메뉴 건너뛰기




Volumn 17, Issue 5, 1984, Pages 50-62

Residue Arithmetic: A Tutorial with Examples

Author keywords

[No Author keywords available]

Indexed keywords

RESIDUE NUMBERING SYSTEM;

EID: 0021428663     PISSN: 00189162     EISSN: None     Source Type: Trade Journal    
DOI: 10.1109/MC.1984.1659138     Document Type: Article
Times cited : (178)

References (43)
  • 1
    • 84944481467 scopus 로고
    • Decimal Arithmetic Unit
    • CSAU, Praha, Czech.
    • “Decimal Arithmetic Unit,” in Stroje Na Zprocovani, A. Nakl, ed., CSAU, Praha, Czech., 1962 (in Czech).
    • (1962) Stroje Na Zprocovani
    • Nakl, A.1
  • 2
    • 0001049670 scopus 로고
    • The Residue Number System
    • H. L. Garner, “The Residue Number System,” IRE Trans. Electronic Computers, Vol. EL-8, No. 6, June 1959, pp. 140–147.
    • (1959) IRE Trans. Electronic Computers , vol.EL-8 , Issue.6 , pp. 140-147
    • Garner, H.L.1
  • 5
    • 84939337452 scopus 로고
    • The Implementation of a Residue Arithmetic Unit via Optical and Other Physical Devices
    • A. Huang, “The Implementation of a Residue Arithmetic Unit via Optical and Other Physical Devices,” Proc. Int’l Optical Computing Conf., 1975, pp. 14–18.
    • (1975) Proc. Int’l Optical Computing Conf. , pp. 14-18
    • Huang, A.1
  • 9
    • 0017956245 scopus 로고
    • G. A. Jullien, “Residue Number Scaling and Other Operations Using ROM Arrays,” IEEE Trans. Computers, Vol. C-27, No. 4, Apr. 1978, pp. 325–336.
    • (1978) IEEE Trans. Computers , vol.C-27 , Issue.4 , pp. 325-336
    • Jullien, G.A.1
  • 10
    • 0020139085 scopus 로고
    • A VLSI Residue Arithmetic Multiplier
    • F. J. Taylor, “A VLSI Residue Arithmetic Multiplier,” IEEE Trans. Computers, Vol. C-31, No. 6, June 1982, pp. 540–546.
    • (1982) IEEE Trans. Computers , vol.C-31 , Issue.6 , pp. 540-546
    • Taylor, F.J.1
  • 11
    • 0016357682 scopus 로고
    • On the Use of Residue Arithmetic for Computation
    • D. K. Banerji, “On the Use of Residue Arithmetic for Computation,” IEEE Trans. Computers, Vol. C-23, Dec. 1974, pp. 1315–1317.
    • (1974) IEEE Trans. Computers , vol.C-23 , pp. 1315-1317
    • Banerji, D.K.1
  • 12
    • 0019654237 scopus 로고
    • An Efficient Residue-to-Decimal Converter
    • F. J. Taylor and A. S. Ramnarayanan, “An Efficient Residue-to-Decimal Converter,” IEEE Trans. Circuits and Systems, Vol. CAS-28, No. 12, Dec. 1981, pp. 1164–1169.
    • (1981) IEEE Trans. Circuits and Systems , vol.CAS-28 , Issue.12 , pp. 1164-1169
    • Taylor, F.J.1    Ramnarayanan, A.S.2
  • 13
    • 0020114805 scopus 로고
    • An Autoscale Residue Multiplier
    • F. J. Taylor and C. H. Huang, “An Autoscale Residue Multiplier,” IEEE Trans. Computers, Vol. C-31, No. 4, Apr. 1982, pp. 321–325.
    • (1982) IEEE Trans. Computers , vol.C-31 , Issue.4 , pp. 321-325
    • Taylor, F.J.1    Huang, C.H.2
  • 14
    • 0019592222 scopus 로고
    • Large Moduli Multipliers for Signal Processing
    • F. J. Taylor, “Large Moduli Multipliers for Signal Processing,” IEEE Trans. Circuits and Systems, Vol. CAS-28, No. 7, July 1981.
    • (1981) IEEE Trans. Circuits and Systems , vol.CAS-28 , Issue.7
    • Taylor, F.J.1
  • 17
    • 0017022029 scopus 로고
    • On the Design of Modulo Arithmetic Units Based on Cyclic Groups
    • S. S. Yau and J. Chung, “On the Design of Modulo Arithmetic Units Based on Cyclic Groups,” IEEE Trans. Computers, Vol. C-25, No. 11, Nov. 1976, pp. 1057–1067.
    • (1976) IEEE Trans. Computers , vol.C-25 , Issue.11 , pp. 1057-1067
    • Yau, S.S.1    Chung, J.2
  • 18
    • 0016626952 scopus 로고
    • A Computation Scheme for an Adder Modulo 2n +1
    • G. Bioul et al., “A Computation Scheme for an Adder Modulo 2n +1,” Digital Processes, Vol. 1, No. 4, winter 1975, pp. 309–318.
    • (1975) Digital Processes , vol.1 , Issue.4 , pp. 309-318
    • Bioul, G.1
  • 19
    • 0018032047 scopus 로고
    • Modulo 2**n + l Arithmetic Logic
    • D. P. Agarwal, “Modulo 2**n + l Arithmetic Logic,” IEEE J. Electronic Circuits and Systems, Vol. 2, No. 6, Nov. 1978, pp. 186–188.
    • (1978) IEEE J. Electronic Circuits and Systems , vol.2 , Issue.6 , pp. 186-188
    • Agarwal, D.P.1
  • 20
    • 0019476826 scopus 로고
    • A Floating-Point Residue Arithmetic Unit
    • F. J. Taylor and C. H. Huang, “A Floating-Point Residue Arithmetic Unit,” J. Franklin Institute, Vol. 311, Jan. 1981, pp. 33–53.
    • (1981) J. Franklin Institute , vol.311 , pp. 33-53
    • Taylor, F.J.1    Huang, C.H.2
  • 21
    • 84915320730 scopus 로고
    • Algorithms for Determination of the Reciprocal of a Number in a Residue Class System
    • Russian
    • V. A. Vyshysky and V. D. Petushchak, “Algorithms for Determination of the Reciprocal of a Number in a Residue Class System,” Soviet Automatic Control, Vol. 6, No. 3, May 1973, pp. 58–61 (in Russian).
    • (1973) Soviet Automatic Control , vol.6 , Issue.3 , pp. 58-61
    • Vyshysky, V.A.1    Petushchak, V.D.2
  • 22
    • 84944480904 scopus 로고
    • Efficient Residue Arithmetic Circuit Using Multiple-Valued Ring Counters and Its Application to Digital Signal Processing
    • N. Tomabechi, M. Kameyama, and T. Higuchi, “Efficient Residue Arithmetic Circuit Using Multiple-Valued Ring Counters and Its Application to Digital Signal Processing,” Proc. 12th Int’l Symp. Multiple-Valued Logic, Feb. 1982, pp. 107–112.
    • (1982) Proc. 12th Int’l Symp. Multiple-Valued Logic , pp. 107-112
    • Tomabechi, N.1    Kameyama, M.2    Higuchi, T.3
  • 23
    • 0000262556 scopus 로고
    • Error Correction in Residue Arithmetic
    • D. Mandelbaum, “Error Correction in Residue Arithmetic, IEEE Trans. Computers, Vol. C-21, No. 6, June 1972, pp. 538–545.
    • (1972) IEEE Trans. Computers , vol.C-21 , Issue.6 , pp. 538-545
    • Mandelbaum, D.1
  • 24
    • 0019074607 scopus 로고
    • Redundant Residue Number Systems for Error Detection and Correction in Digital Filters
    • M. Etzel and W. K. Jenkins, “Redundant Residue Number Systems for Error Detection and Correction in Digital Filters,” IEEE Trans. Acoustics, Speech and Signal processing, Vol. ASSP-29, No. 5, Oct. 1980.
    • (1980) IEEE Trans. Acoustics, Speech and Signal processing , vol.ASSP-29 , Issue.5 , pp. 30
    • Etzel, M.1    Jenkins, W.K.2
  • 26
    • 0017297894 scopus 로고
    • Digital Filtering Using Cotransforms in Finite Fields
    • H. Nussbaumer, “Digital Filtering Using Cotransforms in Finite Fields,” Electronic Letters, Vol. 12, No. 5, Mar. 4, 1976, pp. 113–114.
    • (1976) Electronic Letters , vol.12 , Issue.5 , pp. 113-114
    • Nussbaumer, H.1
  • 27
    • 0017481467 scopus 로고
    • The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters
    • W. K. Jenkins and B. J. Leon, “The Use of Residue Number Systems in the Design of Finite Impulse Response Digital Filters,” IEEE Trans. Circuits and Systems, Vol. CAS-24, No. 4, Apr. 1977, pp. 199–201.
    • (1977) IEEE Trans. Circuits and Systems , vol.CAS-24 , Issue.4 , pp. 199-201
    • Jenkins, W.K.1    Leon, B.J.2
  • 28
    • 0020141255 scopus 로고
    • The Design of Specialized Residue Classes for Efficient Recursive Digital Filter Realization
    • M. H. Etzel and W. K. Jenkins, “The Design of Specialized Residue Classes for Efficient Recursive Digital Filter Realization,” IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-30, No. 3, June 1982, pp. 370–380.
    • (1982) IEEE Trans. Acoustics, Speech and Signal Processing , vol.ASSP-30 , Issue.3 , pp. 370-380
    • Etzel, M.H.1    Jenkins, W.K.2
  • 29
    • 0019045595 scopus 로고
    • Complex Residue Number Arithmetic for High Speed Signal Processing
    • W. K. Jenkins, “Complex Residue Number Arithmetic for High Speed Signal Processing,” Electronics Letters, Vol. 16, No. 17, Aug. 1980, pp. 660–661.
    • (1980) Electronics Letters , vol.16 , Issue.17 , pp. 660-661
    • Jenkins, W.K.1
  • 30
    • 0019692547 scopus 로고
    • Adaptive Digital Control Implemented Using Residue Number Systems
    • C. I. Tan and B. C. McInnis, “Adaptive Digital Control Implemented Using Residue Number Systems,” Proc. 20th IEEE Conf. Decision and Control, Vol. 2, Dec. 1981, pp. 808–812.
    • (1981) Proc. 20th IEEE Conf. Decision and Control , vol.2 , pp. 808-812
    • Tan, C.I.1    McInnis, B.C.2
  • 32
    • 84944481472 scopus 로고
    • Feasibility of Utilizing a System of Residual Classes in Signal Processing Equipment
    • Russian
    • V. Y. Shubs, “Feasibility of Utilizing a System of Residual Classes in Signal Processing Equipment,” Izv Vuz Radioelectron USSR, Vol. 23, No. 1, Sept. 1975, pp. 75–76 (in Russian).
    • (1975) Izv Vuz Radioelectron USSR , vol.23 , Issue.1 , pp. 75-76
    • Shubs, V.Y.1
  • 33
    • 0018331351 scopus 로고
    • Recent Advances in Residue Number Techniques for Recursive Digital Filtering
    • W. K. Jenkins, “Recent Advances in Residue Number Techniques for Recursive Digital Filtering,” IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-27, No. 1, Feb. 1979, pp. 19–30.
    • (1979) IEEE Trans. Acoustics, Speech and Signal Processing , vol.ASSP-27 , Issue.1 , pp. 19-30
    • Jenkins, W.K.1
  • 35
    • 0019611061 scopus 로고
    • A Comparison of DFT Algorithms Using a Residue Architecture
    • England
    • F. J. Taylor and C. H. Huang, “A Comparison of DFT Algorithms Using a Residue Architecture,” Computer and Electrical Engineering (England), Vol. 8, No. 3, Sept. 1981, pp. 161–171.
    • (1981) Computer and Electrical Engineering , vol.8 , Issue.3 , pp. 161-171
    • Taylor, F.J.1    Huang, C.H.2
  • 36
    • 0018545735 scopus 로고
    • Implementation of FFT Structures Using the Residue Number System
    • B. D. Tseng, G. A. Jullien, and W. C. Miller, “Implementation of FFT Structures Using the Residue Number System,” IEEE Trans. Computers, Vol. C-28, No. 11, Nov. 1979, pp. 831–845.
    • (1979) IEEE Trans. Computers , vol.C-28 , Issue.11 , pp. 831-845
    • Tseng, B.D.1    Jullien, G.A.2    Miller, W.C.3
  • 37
    • 0019022343 scopus 로고
    • Residue Number System Implementations of Number Theoretic Transforms in Complex Residue Rings
    • A. Z. Baraniecka and G. A. Jullien, “Residue Number System Implementations of Number Theoretic Transforms in Complex Residue Rings,” IEEE Trans. Acoustics, Speech and Signal Processing, Vol. ASSP-23, No. 3, June 1980, pp. 285–291.
    • (1980) IEEE Trans. Acoustics, Speech and Signal Processing , vol.ASSP-23 , Issue.3 , pp. 285-291
    • Baraniecka, A.Z.1    Jullien, G.A.2
  • 38
    • 0018309857 scopus 로고
    • Microprocessor Implementation of Number Theoretic Transforms
    • S. C. P. Martin et al, “Microprocessor Implementation of Number Theoretic Transforms,” IEEE J. Electronic Circuits and Systems, Vol. 3, No. 1, Jan. 1979, pp. 21–26.
    • (1979) IEEE J. Electronic Circuits and Systems , vol.3 , Issue.1 , pp. 21-26
    • Martin, S.C.P.1
  • 39
    • 0018546837 scopus 로고
    • Convolution Algorithms for Small-Word-Length Digital Filtering Applications
    • N. S. Reddy and V. U. Reddy, “Convolution Algorithms for Small-Word-Length Digital Filtering Applications,” IEEE J. Electronic Circuits and Systems, Vol. 3, No. 6, Nov. 1979, pp. 253–256.
    • (1979) IEEE J. Electronic Circuits and Systems , vol.3 , Issue.6 , pp. 253-256
    • Reddy, N.S.1    Reddy, V.U.2
  • 40
    • 0019436564 scopus 로고
    • Implementation of a Fast Digital Processor Using Residue Number Arithemtic
    • C. Huang et al., “Implementation of a Fast Digital Processor Using Residue Number Arithemtic,” IEEE Trans. Circuits and Systems, Vol. 28, No. 1, Jan. 1981, pp. 32–38.
    • (1981) IEEE Trans. Circuits and Systems , vol.28 , Issue.1 , pp. 32-38
    • Huang, C.1
  • 41
    • 0019655211 scopus 로고
    • Residue-Based Image Processor for Very Large Scale Integration (VLSI) Implementation
    • England
    • S. D. Fouse et al., “Residue-Based Image Processor for Very Large Scale Integration (VLSI) Implementation,” Proc. Intyl Society for Optics (England), Vol. 281, July 1981, pp. 39–43.
    • (1981) Proc. Intyl Society for Optics , vol.281 , pp. 39-43
    • Fouse, S.D.1
  • 43
    • 0020102009 scopus 로고
    • Regular Layout for Parallel Adders
    • R. P. Brent, “Regular Layout for Parallel Adders,” IEEE Trans. Computers, Vol. C-31, No. 2, Mar. 1982, pp. 260–264.
    • (1982) IEEE Trans. Computers , vol.C-31 , Issue.2 , pp. 260-264
    • Brent, R.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.