Compute the binary multiplication: 111 (base 2) × 101 (base 2). What is the product in binary?

Introduction / Context:
Binary multiplication is essential for digital arithmetic units. The operation mirrors decimal long multiplication but uses shifts and additions in base 2. Here we multiply 111₂ by 101₂ and provide the binary product.

Given Data / Assumptions:

• Multiplicand = 111 (base 2) = 7 decimal.
• Multiplier = 101 (base 2) = 5 decimal.
• We perform exact multiplication and present the result in binary.

Concept / Approach:
One approach is to convert to decimal (7×5=35) and convert back to binary (35 = 32+2+1 = 100011₂). Alternatively, perform binary long multiplication using partial products and left shifts corresponding to the multiplier’s 1-bits.

Step-by-Step Solution:

Verification / Alternative check:
Decimal cross-check: 111₂ = 7 and 101₂ = 5; 7×5=35. Convert 35 to binary: 35 = 32 + 2 + 1 → 100011₂, matching the computed result precisely.

Why Other Options Are Wrong:

Common Pitfalls:
Misaligning shifts when forming partial products and forgetting that a 0 bit produces no partial product. Always add carefully and confirm by converting to decimal if in doubt.

Final Answer:
100011 (base 2)