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The decimal value $0.25$

  1. is equivalent to the binary value $0.1$
  2. is equivalent to the binary value $0.01$
  3. is equivalent to the binary value $0.00111$
  4. cannot be represented precisely in binary
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3 Answers

Best answer
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First Multiplication Iteration

Multiply $0.25$ by $2$

$\begin{array}{c c c}0.25 \ast 2 = 0.50\;\text{(Product)} & \text{Fractional part} = 0.50 & \text{Carry} = 0 \textbf{ (MSB)} \end{array}$

Second Multiplication Iteration

Multiply $0.50$ by $2$

$\begin{array}{c c c}0.50 \ast 2 = 1.00\;\text{(Product)} & \text{Fractional part} = 1.00 & \text{Carry} = 1 \textbf{ (LSB)} \end{array}$

The fractional part in the $2$nd iteration becomes zero and hence we stop the multiplication iteration.

Carry from the $1$st multiplication iteration becomes MSB and carry from $2$nd iteration becomes LSB.

So the result is $0.01$

Correct Answer: B.

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Here's the step-by-step conversion of 0.25 to binary: Multiply \(0.25\) by \(2\): \[0.25 \times 2 = 0.5 \quad (\text{quotient} = 0, \text{remainder} = 0.5)\] Multiply the remaining fractional part (\(0.5\)) by \(2\) again: \[0.5 \times 2 = 1.0 \quad (\text{quotient} = 1, \text{remainder} = 0)\] The quotient is \(1\), so we stop. The binary representation of \(0.25\) is: \[0.01 \quad (\text{where} \ 0 \ \text{is the whole number part and} \ 01 \ \text{is the fractional part})\]
Answer:

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