Residue number system's (RNS) non-modular operations efficient implementation based on Chinese remainder theorem II (CRT II)

Residue number system (RNS) is an alternative method of number representation, it is basically different from weighted number system such as decimal and binary. The RNS is based on modular arithmetic.; The RNS system has attracted many researchers in the last decade. The researchers have been focused on the theory of improving the RNS system and applying the RNS in some application areas, such as digital signal processing, fast fourier transform (FFT), digital filter, and image processing.; The RNS system is inherently parallel, modular, and fault isolating. In addition, the main advantage of RNS system is the carry free operation in modular arithmetic operation: addition, subtraction, and multiplication. On the other hand, in non-modular operation such as, magnitude comparison, sign detection, and overflow detection are very slow and time consuming. Therefore, the RNS system is not widely used. Also the implementation of the RNS algorithms require efficient modular adders, and modular multipliers.; This dissertation presents algorithms and implementation techniques that improve the RNS non-modular operations. New methods are proposed for sign detection, RNS to Binary and Binary to RNS converters, number comparison, and overflow detection. These methods are based on chinese remainder theorem II (CRT II). Also in this dissertation new design architectures for modulo 2n-a adders and modulo 2n-a multipliers are presented, where a = 1 or 2m + 1 and m < n.