[dataflow]

Signedness doesn't affect anything here, as long as the representation is in two's complement. The negation of x (i.e. -x) in two's complement is ~x + 1. The interpretation of the bits as signed or unsigned doesn't change any of the following steps.

[MaxBarraclough]

I think strictly speaking signedness does affect things, assuming we're talking C/C++. If x has type int and were to take the value of INT_MIN, then evaluating -x would result in a signed arithmetic overflow, which is undefined behaviour. (Related: the C standard now insists on use of 2's complement, where it used to permit other schemes.)

If x had type unsigned int, this wouldn't introduce undefined behaviour.