Question

If you are given a word of size n bits, the range of 2’s complement of binary numbers is ________

(a) -2^n+1 to +2^n+1

(b) -2^n-1 to +2^n-1

(c) -2^n-1 to +2^n+1

(d) -2^n-1 to +2^n-1-1

This question was addressed to me by my college director while I was bunking the class.

My question comes from Sign Magnitude in chapter Computer Arithmetic of Computer Fundamentals

Answer 1

Right choice is (d) -2^n-1 to +2^n-1-1

To explain I would say: 2’s complement is obtained by adding 1 to the 1’s complement. For e.g. 5 :0101 and 1’s complement=1010  and  2’s complement=1011.