JAMIA 2024 — Computer PYQ

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Question

JAMIA 2024 — Computer PYQ

JAMIA | Computer | 2024

The 2’s complement of 5 is ______

Choose the correct answer:

Explanation

Calculation (8-bit representation)

1. Convert the Decimal number to Binary:

First, we convert the decimal number $5$ into its binary equivalent.

5_{10} = (00000101)_2

2. Find the 1's Complement:

To find the 1's complement, we invert all the bits (change $0$ to $1$ and $1$ to $0$ ).

\text{Binary: } 00000101 \xrightarrow{\text{Invert}} \text{1's Complement: } 11111010

3. Find the 2's Complement:

The 2's complement is obtained by adding $1$ to the 1's complement.

\text{2's Complement} = \text{1's Complement} + 1

11111010 + 1 = 11111011

Mathematical Representation

\text{Decimal Number} = 5

\text{Binary (8-bit)} = 00000101

\text{1's Complement} = \overline{00000101} = 11111010

\text{2's Complement} = 11111010 + 1 = \mathbf{11111011}

Answer: The 2's complement of 5 is 11111011 (in 8-bit) or 1011 (in 4-bit).