余数系统论文.doc

摘 要 余数系统[1]（Residue Number System）源于古老的“中国余数定理（CRT，Chinese Reminder Theory）”，是一个天然的无权、并行的数值表征系统。它在通信和信息处理系统中有着巨大的应用潜力。以16抽头的FIR数字滤波器为例，ABSTRACT 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： Improving the description method of the RNS in light of the algebraic conceptions, making the structural character of RNS more obvious; Summarizing the basic problems of RNS and its typical solutions; studying and developing the high performance scaling technologies and the high performance RNS design schemes according to the FIR implementation in RNS; RNS studying at the help of the algebraic structure; proposing the positional moduli-set residue number system (PMSRNS). Keywords: RNS, CRT, scaling, positional moduli set residue number system  目 录 第一章 绪论 1 1.1 引言 1 1.