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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.25.003078


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Abstract

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

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

Citation
Mir M. Mirsalehi and Thomas K. Gaylord, "Logical minimization of multilevel coded functions," Appl. Opt. 25, 3078-3088 (1986)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-25-18-3078


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References

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