The Remainder Of The System And Its Scaling Problems And Vlsi Implementation

Deriving from CRT ("Chinese Reminder Theory"), Residue Number System (RNS) is an inherent unpositional and parallel number representation system. RNS is perspective for high performance datapaths design that was widely used in communication and information systems. Taking the 16-taps FIR filter implementation in RNS and Sign Digit as an example, the area, delay and power consumption is one out of seven compared to that in the traditional binary system.RNS is a special number representation system with entirely new number representation and computing methods. There are still a lot of hard issues in RNS, one of which is scaling that the paper focus on. In this paper, High performance 2m scaling technology which improved the traditional cascading scheme and avoided multiple 1 bit scaling and parity detecting was developed in light of the Division Remainder Zero Theorem and the conjugate moduli-set. Moreover, A FIR filter was implemented in RNS with scaling which shown the important contribution of scaling for performance enhancement in RNS. Also, the paper summarized the main achievement of RNS systematicly, as the lack of monographic and comprehensive references of RNS in domestic area.The main productions and contributions of this paper are as follows:1. Improving the description method of the RNS in light of the algebraic conceptions, making the structural character of RNS more obvious;2. Summarizing the basic problems of RNS and its typical solutions;3. studying and developing the high performance scaling technologies and the high performance RNS design schemes according to the FIR implementation in RNS;4. RNS studying at the help of the algebraic structure; proposing the positional moduli-set residue number system (PMSRNS).