Division algorithms – do binary division and decimal long division follow the same fundamental procedure?

Introduction / Context:
Long division teaches a sequence of trial, multiply, subtract, and bring-down steps. In binary arithmetic, division uses the same conceptual loop with digits restricted to 0/1, making trial selection simpler. This question tests whether you recognize the shared structure across radices.

Given Data / Assumptions:

• Unsigned integers for clarity.
• Manual long division analogy; hardware may use restoring/non-restoring variants.
• Base (radix) affects digit choices, not the core loop.

Concept / Approach:
Both decimal and binary division iterate: compare partial remainder with divisor, place a quotient digit (1 or 0 in binary), multiply divisor by that digit, subtract, and shift/bring down the next digit. Binary simplifies digit choice to a yes/no (fit/no fit), but the algorithmic skeleton is the same.

Step-by-Step Solution:

Verification / Alternative check:
Hardware division (restoring or non-restoring) mirrors these steps with shift-subtract cycles. Software long division loops implement the same logic with bit tests and subtractions.

Why Other Options Are Wrong:
Restricting to powers of two or no remainder is unnecessary. Restoring vs non-restoring are implementation details; both follow the same overarching pattern.

Common Pitfalls:
Confusing digit set differences (0–9 vs 0–1) with a different algorithm. The control flow remains the same.

Final Answer:
Correct