NIMCET 2014 — Computer PYQ

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Question

NIMCET 2014 — Computer PYQ

NIMCET | Computer | 2014

The binary equivalent of $(531.53125)_{10}$ is:

Choose the correct answer:

Explanation

Solving

Step 1: Convert Integer Part $(531)$

Divide $531$ by $2$ repeatedly and track remainders:

$531 \div 2 = 265$ , Remainder: $1$
$265 \div 2 = 132$ , Remainder: $1$
$132 \div 2 = 66$ , Remainder: $0$
$66 \div 2 = 33$ , Remainder: $0$
$33 \div 2 = 16$ , Remainder: $1$
$16 \div 2 = 8$ , Remainder: $0$
$8 \div 2 = 4$ , Remainder: $0$
$4 \div 2 = 2$ , Remainder: $0$
$2 \div 2 = 1$ , Remainder: $0$
$1 \div 2 = 0$ , Remainder: $1$

Reading bottom to top: $(1000010011)_{2}$

Step 2: Convert Fractional Part $(0.53125)$

Multiply the fraction by $2$ and record the integer part:

$0.53125 \times 2 = 1.0625$ (Integer: $1$ )
$0.0625 \times 2 = 0.125$ (Integer: $0$ )
$0.125 \times 2 = 0.25$ (Integer: $0$ )
$0.25 \times 2 = 0.5$ (Integer: $0$ )
$0.5 \times 2 = 1.0$ (Integer: $1$ )

Reading top to bottom: $.10001$

Step 3: Combine Results

1000010011 + .10001 = (1000010011.10001)_{2}

Correct Option: 4. $(1000010011.10001)_{2}$