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Results of the Synthesis of Optimal Networks of AND and OR Gates for Four-Variable Switching Functions
January 1979 (vol. 28 no. 1)
pp. 76-85
J.N. Culliney, Rockwell International
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.
Index Terms:
n-p-n-equivalence classes, AND gates, branch-and-bound method, four variable switching functions, logical design, optimal networks, OR gates
Citation:
J.N. Culliney, M.H. Young, T. Nakagawa, S. Muroga, "Results of the Synthesis of Optimal Networks of AND and OR Gates for Four-Variable Switching Functions," IEEE Transactions on Computers, vol. 28, no. 1, pp. 76-85, Jan. 1979, doi:10.1109/TC.1979.1675229
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