ITPEC FE Subject A April 2026 Question 18

Topic: Basic TheoryAlso asked in April 2019 and October 2022

For a given decimal data, the check digit is calculated using the method below and appended to the original data. When the given data is 7394, what is the result? Here, the weight is 1234 and the base number is 11.

(1)For each digit of the data, calculate the product with the digit at the same digit position of the weight and sum these products.(2)Calculate the remainder after dividing the total sum by the base number.(3)Subtract the remainder from the base number and let the last digit of the result be the check digit.

Explanation

73940 — the check digit is 0, appended to 7394.

Apply the steps to data 7394 with weight 1234 and base 11:

  1. Weighted sum: 7 × 1 + 3 × 2 + 9 × 3 + 4 × 4 = 7 + 6 + 27 + 16 = 56
  2. Remainder: 56 mod 11 = 1
  3. 11 − 1 = 10; its last digit, 0, is the check digit

Answer (a)

Why not others:

  • •(b) 73941 — uses the remainder 1 as the check digit, skipping step 3
  • •(d) 73947 — applies the weight in reverse (4321): sum 28 + 9 + 18 + 4 = 59, 59 mod 11 = 4, 11 − 4 = 7
  • •(c) 73944 — the same reversed weighting, stopping at the remainder 4

Key rule: Align the weight with the data digit by digit from the left, and finish every step: the check digit is the last digit of base minus remainder, not the remainder.

Basic Theory · AI-written, may contain errors

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