Abstract

In this thesis, novel modulo reduction algorithms are proposed that considerably simplify a large modulo operation to the sum of a number of small modulo operations. By applying the proposed modulo reduction algorithms to the modified Chinese Remainder Theorem (CRT), the complexity of modulo operation in the modified CRT is reduced significantly. The modulo reduction technique and the modulo reduced modified CRT are applied to derive R/B algorithms for two existing three-moduli sets and four newly found three-moduli sets. A novel R/B converter for N 1 = {2 n , 2 n + 1, 2 n - 1} with reduced modulo operations is proposed to show the efficiency of the proposed modulo reduction technique. Novel MUX-based designs of some components needed for constructing the new converter are developed. New unsigned and signed-2's complement incrementer/decrementer are designed to implement the operation of Z ± 1. The new modulo incrementer and decrementer are developed to implement the operations of [Special characters omitted.] and [Special characters omitted.] . (Abstract shortened by UMI.)