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Why 1’s and 2’s representation of +ve signed numbers are same as the signed-magnitude-representation of that number, but 1’s and 2’s representation of -ve signed numbers are different than their signed-magnitude-representation. I mean why don’t we apply the same rule of conversion of 1’s or 2’s representation for +ve number also?

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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.

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