LEADER 05684nam 2200709Ia 450 001 9910819944903321 005 20240402140025.0 010 $a1-281-86758-6 010 $a9786611867584 010 $a1-86094-867-7 035 $a(CKB)1000000000401687 035 $a(EBL)1679314 035 $a(OCoLC)815742108 035 $a(SSID)ssj0000236700 035 $a(PQKBManifestationID)11175579 035 $a(PQKBTitleCode)TC0000236700 035 $a(PQKBWorkID)10193545 035 $a(PQKB)10954051 035 $a(MiAaPQ)EBC1679314 035 $a(WSP)0000P523 035 $a(Au-PeEL)EBL1679314 035 $a(CaPaEBR)ebr10255548 035 $a(CaONFJC)MIL186758 035 $a(EXLCZ)991000000000401687 100 $a20070910d2007 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aResidue number systems $etheory and implementation /$fAmos Omondi, Benjamin Premkumar 205 $a1st ed. 210 $aLondon $cImperial College Press ;$aSingapore ;$aHackensack, NJ $cDistributed by World Scientific Publishing$dc2007 215 $a1 online resource (311 p.) 225 1 $aAdvances in computer science and engineering: Texts ;$vv. 2 300 $aDescription based upon print version of record. 311 $a1-86094-866-9 320 $aIncludes bibliographical references and index. 327 $aContents; 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 327 $a2.7 The Core Function2.8 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 327 $a4.1.2 Carry-skip adder4.1.3 Carry-lookahead adders; 4.1.4 Conditional-sum adder; 4.1.5 Parallel-prex? 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 327 $a5.3 Modular multiplication: arbitrary modulus5.3.1 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 327 $a6.3.1.2 Pseudo-SRT division6.3.2 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 l?ters; 8.1.1.2 Infinite Impulse Response Filters; 8.1.2 Sum-of-products evaluation 327 $a8.1.3 Discrete Fourier Transform 330 $a Residue number systems (RNSs) and arithmetic are useful for several reasons. First, a great deal of computing now takes place in embedded processors, such as those found in mobile devices, for which high speed and low-power consumption are critical; the absence of carry propagation facilitates the realization of high-speed, low-power arithmetic. Second, computer chips are now getting to be so dense that full testing will no longer be possible; so fault tolerance and the general area of computational integrity have become more important. RNSs are extremely good for applications such as digital 410 0$aAdvances in computer science and engineering.$pTexts ;$vv. 2. 606 $aCongruences and residues 606 $aModular arithmetic 606 $aSignal processing$xDigital techniques 615 0$aCongruences and residues. 615 0$aModular arithmetic. 615 0$aSignal processing$xDigital techniques. 676 $a512.72 700 $aOmondi$b Amos R$0770765 701 $aPremkumar$b Benjamin$01691569 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910819944903321 996 $aResidue number systems$94068052 997 $aUNINA