Question

What range of numbers encoded using two’s complement representation can be expressed using 5 bits? Provide your answer in decimal.

Answer 1

Solution:

Given,

=>Number of bits = 5

=>2's complement notation is used.

Explanation:

Finding 2's complement number range:

=>Range of numbers encoded in 2's complement with n bits = [-2^(n-1), 2^(n-1) - 1]

=>Range of numbers encoded in 2's complement with 5 bits = [-2^(5-1), 2^(5-1) - 1]

=>Range of numbers encoded in 2's complement with 5 bits = [-2^4, 2^4 - 1]

=>Range of numbers encoded in 2's complement with 5 bits = [-16, 16 - 1]

=>Range of numbers encoded in 2's complement with 5 bits = [-16, 15]

=>Hence range of numbers encoded with 5 bits in 2's complement notation = -16 to +15

I have explained each and every part with the help of statements attached to the answer above.