Binary division and square-rooting using gray code

Abstract

A new method to perform binary division and take square roots is presented. It produces the Gray Code representation of the quotient/root, by performing a sequence of shift, subtract and absolute value operations on the dividend and the divisor or the square and the root, and converts the result to the binary representation at the same time. The method has a simpler synchronous hardware implementation than the non-restoring algorithm. The division method may be regarded as the digital equivalent of an A/D conversions method proposed earlier. As the division and square rooting operations require rather similar shift-and-subtract logic circuits, they can be incorporated into a multi-function arithmetic unit.