In two's complement representation with a 4-bit allocation, we get _______ when we add 1 to 7.
A) 8
B) 1
C) -7
D) -8

Question

Quizplus · Accepted Answer

In two's complement representation, to add 1 to a number, we need to first take the complement of the number (flip all the bits), then add 1 to the result. 
7 in binary with 4 bits is 0111. 
Taking the complement of 0111, we get 1000. 
Adding 1 to 1000, we get 1001, which is equal to -7 in two's complement notation. 
Therefore, the answer is D, as none of the other choices are equal to -7.

In Two's Complement Representation with a 4-Bit Allocation, We Get