Binary long division: Divide 1100010 (binary) by 0101 (binary 5). What is the decimal remainder of the division?
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A2
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B3
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C4
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D6
Answer
Correct Answer: 3
Explanation
Introduction / Context:Binary division mirrors decimal long division but uses base-2 arithmetic. Understanding remainders is useful for modulus operations, checksums, and cyclic redundancy computations.
Given Data / Assumptions:
- Dividend: 1100010₂.
- Divisor: 0101₂ (which equals 5₁₀).
- Asked: decimal value of the remainder.
Concept / Approach:You can either perform binary long division directly or convert to decimal to quickly find the remainder, since modulo is base-independent for exact integer values: remainder(98, 5) = 98 mod 5.
Step-by-Step Solution:
Convert dividend: 1100010₂ = 64 + 32 + 2 = 98₁₀.Convert divisor: 0101₂ = 5₁₀.Compute remainder: 98 mod 5 = 5*19 = 95; 98 – 95 = 3.Therefore, remainder = 3 (decimal).Verification / Alternative check:Binary long division also yields a remainder of 0011₂, which is 3₁₀. Either path confirms the same result, validating the conversion and arithmetic.
Why Other Options Are Wrong:
- 2, 4, 6: Not equal to 98 mod 5; these would be correct only for different dividends.
Common Pitfalls:Misreading the dividend bits (especially leading zeros) or miscalculating place values when converting to decimal. Always double-check binary weights (…32, 16, 8, 4, 2, 1).
Final Answer:3