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GATE CS 2013 Q4 — Number Representations (Fixed and Floating Point)

The smallest integer that can be represented by an $8\text{-bit}$ number in $2's$ complement form is

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Answer: B

For an $n$ -bit signed integer represented in 2's complement form, the range of representable values is:

$\text{Range} = [-2^{n-1}, \ 2^{n-1} - 1]$

Given that the number of bits is $n = 8$ :

Smallest (minimum) integer: $-2^{8-1} = -2^7 = -128$
Largest (maximum) integer: $2^{8-1} - 1 = 2^7 - 1 = 127$

Thus, the smallest integer that can be represented is $-128$ .

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Published 10 Oct 2026

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