JAMIA 2024 — Computer PYQ

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Question

JAMIA 2024 — Computer PYQ

JAMIA | Computer | 2024

The decimal equivalent of (0.101)2 will be_____

Choose the correct answer:

Explanation

Conversion Logic

In the binary system, the positions to the right of the point represent:

$1^{st}$ place: $2^{-1} = \frac{1}{2} = 0.5$
$2^{nd}$ place: $2^{-2} = \frac{1}{4} = 0.25$
$3^{rd}$ place: $2^{-3} = \frac{1}{8} = 0.125$

Calculation

For the binary number $(0.101)_2$ :

The first digit after the point is 1:

$1 \times 2^{-1} = 1 \times 0.5 = 0.5$
The second digit after the point is 0:

$0 \times 2^{-2} = 0 \times 0.25 = 0$
The third digit after the point is 1:

$1 \times 2^{-3} = 1 \times 0.125 = 0.125$
Sum the values:

$\text{Decimal} = 0.5 + 0 + 0.125 = 0.625$

Mathematical Representation

(0.101)_2 = (1 \times 2^{-1}) + (0 \times 2^{-2}) + (1 \times 2^{-3})

(0.101)_2 = 0.5 + 0 + 0.125

(0.101)_2 = (0.625)_{10}

Answer: The decimal equivalent of $(0.101)_2$ is 0.625.