Calculating digital counters

  • Walter Dosch
Invited Talks
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1181)


Deductive design characterizes a method where a system description is deduced from the functional specification of its behaviour applying formal transformations rules. Following this design methodology, we derive circuit descriptions for various combinational and sequential counters from a common functional specification using equational and inductive reasoning.


digital counters deductive design formal hardware description 


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  1. 1.
    F.L. Bauer, B. Möller, H. Partsch, P. Pepper: Formal Program Construction by Transformations — Computer-Aided, Intuition Guided Programming. IEEE Transactions on Software Engineering 15:2, 165–180 (1989)Google Scholar
  2. 2.
    K. van Berkel: VLSI Programming of a Modulo-N Counter with Constant Response Time and Constant Power. In: S. Furber, M. Edwards: Asynchronous Design Methodologies. IFIP Transaction A-28. Amsterdam: Elsevier 1993, 1–11Google Scholar
  3. 3.
    R.T. Boute: Representational and Denotational Semantics of Digital Circuits. IEEE Transactions on Computers 38:7, 986–999Google Scholar
  4. 4.
    J.J.F. Cavanagh: Digital Computer Arithmetic — Design and Implementation. McGraw-Hill Computer Science Series. New York: McGraw-Hill 1984Google Scholar
  5. 5.
    L. Claesen (ed.): Formal VLSI Specification and Synthesis — VLSI Design Methods-I & Formal VLSI Correctness Verification — VLSI Design Methods-II. Amsterdam: Elsevier 1990Google Scholar
  6. 6.
    C. Delgado Kloos, W. Dosch: Transformational Development of Circuit Descriptions for Binary Adders. In: M. Broy, M. Wirsing (eds.): Methods of Programming — Selected Papers on the CIP-Project. Lecture Notes in Computer Science 544. Berlin: Springer 1991, 217–237Google Scholar
  7. 7.
    C. Delgado Kloos, W. Dosch: Efficient Circuits as Implementations of Non-Strict Functions. Workshops in Computing Series. In: G. Jones, M. Sheeran (eds.): Designing Correct Circuits. London: Springer 1991, 212–230Google Scholar
  8. 8.
    C. Delgado Kloos, W. Dosch, B. Möller: Design and Proof of Multipliers by Correctness-Preserving Transformation. In: P. Dewilde, J. Vandewalle (eds.): Computer Systems and Software Engineering. Proc. 6th Annual European Computer Conference (CompEuro 92). Los Alamitos, Ca.: IEEE Computer Society Press 1992, 238–243Google Scholar
  9. 9.
    M.D. Ercegovac, T. Lang: Digital Systems and Hardware/Firmware Algorithms. New York: John Wiley & Sons 1985Google Scholar
  10. 10.
    F.K. Hanna, N. Daeche, M. Longley: Specification and Verification Using Dependent Types. IEEE Transactions on Software Engineering 16:9, 949–964 (1990)Google Scholar
  11. 11.
    G. Jones, M. Sheeran: Designing Arithmetic Circuits by Refinement in Ruby. Science of Computer Programming 22:1–2, 107–135 (1994)Google Scholar
  12. 12.
    J.L.W. Kessels:Calculational Derivation of a Counter with Bounded Response Time. In: G.J. Milne, L. Pierre (eds): Correct Hardware Design and Verification Methods. Lecture Notes in Computer Science 683. Berlin: Springer 1993, 203–213Google Scholar
  13. 13.
    M.M. Mano: Digital Design. Englewood Cliffs, N.J.: Prentice Hall 1984Google Scholar
  14. 14.
    C. Mead, L. Conway: Introduction to VLSI Systems. Reading, Mass: Addison-Wesley 1980Google Scholar
  15. 15.
    J.T. O'Donnell: Hardware Description With Recursion Equations. Proc. IFIP 8th International Symposium on Computer Hardware Description Languages and their Applications. Amsterdam: North-Holland 1987, 363–382Google Scholar
  16. 16.
    A.R. Omondi: Computer Arithmetic Systems — Algorithms, Architecture and Implementations. Prentice Hall International Series in Computer Science. New York: Prentice Hall 1994Google Scholar
  17. 17.
    H. Partsch: Specification and Transformation of Programs — A Formal Approach to Software Development. Berlin: Springer 1990Google Scholar
  18. 18.
    N.R. Scott: Computer Number Systems and Arithmetic. Englewood Cliffs, N.J.: Prentice Hall 1985Google Scholar
  19. 19.
    J. Staunstrup: A Formal Approach to Hardware Design. The Kluwer International Series in Engineering and Computer Science. Boston: Kluwer 1994Google Scholar
  20. 20.
    N. Wirth: Digital Circuit Design for Computer Science Students — An Introductory Textbook. Berlin: Springer 1995Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Walter Dosch
    • 1
  1. 1.Institut für InformatikUniversität AugsburgAugsburg

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