Logical minimization of multilevel coded functions.

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.

[1]  W. Miceli,et al.  Photonic computing using the modified signed-digit number representation , 1986 .

[2]  C C Guest,et al.  Truth-table look-up optical processing utilizing binary and residue arithmetic. , 1980, Applied optics.

[3]  Kurt Spielberg,et al.  Set Covering by Single-Branch Enumeration with Linear-Programming Subproblems , 1971, Oper. Res..

[4]  Emil L. Post.  Introduction to a General Theory of Elementary Propositions , 1921 .

[5]  T K Gaylord,et al.  Truth-table look-up parallel data processing using an optical content-addressable memory. , 1986, Applied optics.

[6]  Sudhir Ahuja,et al.  Effective Pipelining of Digital Systems , 1978, IEEE Transactions on Computers.

[7]  Donald D. Givone,et al.  A Minimization Technique for Multiple-Valued Logic Systems , 1968, IEEE Transactions on Computers.

[8]  C C Guest,et al.  Reconstruction of binary-data-page thick holograms for an arbitrarily oriented reference beam. , 1981, Applied optics.

[9]  Stephen Y. H. Su,et al.  Computer Minimization of Multivalued Switching Functions , 1972, IEEE Transactions on Computers.

[10]  Thomas K. Gaylord,et al.  Residue Number System Truth-Table Look-Up Processing—Moduli Selection and Logical Minimization , 1984, IEEE Transactions on Computers.

[11]  Stanley L. Hurst,et al.  Multiple-Valued Logic—its Status and its Future , 1984, IEEE Transactions on Computers.

[12]  Thomas K. Gaylord,et al.  Truth-table look-up processing: number representation, multilevel coding, and logical minimization , 1986 .

[13]  T. Ogura,et al.  A 4-Kbit associative memory LSI , 1985, IEEE Journal of Solid-State Circuits.

[14]  Harvey L. Garner,et al.  RESIDUE NUMBER SYSTEM ENHANCEMENTS FOR PROGRAMMABLE PROCESSORS , 2008 .