


[edit] But WHY?

The article does nothing to explain why the hexadecimal system was invented, or why it sees so much use in computer science. Can someone address this please? What is the point of using a base-16 system?

[edit] Verbal hexadecimal "Ax...Fx" pronunciation system?

I've never heard of this, and a quick search turns up no other descriptions of this system (eg. Pronouncing the hex digit “A” as “aye-ecks”). Unless this is actually in use significant use somewhere, the section would be identified as a proposal, rare or just deleted. Rwessel 00:05, 10 November 2006 (UTC)

I'm not an expert, but I didn't encounter it in a basic undergrad education in Computers. That and the info in question seems to have been added by an unregistered user (01:54, 12 October 2006 168.61.10.151 if you want to look it up in the history), and it pre-dated the rest of the content. It's probably been left in place just out of habit, when I'd guess it was just one person's opinion. A tentative second from me(pending, ofc, a good source for the info). At the least, we should probably make the section smaller, a mention rather than an in-depth explanation. --Spyforthemoon 20:07, 13 November 2006 (UTC)

[edit] Order of Sections

I rearranged the sections to try to group into logical areas (math, representations, &c...) I'm probably going to be combing through things more finely in the next few days, but wanted to get any opinions on this change first.

Particularly, is the Converting from other bases section unique from any other base-to-base conversion? If not, shouldn't we just point back to the Radix#Conversion_among_bases section? I agree that the Mapping to binary is importantly unique, but the general case doesn't seem to be. The subsections in Converting from other bases also seem to be unnecessary repetition of the generic base information. If I don't get any objections, I think that section should be axed. --Spyforthemoon 20:07, 13 November 2006 (UTC)


I agree, pointing to the common page on radix conversions is a good idea, perhaps leaving on one or two line quick description of converting to/from decimal since that's a specific (and common) case. Unfortunately that page (or at least that section) is terrible. In attempting to present the subject in an extremely simple way, it ends up being almost incomprehensible. The discussion of the relationship to binary is important to keep, IMO. Rwessel 09:36, 14 November 2006 (UTC)

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