Decimal fraction to binary conversion Convert the decimal number 151.75 (base 10) to binary (base 2).

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

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: Decimal input: 151.75. We want an exact finite binary since 0.75 is a dyadic fraction. No rounding is required for this case. 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): 1) 151 decimal → binary: 151 = 128 + 16 + 4 + 2 + 1.2) Place bits: 2^7=128 → 1; 2^6=64 → 0; 2^5=32 → 0; 2^4=16 → 1; 2^3=8 → 0; 2^2=4 → 1; 2^1=2 → 1; 2^0=1 → 1.3) Integer part = 10010111. Step-by-Step Solution (Fraction): 1) 0.75 * 2 = 1.5 → record 1, keep 0.5.2) 0.5 * 2 = 1.0 → record 1, fraction ends.3) Fractional part = .11. Verification / Alternative check:Reconstruct: 10010111.11₂ = 151 + 0.75 = 151.75, exact. Why Other Options Are Wrong: 10000111.11: equals 135.75, not 151.75. 11010011.01: equals 211.25 in decimal. 00111100.00: equals 60 exactly. Common Pitfalls:Placing 1s for the wrong powers of 2, or mishandling the fractional multiply-by-2 steps. Final Answer:10010111.11

Decimal fraction to binary conversion Convert the decimal number 151.75 (base 10) to binary (base 2).

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