Problem:
Numeric codes can be verified by using a check digit. A check digit is an extra redundant digit added to a code number much as a parity bit is added to a byte. The check digit is computed when a code is initially assigned to a data element. Check digits are computed by applying mathematical calculations to the individual digits in a code number in such a way as to generate a result that is a single digit. The digit becomes the check digit and is added to the original code. In subsequent processing, this same mathematical operation can be performed to ensure that the code has not been recorded incorrectly.
There are numerous check-digit procedures. The following illustration is one version of a technique known as Modulus 11:
The use of check digits is very common because of the high reliability of this procedure. Commercial check-digit packages catch 100% of transposition errors and a very high percentage of random errors. However, check digits do not guard against all possible input errors.
Account number: 1 2 4 0
Multiply each digit separately X X X X
by the corresponding digit in
the sequence 5 4 3 2: 5 4 3 2
Add results of digit multiplication 5 + 8 + (1+2) + 0 = 16
digit by digit:
Subtract results form next highest
Multiple of 11: 22 – 16 = 6
Check digit: = 6
Complete account number: 12406
This question requires using the check-digit formula presented in this chapter.
(a) Calculate check digits for the following hypothetical account numbers: 4388, 5100, and 9106.
(b) Verify the following codes (which include a check digit): 10307, 50008, and 22222.