Contents -- Preface -- Acknowledgements -- 1. Introduction -- 1.1 Conventional number systems -- 1.2 Redundant signed-digit number systems -- 1.3 Residue number systems and arithmetic -- 1.3.1 Choice of moduli -- 1.3.2 Negative numbers -- 1.3.3 Basic arithmetic -- 1.3.4 Conversion -- 1.3.5 Base extension -- 1.3.6 Alternative encodings -- 1.4 Using residue number systems -- 1.5 Summary -- References -- 2. Mathematical fundamentals -- 2.1 Properties of congruences -- 2.2 Basic number representation -- 2.3 Algebra of residues -- 2.4 Chinese Remainder Theorem -- 2.5 Complex residue-number systems -- 2.6 Redundant residue number systems -- 2.7 The Core Function -- 2.8 Summary -- References -- 3. Forward conversion -- 3.1 Special moduli-sets -- 3.1.1 {2n-1, 2n -- 2n+1g} moduli-sets -- 3.1.2 Extended special moduli-sets -- 3.2 Arbitrary moduli-sets: look-up tables -- 3.2.1 Serial/sequential conversion -- 3.2.2 Sequential/parallel conversion: arbitrary partitioning -- 3.2.3 Sequential/parallel conversion: periodic partitioning -- 3.3 Arbitrary moduli-sets: combinational logic -- 3.3.1 Modular exponentiation -- 3.3.2 Modular exponentiation with periodicity -- 3.4 Summary -- References -- 4. Addition -- 4.1 Conventional adders -- 4.1.1 Ripple adder -- 4.1.2 Carry-skip adder -- 4.1.3 Carry-lookahead adders -- 4.1.4 Conditional-sum adder -- 4.1.5 Parallel-prex̄ adders -- 4.1.6 Carry-select adder -- 4.2 Residue addition: arbitrary modulus -- 4.3 Addition modulo 2n-1 -- 4.3.1 Ripple adder -- 4.3.2 Carry-lookahead adder -- 4.3.3 Parallel-prefix adder -- 4.4 Addition modulo 2n + 1 -- 4.4.1 Diminished-one addition -- 4.4.2 Direct addition -- 4.5 Summary -- References -- 5. Multiplication -- 5.1 Conventional multiplication -- 5.1.1 Basic binary multiplication -- 5.1.2 High-radix multiplication -- 5.2 Conventional division -- 5.2.1 Subtractive division.

5.2.2 Multiplicative division -- 5.3 Modular multiplication: arbitrary modulus -- 5.3.1 Table lookup -- 5.3.2 Modular reduction of partial products -- 5.3.3 Product partitioning -- 5.3.4 Multiplication by reciprocal of modulus -- 5.3.5 Subtractive division -- 5.4 Modular multiplication: modulus 2n-1 -- 5.5 Modular multiplication: modulus 2n + 1 -- 5.6 Summary -- References -- 6. Comparison, overflow-detection, sign-determination, scaling, and division -- 6.1 Comparison -- 6.1.1 Sum-of-quotients technique -- 6.1.2 Core Function and parity -- 6.2 Scaling -- 6.3 Division -- 6.3.1 Subtractive division -- 6.3.1.1 Basic subtractive division -- 6.3.1.2 Pseudo-SRT division -- 6.3.2 Multiplicative division -- 6.4 Summary -- References -- 7. Reverse conversion -- 7.1 Chinese Remainder Theorem -- 7.1.1 Pseudo-SRT implementation -- 7.1.2 Base-extension implementation -- 7.2 Mixed-radix number systems and conversion -- 7.3 The Core Function -- 7.4 Reverse converters for f2n ¡ 1 -- 2n -- 2n + 1g moduli-sets -- 7.5 High-radix conversion -- 7.6 Summary -- References -- 8. Applications -- 8.1 Digital signal processing -- 8.1.1 Digital filters -- 8.1.1.1 Finite Impulse Response l̄ters -- 8.1.1.2 Infinite Impulse Response Filters -- 8.1.2 Sum-of-products evaluation -- 8.1.3 Discrete Fourier Transform -- 8.1.3.1 Fourier Series -- 8.1.4 RNS implementation of the DFT -- 8.2 Fault-tolerance -- 8.3 Communications -- 8.4 Summary -- References -- Index.