Binary long division check: When the binary number 1100010₂ is divided by 0101₂ (which equals 5₁₀), what is the remainder in decimal?

Introduction / Context:
Binary division appears in CRC computation, modular arithmetic, and hardware dividers. Translating between bases can simplify mental checks of remainders and quotients.

Given Data / Assumptions:

• Dividend: 1100010₂.
• Divisor: 0101₂ (which is 5 in decimal).
• We need the remainder, reported in decimal.

Concept / Approach:
Either perform binary long division or convert both numbers to decimal, divide, and convert the remainder back if needed. Since only the remainder is asked and the divisor is small, decimal conversion is efficient.

Step-by-Step Solution:
Convert 1100010₂ to decimal: 164 + 132 + 016 + 08 + 04 + 12 + 01 = 98.Divisor 0101₂ = 5.Compute 98 / 5: quotient = 19, remainder = 3 (since 195 = 95).Therefore, the decimal remainder is 3.

Verification / Alternative check:
Binary check: 98 − 19*5 = 98 − 95 = 3; the remainder is less than the divisor, confirming correctness.

Why Other Options Are Wrong:
2 or 4: plausible near values but incorrect; 98 mod 5 equals 3.6: remainder must be less than 5.0: would imply divisibility by 5, which 98 is not.

Common Pitfalls:
Arithmetic slips in base conversion (misvaluing bit weights) or forgetting the remainder must be less than the divisor.

Final Answer:
3