ITPEC FE Morning April 2019 Question 24
Topic: Basic TheoryAlso asked in October 2022 and April 2026
For a given data, the check digit is calculated with the method below and is appended to the original data. When the given data are 7394, what is the result? Here, the weight is 1234 and base number is 11.
(1)For each digit of the data, calculate the product with the digit at the same radix of the weight; then calculate the sum of the products.(2)Calculate the remainder of dividing the sum by the base number.(3)Subtract the remainder from the base number; then take the one’s place of the result as 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:
- 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
- Remainder: 56 mod 11 = 1, since 56 = 5 × 11 + 1
- 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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