The Theory of Modulus N Check Digit Systems
W. G. Wild · ITNOW · 1968
Check digits are incorporated in coding systems in order to provide a check on the validity of codes. Modulus N, probably the most commonly used system, involves the division of the basic code number, or a number derived from the basic code number according to a predetermined set of rules, by an integer N, and the use of the remainder from this division or a derivative of the remainder, as check digits. The performance of check digit systems is normally quoted in terms of 'coverage percentages' eg a modulus 11 system gives an overall coverage of 91 per cent; that is nine per cent of all errors will go undetected. No system can guarantee 100 per cent. coverage of all possible errors but a figure approaching 100 per cent. is normally achieved for the more common types of error. This paper will only deal with check digit systems applied to all numeric codes. The method of approach is equally valid for alpha-numeric codes but the effects of bases other than 10 must be allowed for.