Practical design using programmable logic
Practical design using programmable logic
Logic Design and Switching Theory
Logic Design and Switching Theory
Synthesis and Optimization of Digital Circuits
Synthesis and Optimization of Digital Circuits
Spectral Techniques in Digital Logic
Spectral Techniques in Digital Logic
Output Phase Optimization for AND-OR-EXOR PLAs with Decoders and Its Application to Design of Adders
IEICE - Transactions on Information and Systems
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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This paper presents a design method for AND-OR-EXOR three-level networks, where a single two-input exclusive-OR (EXOR) gate is used. The network realizes an EXOR of two sum-of-products expressions (EX-SOPs). The problem is to minimize the total number of products in the two sum-of-products expressions (SOPs). We introduce the notion of μ-equivalence of logic functions to develop exact minimization algorithms for EX-SOPs with up to five variables. We minimized all the NP-representative functions for up to five variables and showed that five-variable functions require 9 or fewer products in minimum EX-SOPs. For n-variable functions, minimum EX-SOPs require at most 9. 2n-5 (n ≥ 6) products. This upper bound is smaller than 2n-1, which is the upper bound for SOPs. We also found that, for five-variable functions, on the average, minimum EX-SOPs require about 40% fewer literals than minimum SOPs.