Skip to main content
Log in

Abstract

A generalized β-bit least-significant-digit (LSD) first, serial/parallel multiplier architecture is presented with 1≤β≤n wheren is the operand size. The multiplier processes both the serial input operand and the double precision product β-bits per clock cycle in an LSD first, synchronous fashion. The complete two's complement double precision product requires 2n/β clock cycles. This generalized architecture creates a continuum of multipliers between traditional bit-serial/parallel multipliers (β=1) and fully-parallel multipliers (β=n). β-bit serial/parallel multipliers allow anoptimized integrated circuit arithmetic to be designed based on a particular application's area, power, throughput, latency, and numerical precision constraints.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. R.W. Linderman, P.M. Chau, K.H. Ku and P.P. Reusens, “CUSP: A 2μm CMOS Digital Signal Processor,”IEEE Trans. on Solid State Circuits, vol. SC-20, no. 3, 1985, pp. 761–769.

    Article  Google Scholar 

  2. K.C. Chew, P.M. Chau, W.H. Ku, “A Bit-Serial Floating-Point Complex Multiplier-Accumulator for Fault Tolerant Digital Signal Processing Arrays,”Inter. Conf. on Acoustics, Speech and Signal Processing (ICASSP), 1987, pp. 483–486.

  3. P.B. Denyer and D. Renshaw,VLSI Signal Processing: A Bit-Serial Approach, Reading, MA: Addison-Wesley, 1985.

    Google Scholar 

  4. S.G. Smith and P.B. Denyer,Serial-Data Computation, Boston: Kluwer Academic, 1988.

    Google Scholar 

  5. N.R. Powell, J.M. Irwin, “A MOS Monolithic Chip for High Speed Flexible FFT Microprocessors,”IEEE Inter. Solid-State Circuits Conf. (ISSCC), 1975, pp. 18–19.

  6. N.R. Powell, J.M. Irwin, “Signal Processing with Bit-Serial Word-Parallel Architectures,”SPIE Vol. 154 Real-Time Signal Processing, 1978, pp. 98–104.

  7. D.J. Myers and P.A. Ivey, “STAR-A VLSI Architecture for Signal Processing,”1984 Conference on Advanced Research in VLSI, MIT, 1984, pp. 179–193.

  8. D. Hampel, K.E. McGuire and K.J. Prost, “CMOS/SOS Serial-Parallel Multiplier,”IEEE Trans. on Solid State Circuits, vol. SC-10, no. 5, 1975, pp. 307–313.

    Article  Google Scholar 

  9. R.F. Lyon, “Two's Complement Pipeline Multipliers,”IEEE Trans. Communication, vol. COM-24, 1976, pp. 418–425.

    Article  Google Scholar 

  10. K.K. Primlani and J.L. Meador, “A Nonredundant-Radix-4 Serial Multiplier,”IEEE Journal of Solid-State Circuits, vol. SC-24, no. 6, 1989, pp. 1729–1736.

    Article  Google Scholar 

  11. L. Dadda, “Fast Multipliers for Two's Complement Numbers in Serial Form,”IEEE Proceedings 7th Symposium on Computer Arithmetic, 1985, pp. 57–63.

  12. R. Gnansekaran, “On a Bit-Serial Input and Bit-Serial Output Multiplier,”IEEE Trans. on Computers, vol. C-32, 1983, pp. 878–880.

    Article  Google Scholar 

  13. T. Rhyne and N.R. Strader, “A Signed Bit-Sequential Multiplier,”IEEE Trans. on Computers, vol. C-35, 1986, pp. 896–901.

    Article  Google Scholar 

  14. I-Chen Wu, “A Fast 1-D Serial-Paralled Systolic Multiplier,”IEEE Trans. on Computers, vol. C-36, 1987, pp. 1243–1247.

    Google Scholar 

  15. J. Kane, “A Low-Power, Bipolar, Two's Complement Serial Pipeline Multiplier Chip,”IEEE Trans. on Solid State Circuits, vol. SC-11, no. 5, 1976, pp. 669–678.

    Article  Google Scholar 

  16. R. Gnansekaran, “A Fast Serial-Parallel Binary Multiplier,”IEEE Trans. on Computers, vol. C-34, 1985, pp. 741–744.

    Article  Google Scholar 

  17. T.G. McDanel and R.K. Guha, “The two's complement quasiserial multiplier,”IEEE Trans. on Computers, vol. C-24, 1975, pp. 1233–1235.

    Google Scholar 

  18. R.I. Hartley and P.F. Corbett, “A Digit-Serial Silicon Compiler,”25th ACM/IEEE Design Automation Conference, paper no. 40.4, 1988, pp. 646–649.

  19. M.D. Ercegovac, “An Area-Time Effcient VLSI Design of a Radix-4 Multiplier,”Proc. IEEE Inter. Conf. Computer Design (ICCD), Port Chester, NY, 1983, pp. 684–687.

  20. O.L. MacSorley, “High-speed arithmetic in binary computers,”Proc. of the IRE, vol. 49, 1961, pp. 67–91.

    Article  MathSciNet  Google Scholar 

  21. W.J. Dally, “A High-Performance VLSI Quaternary Serial Multiplier,”Proc. IEEE Inter. Conf. Computer Design (ICCD), 1987, pp. 649–653.

  22. S.A. White, “Results of a Preliminary Study of a Novel IC Arithmetic Unit for an FFT Processor,”Proc. 18th Asilomar Conf. on Circuits, Systems, and Computers, Pacific Grove, CA, 1983, pp. 67–71.

  23. D.A. Henlin, M.T. Fertsch, M. Mazin, and E.T. Lewis, “A 16 bit ×16 bit Pipelined Multiplier Marcrocell,”IEEE Journal of Solid-State Circuits, vol. SC-20, no. 2, 1985, pp. 542–547.

    Article  Google Scholar 

  24. K. Hwang,Computer Arithmetic: Principles, Architecture, and Design, New York: John Wiley, 1979.

    Google Scholar 

  25. F.A. Ware, W.H. McAllister, J.R. Carlson, D.K. Sun, and R.J. Vlach, “64-bit Monolithic Floating Point Processors,”IEEE Journal of Solid-State Circuits, vol. SC-17, no. 5, 1982, pp. 899–907.

    Article  Google Scholar 

  26. L.P. Rubinfield, “A Proof of the Modified Booth's Algorithm for Multiplication,”IEEE Trans. on Computers, vol. C-24, no. 10, 1975, pp. 1014–1016.

    Article  MathSciNet  MATH  Google Scholar 

  27. C.S. Wallace, “A Suggestion for a Fast Multiplier,”IEEE Trans. on Electronic Computers, vol. EC-13, no. 2, 1964, pp. 14–17.

    Article  MATH  Google Scholar 

  28. L. Dadda, “Some Schemes for Parallel Multipliers,”Alta Frequenza, vol. 34, 1965, pp. 349–356.

    Google Scholar 

  29. M.R. Santoro, M.A. Horwitz, “SPIM: A Pipelined 64×64-bit Iterative Multiplier,”IEEE Trans. on Solid State Circuits, vol. SC-24, no. 2, 1989, pp. 487–493.

    Article  Google Scholar 

  30. J.F. Cavanagh,Digitial Computer Arithmetic, New York: McGraw-Hill, 1984.

    Google Scholar 

  31. A. Habibi and P.A. Wintz, “Fast Multpliers,”IEEE Trans. on Computers, vol. C-19, 1970, pp. 153–157.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This project was pratically funded by the UCSD-NSF I/UCR Center on Ultra-High Speed Intergrated Circuits and Systems.

Rights and permissions

Reprints and permissions

About this article

Cite this article

North, R.C., Ku, W.H. β-bit serial/parallel multipliers. J VLSI Sign Process Syst Sign Image Video Technol 2, 219–233 (1991). https://doi.org/10.1007/BF00925467

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00925467

Keywords

Navigation