Binary long division: Divide 1100010 (binary) by 0101 (binary 5). What is the decimal remainder of the division?

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:

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