Error detection and correction for addition and subtraction, through use of higher radix extensions of hamming codes

Abstract

The properties of Hamming codes for error detection and correction can be extended from the binary parity check to addition, modulo 2r. Malfunctions in hardware during addition, modulo 2r, can be detected and corrected. Since carry-save and signed-digit addition, radix r, are included in addition, modulo 2r, this extension of Hamming codes makes possible new techniques for detection and correction of hardware malfunctions during signed-digit and carry-save addition.