Reducing Computing Time for Synchronous Binary Division

The computing time for binary division is shortened by performing division, radix 2p on the binary operands, where p is a positive integer. Each quotient digit radix 2p is computed in almost the same time required to determine a binary quotient digit. Therefore, computing time is reduced by approximately the factor p over conventional binary division. The method is most useful for synchronous machines but can be applied to either serial or parallel operation. The theory of nonrestoring division in any integral radix r is discussed. Each quotient digit is considered as the sum of two recursive variables ak and bk, whose values depend on the divisor multiplier and relative signs of the partial remainders. The divisor multiplier is limited to odd integers in order to determine the quotient digit unambiguously. Using ak and bk, a single recursive equation combining all sign conditions is derived. This permits the derivation of the correct round-off procedure and shows that binary nonrestoring division is a particular case of nonrestoring division, radix r. An arrangement of components for a serial computer and a sample division for radix four are given.