Talk:Hexadecimal

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Other characters used[edit]

NEC in the NEAC 1103 computer documentation from 1958, uses the term "sexadecimal" and the sequence 0123456789DGHJKV. See the brochure at http://archive.computerhistory.org/resources/text/NEC/NEC.1103.1958102646285.pdf.

Unique names above ten[edit]

Not that it's of critical importance, but this line "most European languages lack non-decimal names for the numerals above ten" is incorrect. English has unique names to 12, after that it starts using the -teen system. Same with German and Norwegian. Spanish goes to 15 in one pattern before switching to another pattern, French goes to 16. I tried changing that line, but it was reverted, so I thought some discussion on the issue might be worthwhile. Probably the point is, no language naturally has a hexadecimal numbering system built into the language (although there is some support for base 12, or the proposed "dozenal"), so we've had to invent some adaptations for hex. Nerfer (talk) 18:22, 1 September 2015 (UTC)

My two cents: In the Indo-European languages I'm familiar with, words for "eleven" and "twelve" don't follow the regular pattern of the integers below 20, but they are still following a pattern that I would describe as "decimal": "eleven" and "twelve" echo "one" and "two", "onze" and "douze" echo "un" and "deux", etc. -- there's an unambiguous reset that happens at 10, which is then followed by another unambiguous reset to the "-teen" system. (Maybe in the case of French one should understood their number words as a hybrid of decimal and base 20.) Also Hungarian (which is not Indo-European) is very decimal. Of course the best way to settle this would be with a decent reference to something in the linguistics literature .... --JBL (talk) 19:01, 1 September 2015 (UTC)
Yes, the putative "unique names" for the early teens in several IE languages (eleven, twelve; elf, zwolf; once, doce, trece, catorce; etc.) are all originally compounds involving the basic names for "one", "two", and so forth. They clearly reflect a decimal origin. -- Elphion (talk) 19:13, 1 September 2015 (UTC)

Color coding of prime factors in real number table[edit]

For some reason the prime factors listed in this table have been color coded. Two has been blue, three green, and "11" (decimal on one side, hex on the other) yellow on both sides of the table (although decimal 11 and, five is blue on the left and green on the right. Others have been red. Recently the red ones were changed to black by 87.254.76.191, but that was revered by Arthur Rubin and Sapphorain. What exactly is the color coding supposed to show? Why are the factors of the base+/-1 interesting? And why are "all others" red? If they're not interesting, why is black not appropriate? Frankly I don't see what this accomplishes, and I think we should remove the color coding entirely. Rwessel (talk) 15:22, 21 October 2015 (UTC)

In any base b, fractions involving factors of (b − 1) in the denominator will have a repeating period of 1, and fractions involving factors of (b + 1) in the denominator will have a repeating period of 2. The shorter the repeating period, the better; so long repeating periods like an eleventh in hexadecimal are rather bad, hence coloured red. The red numbers have no good divisibility tests, while the green digits have easy tests thanks to being divisors, the blue digits can use the digit-sum test, and the yellow digits can use the digit-alternating-sum test. Double sharp (talk) 15:24, 21 October 2015 (UTC)
Why is any of that relevant to an article on hex? And there's a reasonably straight-forward divisibility test for seven as well (at least in decimal), why not highlight that? Rwessel (talk) 15:40, 21 October 2015 (UTC)
Actually, according to Divisibility rule there are *five* divisibility tests for seven - I only knew of the first... Rwessel (talk) 15:44, 21 October 2015 (UTC)
These are properties of hexadecimal: they are colour-coded for the base. If you want to see if a hexadecimal number is divisible by 5 (coloured blue), for example, you sum the digits. Hence, for example, hexadecimal D890hex is divisible by 5 as D + 8 + 9 + 0 = 1E and 1 + E = F, a multiple of 5. Additionally, we have 1/3 = 0.555... and 1/5 = 0.333... in hexadecimal, and aren't the fifths #000, #333, #666, #999, #CCC, and #FFF pretty common colour choices?
The decimal divisibility test for seven is light-years away from being as straightforward as the divisor tests (for 2 and 5) or the modulo-±1 tests (for 3 and 11). The test you mention (alternating blocks of three) not only requires difficult mental addition and subtraction of three-digit numbers, but you need to remember all 142 multiples of 7 below a decimal thousand to use it. Can you recognize that 889 is a multiple of 7 at a glance? Contrast this to simply summing the digits to test for decimal 3 or 9, or hexadecimal 3, 5, and F! Additionally, 1/7 in decimal is the ugly 0.142857... with a six-place period. Double sharp (talk) 16:18, 21 October 2015 (UTC)
I'm still failing to grasp why these should be highlighted by color though. If 5 is a factor there's a "5". How does making it blue help? Rwessel (talk) 03:55, 22 October 2015 (UTC)
I am inclined to agree with Rwessel here. --JBL (talk) 11:46, 22 October 2015 (UTC)
The colour helps make the difference between prime factors of b, (b − 1), (b + 1), and any other primes immediately noticeable, so that the list at the top doesn't have to be referred to all the time. Double sharp (talk) 12:25, 22 October 2015 (UTC)
For one particular task, possibly this color-coding might be useful. For any other task, or for someone just glancing through the article, it is redundan and distracting. Moreover the color red is not explained anywhere. I really see no justification at all for giving the most generic piece of information in the table the most visible color. Consequently, I have removed the red. I would also not object to removing the other colors, but at least I have been convinced that they might be useful to someone. --JBL (talk) 13:43, 22 October 2015 (UTC)
Looking at it now, I think the black is too dark, and looks too similar to the green. And now we still have the problem that the colour black is not explained anywhere: it's just that it's now black instead of red. And really, is it that difficult to ignore the colours? I did not expect that to be the case. Perhaps I was wrong. Double sharp (talk) 13:58, 22 October 2015 (UTC)
I have no problem with the colors, but there needs to be a note explaining them. Using them in the header is not sufficient. -- Elphion (talk) 19:14, 22 October 2015 (UTC)
Black is the default color for text; it does not need to be explained. I find it easy to distinguish the green from the black, but of course you could always replace green with red or something to resolve this. --JBL (talk) 01:32, 23 October 2015 (UTC)

Why was my number->numeral edit reverted?[edit]

I changed some instances of "number" to "numeral" to be consistent both with Wikipedia usage in other articles and with mathematical accuracy. This edit was reverted by Elphion. Why? Briankharvey (talk) 03:50, 10 February 2016 (UTC)

The edit summary by Elphion (talk · contribs) was " 'numeral' refers to a glyph, not a representation using them", which I would agree with. "2AF3" is a hexadecimal number, not a numeral, but the "2", "A", "F" and "3" are each numerals. Rwessel (talk) 05:32, 10 February 2016 (UTC)