This text should prove a useful reference for both professional and academic researchers in the field of VLSI using residue number systems. It should also be of interest to those working in the general fields of VLSI design, DSP design, and cryptography. Topics covered include: choice of moduli; architectures for conversion from binary to RNS; RNS to binary conversion techniques; quadratic RNS; and applications. Numerous examples illustrate the ideas developed. The area and computational requirements are highlighted for all designs, so the selection of a particular architecture is facilitated. Some of the topics covered have application in cryptography.