Talk:Signed number representations

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Contents 1 One's versus ones' complement 2 Redirects 3 addition 4 end-around carry

[edit] One's versus ones' complement

According to the Bible, one's complement should be properly called ones' complement:

Detail-oriented readers and copy editors should notice the position of the apostrophe in terms like "two's complement" and "ones' complement": A two's complement number is complemented with respect to a single power of 2; while a ones' complement is complemented with respect to a long sequence of 1s. (TAOCP, Volume 2: Seminumerical Algorithms, chapter 4.1)

Although Google seems to imply that "one's complement" is used often (but it is hard to compare, as AFAIK you cannot force Google to consider punctuation), Knuth's view seems logical at the very least. -- Mormegil 19:56, 29 Jul 2004 (UTC)

OK, no reaction, so I have changed it in the article. --Mormegil 15:59, 3 Oct 2004 (UTC)

I'm not sure it's so obvious, despite what Knuth says in the bible. Google can distinguish "one's complement" versus ("ones' complement" or "ones complement"). The first gets 35,700 hits versus 13,500 for the others. (Also, judging from the first page of excerpts, "ones" predominates over "ones' "). For comparison, "two's" gives 69,700 versus 28,600 for twos'/twos. The tens and nines complements are fairly evenly split (and few). -R. S. Shaw 19:40, 21 July 2005 (UTC)

All the computer engineering textbooks and computer/CPU manuals in my not-so-modest collection use either "ones/twos complement" (i.e., no apostrophes at all) or "one's/two's complement" (i.e., "common" non-Knuth). M. Morris Mano's book Digital Design (1984) generally refers to "r's complement", r being the radix. --Wernher 20:55, 8 October 2005 (UTC)

Based on the idea that an encyclopedia should be correct, I've changed all instances of "one's complement [sic]" to "ones' complement" again. --Quuxplusone 02:01, 30 September 2006 (UTC)

I came to this talk page pondering about the grammar issue. Interesting. –– Constafrequent ^{(talk page)} 15:32, 23 November 2006 (UTC)

from Talk:Two's complement: Detail-oriented readers and copy editors should notice the position of the apostrophe in terms like two's complement and ones' complement: A two's complement number is complemented with respect to a single power of 2, while a ones' complement number is complemented with respect to a long sequence of 1s. (Volume 2, p. 203, according to [1]) 129.31.72.52 13:35, 15 June 2007 (UTC)

I always thought about it thusly: "the complement of the ones" and "the complement of the twos", which give "ones' complement" and "twos' complement". If the latter is written "two's complement", then that would mean "the complement of a two" probably, which seems a bit odd (2ⁿ is, after all, lots of 2s -- just as much as the string of 1s is lots of 1s -- when it's expanded). If that makes sense. —Sam Wilson (Australia) 00:33, 29 October 2007 (UTC)

Changed the article to use the ones' / two's convention as per Knuth. According to "Principles and Applications of Electrical Engineering" by Giorgio Rizzoni, there are no apostrophes at all, but I'm more inclined to follow the Bible. Feel free to change it, but at least the whole article is consistent now. LancerSix (talk) 02:14, 28 February 2008 (UTC)

Wow. I came here for the same reason. "Ones'" with "two's" rather than "twos'" doesn't really make sense, but I'll leave it alone. Perhaps Knuth knows more about math than language, but the convention he settled on is illogical, and I'm sure he understands logic! Alanlarue (talk) 20:51, 28 February 2008 (UTC)

I'm here for the same detail. I was reading the article, found an apparent error, saw that the error was very consistent, and so, checked out the talk page. Fortunately, what I was looking for was right at the top of the talk page. Perhaps this is important enough to mention in the article itself. Maybe find a way to somehow gracefully acknowledge the apparent grammatical inconsistency on first use of ones' and two's, and add a paragraph explaining the grammar somewhere toward the bottom of the article. I'm just passing through, and found the answer I was looking for here in the talk page, but if a significant number of people are spotting an error that's not actually an error, maybe it's time to somehow include an explanation right in the article. --Loqi T. (talk) 01:06, 4 April 2008 (UTC)

[edit] Redirects

I had a hard time finding this page for information about ones complement. Maybe the "ones complement" and "one's complement" pages could redirect to this page, since those were the ones I tried. I ended up going through a few complement redirect pages to find this.

Well, "one's complement" already redirects here, as does "ones' complement". I suppose adding one more wouldn't hurt, and could help people find information more easily, so I added "ones complement". --Rick Sidwell 00:49, 14 September 2005 (UTC)

[edit] addition

I've spent ages trying to find this article! I think 'ones complement sum' should redirect here, too. I want to add that ones complement sum is used not only in IP header, but in TCP and UDP data as well. Its widespread is due to easy checksum verification - if there is arbitrary sequence of bytes, its checksum calculated according to ones complement arithmetic, always gives all-ones if you sum all data and checksum. But this checksum very simple and don't detect errors like swapped bytes.

[edit] end-around carry

The process of "adding back the carry", as it is termed in this article about ones' complement arithmetic, was always referred to as an "end-around" carry.

Well - not important. By the time I read down to the section concerning two's complement, I see that the proper term for this ones' complement operation is introduced at that point in the article. So it's there!

Mea 01:55, 23 September 2007 (UTC) mea