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NIMCET 2009 — Computer PYQ

NIMCET | Computer | 2009

A Computer with a 32 bit word size uses 2’s complement to represent numbers. The range of integers that can be represented by this computer is

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Choose the correct answer:

A.
$-2^{32}$ to $2^{32}$
B.
$-2^{31}$ to $2^{32}$
C.
$-2^{31}$ to $2^{31} - 1$
(Correct Answer)
D.
$-2^{32}$ to $2^{31}$

Correct Answer:
$-2^{31}$ to $2^{31} - 1$

Explanation

For a computer using an $n$ -bit word size with $2$ 's complement representation, the range of representable integers is determined by the following formula:

$\text{Range} = -(2^{n-1}) \text{ to } (2^{n-1} - 1)$

Given:

Word size ( $n$ ) = $32$ bits

Plugging the value into the formula:

Lower Limit: $-(2^{32-1}) = -2^{31}$

Upper Limit: $(2^{32-1} - 1) = 2^{31} - 1$

Therefore, the range is $-2^{31}$ to $2^{31} - 1$ .

Explanation

For a computer using an $n$ -bit word size with $2$ 's complement representation, the range of representable integers is determined by the following formula: