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Binary Division — Compute 01011000₂ ÷ 00001011₂ and give the integer (truncated) quotient in binary.

Difficulty: Easy

Correct Answer: 1000

Explanation:


Introduction:
Here we divide two unsigned 8-bit numbers and report the integer quotient. Understanding binary division and being able to cross-check quickly in decimal helps ensure correctness and avoid bit-level mistakes.

Given Data / Assumptions:

  • Dividend = 01011000₂ (decimal 88).
  • Divisor = 00001011₂ (decimal 11).
  • Unsigned division with integer (floor) quotient; no remainder requested.


Concept / Approach:
Translate to decimal to validate the magnitude, then map back to binary. Alternatively, perform long division in base-2. Since 88 ÷ 11 = 8 exactly, we expect a clean binary power of two for the quotient.

Step-by-Step Solution:

Step 1: Convert operands: 01011000₂ = 88, 00001011₂ = 11.Step 2: Compute 88 ÷ 11 = 8 (integer, remainder 0).Step 3: Convert 8 to binary: 8 = 2^3 ⇒ 1000₂.Step 4: Match with options: 1000 is present.


Verification / Alternative check:

Binary long division corroborates a clean 1000 quotient with zero remainder since 11 × 8 = 88.


Why Other Options Are Wrong:

1010 = 10 decimal; would imply 10 × 11 = 110 ≠ 88.0110 = 6 decimal; 6 × 11 = 66, too small.1110 = 14 decimal; 14 × 11 = 154, too large.


Common Pitfalls:

Confusing 1010 (10) or 1110 (14) with the exact quotient.Forgetting to reconvert to binary after computing in decimal.


Final Answer:

1000
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