Binary multiplication check – is the product of 1011 (base 2) and 0110 (base 2) equal to 01100110?

Introduction / Context:
This item checks binary multiplication and result verification. Multiplying two unsigned binary numbers follows the same partial-products idea as decimal multiplication, but with base 2 digits (0/1). The claim proposes a specific product; we must compute and compare.

Given Data / Assumptions:

• Multiplicand: 1011 (base 2) = 11 (decimal).
• Multiplier: 0110 (base 2) = 6 (decimal).
• Unsigned multiplication; no overflow truncation assumed.
• Exact equality to 01100110 is asserted.

Concept / Approach:
Convert to decimal (sanity check) or perform binary partial products. 11 * 6 = 66 (decimal). The correct 66 in binary is 1000010 (base 2). The proposed 01100110 equals 102 (decimal), which does not match 66, so the statement is wrong.

Step-by-Step Solution:

Verification / Alternative check:
Decimal first: 11 * 6 = 66. Convert 66 to binary by successive division: 66 = 64 + 2 → 1000010. Matches the computed binary sum, confirming correctness of our evaluation.

Why Other Options Are Wrong:
“Correct” is false because 01100110 ≠ 66. “Only if leading zeros are kept” is irrelevant; leading zeros change width, not value. “Only with signed operands” does not change 11 * 6. “Depends on bit-width wrapping” would matter only if truncation were specified; it was not, and even then, the given pattern still doesn’t match 66 exactly.

Common Pitfalls:
Misreading 01100110 as 66 due to hex association (0x66 = 102). Also, forgetting that shifting left by k equals multiplying by 2^k.

Final Answer:
Incorrect