ITPEC FE Morning April 2022 Question 8

Integer Division via Subtraction — flowchart computes quotient and remainder of x ÷ y.

The algorithm initializes q ← 0, r ← x, then repeatedly subtracts y from r while r ≥ y, incrementing q each time.

• •q counts how many times y fits into x → quotient
• •r holds whatever is left over → remainder

Example: x = 13, y = 4
- r = 13 - 4 = 9, q = 1
- r = 9 - 4 = 5, q = 2
- r = 5 - 4 = 1, q = 3
- r < y → stop → q = 3, r = 1

Why not others:
- (b) Quotient/remainder of y ÷ x — division is x by y, not reversed
- (c) Swaps quotient and remainder — q counts subtractions (quotient), r holds leftover (remainder)
- (d) Both reversed and swapped

Key rule: Repeated subtraction is the most basic division algorithm: subtract divisor from dividend, count iterations (quotient), stop when remainder < divisor.

AI-generated — may contain errors