Generalized Parity Checking

The usual definition given for the parity check is unwieldy and not particularly suited for the analysis or the study of the arithmetic properties of parity checking. The definition of parity by means of congruences provides a convenient mathematical basis for the concepts of the parity check. In this paper congruence notation is used to generalize the concepts of parity to include nonbase two number systems. Consideration is given to the cases where the check base is equal to the number base, and where it is not equal to the number base. The arithmetic properties of each case are considered by means of congruences.