Error Codes for Arithmetic Operations

This paper classifies error correcting codes for arithmetic and provides the necessary and sufficient conditions for the various code classes. Particular attention is given to the arithmetic properties of the codes. It is shown that the Brown codes and the Henderson codes are examples of a general class of nonseparate, nonsystematic codes. Henderson's systematic code is shown to be the only systematic, nonseparate code. Finally, conditions are given for the existence of code classes for both radix complement and diminished radix complement coded arithmetic systems.