How do omputers negate binary?

Question

Computers are only able to add, if they want to substract they have to negate one of the summands. But there is my question: how can computer do that by avoiding that 0 gets to -1? Have computers two 0s (+0 and -0)?

000 -4
001 -3
010 -2
011 -1
100 +0
101 +1
110 +2
111 +3

Problem: 0 turns to -1

000 -3
001 -2
010 -1
011 -0
100 +0
101 +1
110 +2
111 +3

Problem: -0 plus 1 = +0

Dan · Accepted Answer

Computers represent signed integers using something called twos-complement arithmetic.  For numbers of a certain size, the first bit is reserved for negative numbers.  A negative number is represented as the one that, when added to it's positive, would give zero.

So in your example (where numbers are 3 bits long):

-1 is represented as 111 because 111 + 001 = 000 (ignoring the carry to the nonexisting 4th bit).
-2 is represented as 110 because 110 + 010 = 000.

You can think of it like an odometer.  To see how to represent the positive number n, it's like running the odometer forward n units starting from zero.  To see the negative number, run it backward n units starting from zero.

How do omputers negate binary?

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