[lizardactivist]

A consequence of most, if not all, CPUs today using two's complement integers.

I think one's complement is more sensible since it doesn't have this problem, but it loses out because it requires a more complex ISA and implementation.

[veltas]

It's annoying that negation, ABS, and division can overflow with two's complement. But how I look at it: lots of operations can already overflow, just a fact of signed integers, and you need to guard against that overflow in portable code already. It doesn't seem to be fundamentally worse that those extra operations can overflow.

[nayuki]

Ones' complement (correct spelling) has negative zero, which I would argue is a far worse problem.

[xigoi]

Why in the fuck is it “ones' complement”, but “two's complement”?

[tsimionescu]

According to Wikipedia:

> The name "ones' complement" (note this is possessive of the plural "ones", not of a singular "one") refers to the fact that such an inverted value, if added to the original, would always produce an 'all ones' number

[xigoi]

And two's complement refers to what?

[tsimionescu]

The radix complement in base two. They are closely related but not identical - the two's complement representation of a negative number is the ones' complement representation + 1 (ignoring the final carry). In ones' complment there are two representations for 0 (all 0s or all 1s), but every number has a positive and negative representation. In two's complement, there is a single 0, but there is also negative number that doesn't have a corresponding positive representation (INT_MIN).

In fact, for every numerical base there is an equivalent. For example, in base 3 you can represent a number in twos' complement notation (each trit X is replaced with 2-X, so -3 is represented as 212 on three trits, with +3 being 010) is or in three's complement by adding 1 (212+1 = 220). For base 10, you can do nines' complement (-3 on 3 digits is 996) or ten's complement (996+1 = 997).