Integer Division: DIV (Quotient) & MOD (Remainder)

In computer science, integer arithmetic frequently requires decomposing divisions into two distinct components: the whole number of times a divisor fits into a dividend, and the leftover remainder.

1. The Distinction Between /, DIV, and MOD

Fundamental Mathematical Identity:

2. Common Exam Applications in Cambridge Paper 2

1. Unit & Time Conversions

Transforming flat units (e.g. seconds, cents, grams) into compound units (e.g. hours/minutes/seconds, dollars/cents, kilograms/grams):

Hours <- TotalSeconds DIV 3600
RemainingSeconds <- TotalSeconds MOD 3600
Minutes <- RemainingSeconds DIV 60
Seconds <- RemainingSeconds MOD 60

2. Odd and Even Number Determination

Any integer N is even if and only if dividing by 2 leaves zero remainder:

IF Number MOD 2 = 0 THEN
    OUTPUT "Number is Even"
ELSE
    OUTPUT "Number is Odd"
ENDIF

3. Extracting and Stripping Digits

• Extract units digit: Units <- Value MOD 10 (e.g. 247 MOD 10 = 7)
• Strip units digit: Value <- Value DIV 10 (e.g. 247 DIV 10 = 24)