Compute the binary division: 100011 (base 2) ÷ 101 (base 2). What is the quotient in binary?

Introduction / Context:
Binary arithmetic mirrors decimal arithmetic, but it operates with base 2 digits (0 and 1). Dividing binary numbers is a fundamental digital design skill used in computer arithmetic, error checking, and algorithm analysis. Here, we divide 100011 (base 2) by 101 (base 2) and report the binary quotient.

Given Data / Assumptions:

• Dividend = 100011 (base 2).
• Divisor = 101 (base 2).
• We want the exact quotient (no remainder reported, but we will check).

Concept / Approach:
The fastest way is to convert to decimal for validation, or to perform long division directly in binary. In decimal, 100011₂ = 32 + 2 + 1 = 35, and 101₂ = 4 + 1 = 5. Since 35 ÷ 5 = 7 and 7 in binary is 111₂, the expected quotient is 111₂. We can also verify by binary long division or by multiplying back: 111₂ * 101₂ should yield 100011₂.

Step-by-Step Solution:

Verification / Alternative check:
Multiply to confirm: 111₂ * 101₂. Compute: 111₂ * 101₂ = 111₂*(1*2^2 + 0*2^1 + 1*2^0) = (111₂ << 2) + (111₂ << 0) = 11100₂ + 111₂ = 100011₂. This matches the original dividend exactly, confirming no remainder.

Why Other Options Are Wrong:

Common Pitfalls:
Dropping leading zeros or misaligning shifts during binary long division; forgetting that subtraction in binary uses the same borrow rules as decimal but with base 2. Always verify by multiplying quotient and divisor to recover the dividend.

Final Answer:
111 (base 2)