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Computer Science IGCSEPDF 17
142 pagesrevision 46930
PDF 17
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Calculation 1 - Generation of the check digit from the other digits in a number
(In this example, we will assume the original number contained only 7 digits.)
The following algorithm generates the check digit from the other 7 digits:
1 each digit in the number is given a weighting of 8, 7, 6, 5, 4, 3 or 2 starting from the
left [weightings start from 8 since the number will become eight-digit when the
check digit is added)
the digit is multiplied by its weighting and then each value is added to make a total
the total is divided by 11
the remainder is then subtracted from 11 to find the check digit (note if the
remainder is 10 then the check digit *X’ is used).
BRON
The example to be used has the following seven-digit number:
1 7-digitnumber: 4156710
weighting values: 8765432
2 sum: (8 x 4) + (7 « 1) + (6 x 5) + (5 » 6) + (4 % 7) + (3 x 1) 4+ (2 x 0)
= 32 + 7 + 30+ 30 + 28 + 3 + O
total = 130
3. divide total by 11: 130/11 = 11 remainder 9
4 subtract remainder from 11: 11 - 9 = 2 (check digit)
So we end up with the following eight-digit:4 15467 102
Calculation 2 - Re-calculation of the check digit from the eight-digit number (which
now includes the check digit)
To check that the eight-digit number is correct, including its check digit, a similar
process is followed:
1 each digit in the number is given a weighting of 8, 7, 6,5, 4, 3, 2 or 1 starting from
the left
2 the digit is multiplied by its weighting and then each value is added to make a total
3 the total is divided by 11
4 the number is correct if the remainder is zero
Usingthe 8-digitnumber: 4 1 5 6 7 4 Q 2
1 weighting values: & 2 6&6 @& &.@. 2 4
2 sum: (8 x 4) +(7 = 1) + (6 x 5) + (5x 6) + (4 x 7) + (3 x 1) + (2 x 0) + (1 x 2)
= 32 + 7 * 30 + 30 + 28 + 3 + O + 2
total = 132
3 divide total by 11: 132/11 = 12 remainder 0
4 remainder is 0, therefore number is correct