Residue Number Systems Algorithms and Architectures

1. Introduction : 1.1. Historical survey -- 1.2. Basic definitions of RNS -- 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-l,2k,2k+1} : -- 3.1. Introduction -- 3.2. Forward conversion architectures -- 3.3. Reverse converters for the moduli set {2k-1, 2k, 2+l} -- 3.4. Forward and Reverse converters for the moduli set {2k, 2k-l, -- 2 k- -1} -- 3.5. Forward and reverse converters for the moduli sets {2n+l, -- 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 num ber systems -- 5.4. Scaling in the Moduli set {2n-1, 2n, 2'+1} -- 5.5. Conclusion -- 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 systms -- 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 form r -- 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.