Abstract: A method and apparatus for radix-.beta. non-restoring division. The division process occurs in four phases. In a first phase, the input operands are transformed to produce a divisor lying in a designated numerical range. Next, a transitional phase involves generating an initial radix-.beta. quotient digit from the transformed numerator. An iterative phase of the process generates successive partial remainders according to a recursive method. From the sign and a single radix-.beta. digit of each of these partial remainders, the process generates a radix-.beta. quotient digit. Further, a fourth phase, which may run concurrently with the transitional and iterative phases, involves accumulating successively generated quotient digits to produce a final quotient value.

Abstract: A range transformation method for transforming the normalized divisor in a division calculation to a range wherein the transformed value differs from one by no more than the quantity 2.sup.-n. The method and apparatus generate the transform multiplier value from a first high order "q" digits of the divisor and generate an out-of-range indicator signal from at least those same digits. The thus generated multiplier value is modified in response to the out-of-range indicator signal when an out-of-range condition is indicated. The apparatus employs a read-only-memory for enabling the generation of the transform multiplier value without requiring either large table look-up storage or multiplicative functions. As a result, various division methods requiring an initial transformation to provide a divisor which approaches one in value can be efficiently implemented.