Neat quiz. Reminds me that the absolute value of INT_MIN in C (and many other languages) is undefined, but will generally still return a negative value. This is a "gotcha" that a lot of people are unaware of.
> abs(-2147483648) = -2147483648
> abs(-2147483648) = -2147483648
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.
> 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
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).