Arithmetic Operations for Digital Computers Using a Modified Reflected Binary Code

The reflected binary or Gray code has been used chiefly in analog-to-digital conversion devices because its code sequences, representing any two consecutive integral numbers, differ in only one digit. This paper presents a method for performing the arithmetic operations of addition, subtraction, multiplication, and division using a modified reflected binary code. The modification for integral numbers is essentially the addition of an even parity check bit to the Gray code representation. This facilitates both the arithmetic operations and the detection of errors-in the arithmetic process as well as in transmission. An adder using this code requires circuitry which is more complex than that of a conventional binary adder by a factor of about two or three. However, the adder can be used also for subtraction with little additional circuitry and without complementation. In applications where reliability requirements justify the extra circuitry needed for arithmetic error detection, the modified reflected binary code may compare favorably with the conventional binary.