NIMCET 2012 — Computer PYQ

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Question

NIMCET 2012 — Computer PYQ

NIMCET | Computer | 2012

$(2FA0C)_{16}$ is equivalent to

Choose the correct answer:

Explanation

The correct answer is (c) Both (a) and (b).

1. Hexadecimal to Binary Conversion:

Each hex digit corresponds to a 4-bit binary group:

$2 \rightarrow 0010$
$F \rightarrow 1111$
$A \rightarrow 1010$
$0 \rightarrow 0000$
$C \rightarrow 1100$

Concatenating these gives:

(2FA0C)_{16} = (00101111101000001100)_2

This matches option (b).

2. Hexadecimal to Decimal Conversion:

Using the positional weight method:

\text{Value} = 2 \times 16^4 + 15 \times 16^3 + 10 \times 16^2 + 0 \times 16^1 + 12 \times 16^0

Calculation:

$2 \times 65536 = 131072$
$15 \times 4096 = 61440$
$10 \times 256 = 2560$
$0 \times 16 = 0$
$12 \times 1 = 12$

Summing the values:

131072 + 61440 + 2560 + 0 + 12 = 195084

This matches option (a).

Since both (a) and (b) are correct, the answer is Both (a) and (b).