Difficulty: Easy
Correct Answer: Correct
Explanation:
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:
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:
1) Initialize partial remainder from the highest-order bits/digits.2) Decide quotient digit (binary: 1 if divisor fits, else 0).3) Multiply divisor by chosen digit and subtract from partial remainder.4) Bring down/shift next bit and repeat until all bits are processed.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
Discussion & Comments