Logical minimization of multilevel coded functions

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.