Residue Number Systems Algorithms and Architectures P.V. Ananda Mohan

References : pp. 235 - 251, index : pp. 253 - 254

Preface 1. Introduction 1.1 Historical survey 1.2 Basic definitions of PNS 1.3 Addition operation in RNS 1.4 Conclusion 2. Forward and Reverse Converters for General Moduli Set 2.1 Introduction 2.2 Mixed Radix Conversion based techniques 2.3 CRT based conversion techniques 2.4 Binary to RNS conversion techniques 2.5 Conclusion 3. Forward and Reverse Converters for General Moduli Set {2k-1,2k, 2k+1} 3.1 Introduction 3.2 Forward conversion architectures 3.3 Reverse converters for the moduli set {2k - 1, 2k, 2k + 1} 3.4 Forward and Reverse converters for the moduli set {2k, 2k - 1, 2k-1 -1} 3.5 Forward and reverse converters for the moduli sets {2n =1, 2n, 2n -1} 3.6 Conclusion 4. Multipliers for RNS 4.1 Introduction 4.2 Multipliers based on index calculus 4.3 Quarter Square multipliers 4.4 Taylor's multipliers 4.5 Multipliers with in - built scaling 4.6 Razavi and battelini architectures using periodic properties of residues 4.7 Hiasat's Modulo multipliers 4.8 Elleithy and Bayoumi modulo multiplication technique 4.9 Brickell's algorithm based multipliers and extensions 4.10 Stouraitis et al architectures for (A.X + B) mod mi realization 4.11 Multiplication using Redundant Number system 4.12 Conclusion 5. Base extension, scaling and division techniques 5.1 Introduction 5.2 Base extension and scaling techniques 5.3 Division in residue number systems 5.4 Scaling in the Moduli set {2n - 1, 2n, 2n +1} 6. Error detection and Correction in RNS 6.1 Introduction 6.2 Szabo and Tanaka technique for Error detection and Correction 6.3 Mendelbaum's Error correction technique 6.4 Jenkins's Error correction techniques 6.5 Ramachandran's Error correction technique 6.6 Su and Lo unified technique for scaling and error correction 6.7 Orto et al technique for error correction and detection using only one redundant modulus 6.8 Conclusion 7. Quadratic Residue Number Systems 7.1 Introduction 7.2 Basic operations in QRNS 7.3 Modified quadratic residue number systems 7.4 Jenkins and Krogmeier implementations 7.5 Taylor's single modulus ALU for QRNS 7.6 Conclusion 8. Applications of Residue Number Systems 8.1 Introduction 8.2 Digital Analog Converters 8.3 FIR Filters 8.4 Recursive RNS filter implementation 8.5 Digital frequency synthesis using RNS 8.6 Multiple Valued Logic Based RNS designs 8.7 Paliouras and Stouraitis architectures using moduli of the from rn 8.8 Taheri, Jullien and Miller technique of High-speed computation in rings using systolic Architectures 8.9 RNS based implementation of FFT structures 8.10 Optimum Symmetric Residue Number System 8.11 Conclusion 9. References Index