Error Detecting and Correcting Binary Codes for Arithmetic Operations

Abstract

The most important property of the codes derived in this paper is that two numbers, i and j, have coded forms, C(i) and C(j) that when added in a conventional binary adder, give a sum C(i)+C(j) that differs from C(i+j), the code for the sum, by (at most) an additive constant. This makes possible the detection and/or correction of errors committed by the arithmetic element of a computer. In addition, messages can be coded and decoded and errors can be detected and corrected by arithmetic procedures, making it possible to elininate some or all of the special-purpose equipment usually associated with error-detecting or correcting codes. This property may make these codes useful for data transmission as well as for computation.