NIMCET 2022 — Computer PYQ

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Question

NIMCET 2022 — Computer PYQ

NIMCET | Computer | 2022

The maximum and minimum value represented in signed 16 bit 2’s complement representation are

Choose the correct answer:

Explanation

To find the range of a signed $n$ -bit 2's complement number, we use the standard range formula:

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

Given that the number of bits $n = 16$ :

1. Calculate the Minimum Value:

\text{Min Value} = -(2^{16-1})

\text{Min Value} = -(2^{15})

\text{Min Value} = -32768

2. Calculate the Maximum Value:

\text{Max Value} = +(2^{16-1} - 1)

\text{Max Value} = +(2^{15} - 1)

\text{Max Value} = 32768 - 1

\text{Max Value} = 32767

\therefore \text{The range is } -32768 \text{ to } 32767

\therefore \text{Correct Option: } \mathbf{C}