## Logical minimization of multilevel coded functions

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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