Question

Perform binary subtraction of A−B under signed representation (by doing A+(−B) ). What is the result? Does overflow occur?

i) A=11011 B=01101
ii) A=111 B=010
iii) A=0011 B=1000

Answer 1

Performing binary subtraction under signed representation, A + (-B), results in -18, -6, and 7 for the given cases. Overflow does not occur for any of the cases.

Step-by-step explanation:

In binary subtraction under signed representation, we perform A + (-B). Here are the results for each given pair of numbers:

1. A = 11011 and B = 01101.

   A + (-B) = 11011 + (-01101) = 11011 + 10011 (2's complement representation of -01101) = 101110 (in binary).

   The result is 101110 (in binary) or -18 (in decimal). Overflow does not occur because the result can be represented within the given number of bits.

2. A = 111 and B = 010.

   A + (-B) = 111 + (-010) = 111 + 101 (2's complement representation of -010) = 1010 (in binary).

   The result is 1010 (in binary) or -6 (in decimal). Overflow does not occur because the result can be represented within the given number of bits.

3. A = 0011 and B = 1000.

   A + (-B) = 0011 + (-1000) = 0011 + 1000 (2's complement representation of -1000) = 00111 (in binary).

   The result is 00111 (in binary) or 7 (in decimal). Overflow does not occur because the result can be represented within the given number of bits.