Question

Answer Exercise 36 for two's complement expansions.

36. If m is a positive integer less than$2^{n-1}$how is the one's complement representation of -m obtained from the one's complement of m, when bit strings of length n are used?

Short answer

$\left(2s\text{complement representation}\right)=\left(1s\text{complement representation}\right)+1$

Step-by-step solution

Step 1

Procedure to find 2s complement representation of -m when we know 2s complement representation of +m represented using n bits :

step1 : Find the 1s complement representation of -m. This can be done by flipping (or complementing) each of the n bits in +m'srepresentation.

step 2: 'Add 1' to 1s complement representation of -m to obtain +m's complement representation of