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Results of the Synthesis of Optimal Networks of AND and OR Gates for Four-Variable Switching Functions

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4 Author(s)
J. N. Culliney ; Rockwell International ; M. H. Young ; T. Nakagawa ; S. Muroga

This correspondence presents the results of the synthesis of optimal feed-forward networks of just AND and OR gates for representative functions of the 222 n-p-n-equivalence classes into which all functions of four or fewer variables can be categorized. (Optimality here means minimization of the number of gates as the primary objective and minimization of the number of connections as the secondary objective, regardless of the number of levels. No fan-in or fan-out restriction is imposed.) Based on these results, instructions are given for obtaining optimal networks for desired functions of four or fewer variables which are not representative functions. The branch-and-bound computer program ILLOD-(AND-OR-B) was used to obtain the optimal networks presented.

Published in:

IEEE Transactions on Computers  (Volume:C-28 ,  Issue: 1 )