Discussion
Assertion (A) : 2's complement arithmetic is preferred in digital computers.
Reason (R) : The hardware required to obtain 2's complement of a number is simple.
Answer: A
Both (A) and (R) are true and (R) is the correct explanation of (A).
Computers use 2's complement because the same adder then handles both addition and subtraction: A - B is computed as A + (2's complement of B). There is only one representation of zero, and no end-around carry is needed as in 1's complement.
The 2's complement itself is obtained with very simple hardware: invert every bit (an XOR or NOT gate per bit) and add 1 through the carry input of the adder. That simplicity is the reason the scheme is preferred, so the reason explains the assertion.
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