RNS‐Based Arithmetic Circuits and Applications

Residue number system (RNS) is a well developed computing technique and popularly used in several digital signal processing, communication, and security applications. For RNS‐based computation, one need to do the following: converting the decimal or binary number to RNS representation by evaluating the residues; performing all arithmetic operations in residue domain; and convert back the result in residue representation to decimal or binary representation. An RNS‐based processor consists of binary to RNS convertor, residue domain processors, and the RNS to binary converter. This chapter deals with various issues involved in the design of RNS‐based processors. It discusses RNS to binary conversion, and considers the topic of scaling and base extension. It further describes modulo addition and subtraction, and modulo multiplication and squaring. Several applications of RNS for realizing FIR filters, cryptographic hardware and digital communication systems have been described in literature. The chapter concludes by reviewing these applications.