# Is 2's complement the only way that singed binary numbers are represented?

I have only seen mention 2's complement practically everytime signed number representation is mentioned. However, I have found that there are other ways to represent signed numbers also, these are 1's complement, excess-k and base -2.

Except 1's complement I do not really understand how the other two work. However, what I want to know is, are these other representations ever used at all? If so, where and why? I know that the strength of 2's complement is that addition and subtraction become the same. However, I am not sure about the strengths of the other mentioned methods.

• You need a textbook, I think. – TisteAndii Nov 23 '16 at 1:14
• which textbook? – quantum231 Nov 23 '16 at 1:21
• In the dominant IEEE P754 standard for floating point numbers, sign&magnitude is used for the mantissa (aka significand) and excess- for the exponent. S&M is a bit simpler with rounding, has no asymmetry (-128... +127 in 8bits two's complement, which is a pain for operations as multiplications and divisions...), how while excess- allows continuity between small exponents and zero which is represented with zeros. – TEMLIB Nov 23 '16 at 1:55
• There were a lot of different ideas tried in the past. But a huge advantage for twos complement comes in the implementation details of add/subtract hardware logic. Some early Russian computers even used balanced trinary. But that was a long time back, as well. The world has explored the options and, for mainstream computing work, has settled on twos complement notation. For integers. Floating point is a different problem, entirely. Normalization, easy ordering, and other factors play there. So it's handled differently. You probably do need an historical book for details about 'why'. – jonk Nov 23 '16 at 2:33
• The Apollo Guidance Computer used 1's complement IIRC. – Wossname Nov 23 '16 at 9:15