Why are the bits inverted in one's complement?

Question

When storing a negative number with one's complement before you add the 1 for two's complement, why are all the bits other than the sign inverted? I suppose It would just be simpler if the only thing different was the sign. The only reason I can think of is it somehow make it easier for the computer.

having +0 and -0 is troublesome at best – msw Jun 09 '11 at 01:59 — msw, Jun 09 '11 at 01:59

score 3 · Answer 1 · answered Jun 09 '11 at 01:53

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Because that what one's complement is defined to do. See http://en.wikipedia.org/wiki/Signed_number_representations

answered Jun 09 '11 at 01:53

Richard Schneider

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Yep, you're right: *History: The early days of digital computing were marked by a lot of competing ideas about both hardware technology and mathematics technology (numbering systems). `One of the great debates was the format of negative numbers, with some of the era's most intelligent people having very strong and different opinions`.* --http://bit.ly/iO68tw – John K Jun 09 '11 at 01:55
Thank you for the actual helpful answer John. – Greener Jun 09 '11 at 21:23

score 1 · Accepted Answer · answered Jun 09 '11 at 01:59

See, for example, http://en.wikipedia.org/wiki/One%27s_complement, or other sources a quick google can give you. Basically, yes, it makes addition and subtraction easier to implement compared to sign magnitude numbers (though 2's complement makes maths even easier).

Why are the bits inverted in one's complement?

2 Answers2