The whole concept of using 2’s complement representation is to use the same circuit for both both additions and subtractions.
We use same representation for +ve numbers in 1’s, 2’s complement and sign magnitude form since we do addition the same way in all the representations
ex: X – Y
. But to perform subtraction using addition circuit we we will find 2’s complement of Y and we will add them both and get result
X – Y = X + (2’s complement of Y = $2^{n}$ – Y) , we discard the carry when X – Y >= 0 , we get 2’s complement representation of answer if X-Y<0.