Convert the decimal value 61 (base 10) to its binary (base 2) equivalent using division-by-2 and verify by place-value expansion.

Introduction / Context:
Binary conversion is essential for understanding data representation and hardware operations. This problem reinforces repeated-division conversion and verification by expanding powers of 2.

Given Data / Assumptions:

• Given: 61 in base 10.
• Target: base 2 (binary).
• No fractional part is involved.

Concept / Approach:
Use repeated division by 2, recording remainders, then read them in reverse. Alternatively, sum powers of 2 that equal the decimal number to verify the result.

Step-by-Step Solution:

Verification / Alternative check:
111101₂ = 1*2^5 + 1*2^4 + 1*2^3 + 1*2^2 + 0*2^1 + 1*2^0 = 32 + 16 + 8 + 4 + 0 + 1 = 61. Verified.

Why Other Options Are Wrong:

• 110011₂: equals 51.
• 11001110₂: equals 206.
• 11111₂: equals 31.
• None of the above: incorrect because 111101₂ is correct.

Common Pitfalls:
Writing remainders in forward order, dropping a remainder, or miscomputing powers of 2 during verification.

Final Answer:
111101₂