Why doesn’t the PC use 1’s complement?

Answer 1

1's Complement is not used because it has two representations of 0. It means that in 1's complement form, +0 =00000000 and -0=11111111.
But +0 and -0 are same, so 2' complement is used.
+0=00000000
2'sComplement(-0)=1's complement(0)+1
=> 11111111+1=1 (00000000)
which is same as of +0.
I hope it clarifies. If you have any question, plz mail.

Answer 2

The microprocessors that PCs use as CPUs *do* use 1's complement internally for many operations...that the assembly language (and other higher programming language) instructions hide that fact is simply because humans find it more difficult to think that way :)