Skip to main content

Hardware algorithms for VLSI systems

  • Chapter 3 VLSI Algorithms
  • Chapter
  • First Online:
Book cover VLSI Engineering

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 163))

Abstract

In this paper, we discussed several problems in the design and analysis of hardware algorithms. The complexity theory of logic circuits and parallel computation will form the theoretical foundation of design and analysis of hardware algorithms which will become more important for large VLSI systems.

A formal description method of hardware algorithms will be proposed on a general model of parallel computation. Design tools for hardware algorithms will be developed such as a hardware description language, an automatic translation system from the language to circuits, a verification support system for algorithms, etc. Results of theoretical researches on the circuit complexity will play an important role in the development of these design tools.

Many hardware algorithms will be designed to various problems. Design methodologies such as systolic algorithms or BCA algorithms will become more important and be studied. Since a large system is a combination of software and hardware, a design methodology including design of both software and hardware algorithms will be discussed.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. S.Yajima and H.Yasuura, “Hardware Algorithms and Logic Deign Automation — An Overview and Progress Report —“, Kyoto Univ. Yajima Lab. Research Rep. ER 82-01, June 1982. Also to appear in Lecture Notes on Computer Science, Springer-Verlag.

    Google Scholar 

  2. “Highly Parallel Computing“ Edited by L.S. Hayens, IEEE Computer, vol.15, no.1, pp. 7–96, Jan. 1982.

    Google Scholar 

  3. S.Yajima, H.Yasuura and Y.Kambayashi, “Design of Hardware Algorithms and Related Problems“, IECE Technical Rep. AL81–86, Dec. 1981 (in Japanese).

    Google Scholar 

  4. N. Tokura, “VLSI Algorithms and Area-Time Complexity“, Joho-Shori vol.23, no.3, pp.176–186, March 1982 (in Japanese).

    Google Scholar 

  5. C.A. Mead and L.A. Conway, “Introduction to VLSI Systems“, Addison-Wesley, Reading, Mass., 1980.

    Google Scholar 

  6. H.T.Kung, “The Structure of Parallel Algorithms“, Advanced in Computers, vol.19, Academic Press, 1980.

    Google Scholar 

  7. M.Foster and H.T.Kung, “The Design of Special-Purpose VLSI Chips“, IEEE Computer, vol.13, no.1, Jan. 1980.

    Google Scholar 

  8. S. Yajima and K. Inagaki, “Power Minimization Problems of Logic Network“, IEEE Trans. on Comput., vol.C-23, no.2, pp.153–165, Feb. 1974.

    Google Scholar 

  9. G.F.Pfister, “The Yorktown Simulation Engine: Introduction“, Proc. 19th Design Automation Conf.pp.51–54, June 1982.

    Google Scholar 

  10. H.G.Adshead, “Towards VLSI Complexity: The DA Algorithm Scaling Problem: Can Special DA Hardware Help?“, Proc. 19th Design Automation Conf. pp.339–344, June 1982.

    Google Scholar 

  11. R.A. Wood, “A High Density Programmable Logic Array Chip“, IEEE Trans. on Comput. vol.C-28, no.9, pp.602–608, Sept. 1979.

    Google Scholar 

  12. S. Yajima and T. Aramaki, “Autonomously Testable Programmable Logic Arrays“, Proc. FTCS-11, pp.41–43, June 1981.

    Google Scholar 

  13. T. Williams and K.P. Parker, “Design for Testability — A Survey“, IEEE Trans. on Comput., vol.C-31, no.1, pp.2–15, Jan. 1982.

    Google Scholar 

  14. J.E. Savage, “The Complexity of Computing“, Wiley-Interscience, Reading Mass., 1976.

    Google Scholar 

  15. C.D.Thompson, “Area-Time Complexity for VLSI“, Proc. 11th Symposium on the Theory of Computing, pp.81–88, May 1979.

    Google Scholar 

  16. R.P. Brent and H.T. Kung, “The Area-Time Complexity of Binary Multiplication“, JACM, vol.28, no.3, pp.521–534, July 1981.

    Google Scholar 

  17. A.V. Aho, J.E. Hopcroft and J.D. Ullman, “Design and Analysis of Computer Algorithms“, Addison-Wesley, Reading, Mass., 1974.

    Google Scholar 

  18. B.Chazelle and L.Monier, “Towards More Realistic Models of Computation for VLSI“, Proc. 11th Symposium on the Theory of Computing, pp.209–213, April 1979.

    Google Scholar 

  19. Z.M.Kedem and A.Zorat, “On Relations between Inputs and Communication/Computation in VLSI“, Proc. 22nd Symp. on the Foundations of Computer Science, pp.37–44, Oct.1981.

    Google Scholar 

  20. J.Vuillemin, “A Combinatorial Limit to the Computing Power of VLSI Circuits“, Proc. 21st Symp. on the Foundation of Computer Sience, pp.294–300, Oct. 1980.

    Google Scholar 

  21. H. Yasuura, “Theory of Complexity of Logic Functions and its Application to Logical Design of High-Speed Logic Circuits“, Trans. of the Information Processing Society of Japan, vol.21, no.4, pp.268–278, July 1980 (in Japanese).

    Google Scholar 

  22. A. Borodin, “On Relating Time and Space to Size and depth“, SIAM Jornal of Computing, vol.6, no.4, pp.733–744, Dec. 1977.

    Google Scholar 

  23. S.H. Unger, “Tree Realizations of Interactive Circuits“, IEEE Trans. on Comput., vol.C-26, no.4, pp.365–383, April 1977.

    Google Scholar 

  24. H. Yasuura, “Width and Depth of Combinational Logic Circuits“, Information Processing Letters, vol.13, no.4, 4,end, pp.191–194, 1981.

    Google Scholar 

  25. H. Yasuura and S. Yajima, “On the Area of Logic Circuits in VLSI“, Trans. of Institute of Electronics and Communication Engineers of Japan, vol.J65-D, no.8, Aug. 1982.

    Google Scholar 

  26. K. Hwang, “Computer Arithmetic:Principle, Architecture and Design“, John-Wiley & Sons, Reading, Mass., 1979.

    Google Scholar 

  27. L.B.Jackson, S.F.Kaiser and H.S.McDonald, “An Approach to the Implementation of Digital Filters,” IEEE Trans. Audio Electro., AU-16, Sept. 1968.

    Google Scholar 

  28. W.J. Stenzel, W.J. Kubitz and G.H. Garcia, “A Compact High-Speed Parallel Multiplication Scheme,” IEEE Trans. on Comput., vol.C-26, no.10, pp.948–957, Oct. 1977.

    Google Scholar 

  29. A.Karatsuba and Y.Ofman, “Multiplication of Multidigit Numbers with Computers“, Dokl. Akad. Nauk. SSSR, no.145, Feb. 1962.

    Google Scholar 

  30. C.S. Wallace, “A Suggestion for a Fast Multiplier“, IEEE Trans. on Electro. Comput., vol EC-13, no.1, pp.14–17, Feb. 1964.

    Google Scholar 

  31. N.Takagi, H.Yasuura and S.Yajima, “A High-Speed Array Multiplier Using Redundant Binary Representation,” to appear.

    Google Scholar 

  32. H.Yasuura and S.Yajima, “On the Delay Complexity of Square Rooting in Combinational Logic Circuits“, Tech. Rep. of IECEJ, AL79–29, July 1979.

    Google Scholar 

  33. H. Alt, “Square Rooting is as Difficult as Multiplication“, Computing, vol.21, pp.221–232, Jan.1979.

    Google Scholar 

  34. H. Yasuura and N. Takagi, “A High-Speed Sorting Circuit Using Parallel Enumeration Sort“, Trans. IECE, vol.J65-D, no.2, pp.179–186, Feb.1982 (in Japanese).

    Google Scholar 

  35. H. Yasuura, N. Takagi and S. Yajima, “The Parallel Enumeration Sorting Scheme for VLSI“, to appear in IEEE Trans. on Computer vol.C-31, no.12, Dec.1982.

    Google Scholar 

  36. H.Yasuura, “Hardware Algorithms for VLSI“, Proc. Joint Conf. of 4 Institutes Related on Electric Engineering, 34–4, Oct. 1981 (in Japanese).

    Google Scholar 

  37. H.Miyata, H.Yasuura and S.Yajima, “Hardware Algorithm for Large Integer Multiplication“, Tech. Rep. of IECEJ, AL81–99, Jan.1982 (in Japanese).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Tosiyasu L. Kunii

Rights and permissions

Reprints and permissions

Copyright information

© 1984 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Yasuura, H., Yajima, S. (1984). Hardware algorithms for VLSI systems. In: Kunii, T.L. (eds) VLSI Engineering. Lecture Notes in Computer Science, vol 163. Springer, Tokyo. https://doi.org/10.1007/BFb0043450

Download citation

  • DOI: https://doi.org/10.1007/BFb0043450

  • Published:

  • Publisher Name: Springer, Tokyo

  • Print ISBN: 978-4-431-70002-9

  • Online ISBN: 978-4-431-36817-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics