ITPEC FE Morning October 2022 Question 23

Check Digit Calculation — append a verification digit using weighted sum modulo a base.

Given data 7394, weight 1234, base 11:

Step 1 — weighted sum (weights applied left to right as given):
- 7×1 + 3×2 + 9×3 + 4×4 = 7 + 6 + 27 + 16 = 56

Step 2 — remainder:
- 56 mod 11 = 1

Step 3 — check digit:
- 11 - 1 = 10 → last digit of 10 = 0

Result: 7394 + 0 = 73940 → (a)

Why not others:
- (b) 73941 — would require remainder = 10, i.e. 11 - 10 = 1
- (c) 73944 — would require remainder = 7, i.e. 11 - 7 = 4
- (d) 73947 — would result from applying weights in reverse order (4,3,2,1)

Key rule: Apply weights exactly as given (left to right). The check digit is the last digit of (base - remainder) — when the result is two digits (e.g. 10), take only the ones digit (0).

AI-generated — may contain errors