OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 25, Iss. 18 — Sep. 15, 1986
  • pp: 3078–3088

Logical minimization of multilevel coded functions

Mir M. Mirsalehi and Thomas K. Gaylord  »View Author Affiliations

Applied Optics, Vol. 25, Issue 18, pp. 3078-3088 (1986)

View Full Text Article

Enhanced HTML    Acrobat PDF (1356 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Discrete numerical values in digital processing systems may be encoded in two-level (binary) or higher-level (multilevel) representations. Multilevel coding can produce smaller and more efficient processors. In truth-table lookup processing, the number of entries (reference patterns) can be reduced using multilevel coding. Since parallel-input/parallel-output optical truth-table lookup processors can be constructed based on holographic content-addressable memories, it is essential to know the minimum storage required to implement various functions. A new simple method for reducing multivalued functions is presented. This method is based on an extension of the Quine-McCluskey minimization method used for binary logic functions. This minimization method is then applied to the truth tables representing (1) modified signed-digit addition, (2) residue addition, and (3) residue multiplication. A programmable logic array gate configuration for the modified signed-digit adder is presented.

© 1986 Optical Society of America

Original Manuscript: March 30, 1986
Published: September 15, 1986

Mir M. Mirsalehi and Thomas K. Gaylord, "Logical minimization of multilevel coded functions," Appl. Opt. 25, 3078-3088 (1986)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. e.g., F. J. Hill, G. R. Peterson, Digital Systems: Hardware Organization and Design (Wiley, New York, 1978).
  2. e.g., J. R. Jump, S. R. Ahuja, “Effective Pipelining of Digital Systems,” IEEE Trans. Comput. C-27, 855 (1978). [CrossRef]
  3. C. C. Guest, T. K. Gaylord, “Truth-Table Look-Up Optical Processing Utilizing Binary and Residue Arithmetic,” Appl. Opt. 19, 1201 (1980). [CrossRef] [PubMed]
  4. T. Ogura, S-I. Yamada, T. Nikaido, “A 4-kbit Associative Memory LSI,” IEEE J. Solid-State Circuits SC-20, 1277 (1985). [CrossRef]
  5. C. C. Guest, M. M. Mirsalehi, T. K. Gaylord, “Residue Number System Truth-Table Look-Up Processing—Moduli Selection and Logical Minimization,” IEEE Trans. Comput. C-33, 927 (1984). [CrossRef]
  6. T. K. Gaylord, M. M. Mirsalehi, “Truth-Table Look-Up Processing: Number Representation, Multilevel Coding, and Logical Minimization,” Opt. Eng. 25, 22 (1986). [CrossRef]
  7. M. M. Mirsalehi, T. K. Gaylord, “Truth-Table Look-Up Parallel Data Processing Using an Optical Content-Addressable Memory,” Appl. Opt. 25, 2277 (1986). [CrossRef] [PubMed]
  8. e.g., S. Muroga, Logical Design and Switching Theory (Wiley, New York, 1979).
  9. E. I. Post, “Introduction to a General Theory of Elementary Propositions,” Am. J. Math. 43, 163 (1921). [CrossRef]
  10. D. C. Rine, Ed., Computer Science and Multiple-Valued Logic (North-Holland, Amsterdam, 1977).
  11. See the annual issues of Proceedings, International Symposium on Multiple-Valued Logic (IEEE, New York, 1971–1986).
  12. S. L. Hurst, “Multiple-Valued Logic—Its Status and Its Future,” IEEE Trans. Comput. C-33, 1160(1984). [CrossRef]
  13. Special issue on Digital Optical Computing, Multiple-Valued Logic/Digital Logic, Opt. Eng. 25, (1986).
  14. C. M. Allen, D. D. Givone, “A Minimization Technique for Multiple-Valued Logic System,” IEEE Trans. Comput. C-17, 182 (1968). [CrossRef]
  15. C. M. Allen, D. D. Givone, “The Allen-Givone Implementation Oriented Algebra,” in Ref. 10, Chap. 9.
  16. S. Y. H. Su, P. T. Cheung, “Computer Minimization of Multi-Valued Switching Functions,” IEEE Trans. Comput. C-21, 995 (1972). [CrossRef]
  17. S. Y. H. Su, P. T. Cheung, “Computer Simplification of Multi-Valued Switching Functions,” in Ref. 10, Chap. 7.
  18. W. R. Smith, “Minimization of Multivalued Functions,” in Ref. 10, Chap. 8.
  19. e.g., C. E. Lemke, H. M. Salkin, K. Spielberg, “Set Covering by Single Branch Enumeration with Linear Programming Subproblems,” Oper. Res. 19, 988 (1971). [CrossRef]
  20. H. J. Gallagher, T. K. Gaylord, M. G. Moharam, C. C. Guest, “Reconstruction of Binary-Data-Page Thick Holograms for an Arbitrarily Oriented Reference Beam,” Appl. Opt. 20, 300 (1981). [CrossRef] [PubMed]
  21. B. L. Drake, R. P. Bocker, M. E. Lasher, R. H. Patterson, W. J. Miceli, “Photonic Computing Using the Modified Signed-Digit Number Representation,” Opt. Eng. 25, 38 (1986). [CrossRef]
  22. H. L. Garner, “The Residue Number System,” IRE Trans. Electron. Comput. EC-8, 140 (1959). [CrossRef]
  23. N. S. Szabo, R. I. Tanaka, Residue Arithmetic and Its Applications to Computer Technology (McGraw-Hill, New York, 1967).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited