ITPEC FE Morning October 2022 Question 23

Topic: Basic TheoryAlso asked in April 2019 and April 2026

For a given decimal data, the check digit is calculated with the method below and is 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 radix of the weight and calculate the sum of these products.(2)Calculate the remainder after the division of the 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, pairing each data digit with the weight digit in the same position: 7 × 1 + 3 × 2 + 9 × 3 + 4 × 4 = 7 + 6 + 27 + 16 = 56
  2. Remainder: 56 mod 11 = 1, since 56 = 5 × 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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