NIMCET 2025 — Computer PYQ

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Question

NIMCET 2025 — Computer PYQ

NIMCET | Computer | 2025

Consider a 9-bit representation. Which of the following correctly gives the smallest number that can be represented in:

(i) 1's complement,

(ii) 2's complementsa

Choose the correct answer:

Explanation

Solution

Correct Option: (A) (i) $-255$ , (ii) $-256$

1. 1's Complement Smallest Number

The formula for the smallest number in $n$ -bit 1's complement is:

-(2^{n-1} - 1)

For $n = 9$ :

-(2^{9-1} - 1) = -(2^8 - 1)

-(256 - 1) = -255

2. 2's Complement Smallest Number

The formula for the smallest number in $n$ -bit 2's complement is:

-2^{n-1}

For $n = 9$ :

-2^{9-1} = -2^8

-256

Final Equation

\text{Minimum Value (1's Comp)} = -(2^8 - 1) = -255

\text{Minimum Value (2's Comp)} = -2^8 = -256