Difficulty: Medium
Correct Answer: 10010111.11
Explanation:
Introduction / Context:
Converting mixed decimal numbers (integer plus fraction) to binary involves two coordinated processes: repeated division by 2 for the integer part and repeated multiplication by 2 for the fractional part. Mastery of both is essential for representing fixed-point values in binary.
Given Data / Assumptions:
Concept / Approach:
Split the number into 151 (integer) and 0.75 (fraction). Convert 151 using division-by-2; convert 0.75 by multiplying by 2 repeatedly and recording integer bits produced at each step.
Step-by-Step Solution (Integer):
Step-by-Step Solution (Fraction):
Verification / Alternative check:
Reconstruct: 10010111.11₂ = 151 + 0.75 = 151.75, exact.
Why Other Options Are Wrong:
Common Pitfalls:
Placing 1s for the wrong powers of 2, or mishandling the fractional multiply-by-2 steps.
Final Answer:
10010111.11
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