Multiple-valued programmable logic arrays
Parthasarathy P. Tirumalai · 1989
Recent advances in charge-coupled device (CCD) technology have made it possible to implement high-radix functions using these devices. A review of basic CCD technology and logic operations is presented and existing synthesis techniques for designing multiple-valued logic circuits are examined. This dissertation presents CCD programmable logic arrays (PLA's) for implementing multiple-valued logic (MVL) functions. These PLA's provide a structured and modular solution to the problem of multiple-valued logic design. However, the results presented here are technology independent. Thus while the need for MVL design techniques is motivated by the existence of a CCD PLA, the results shown here are applicable to other technologies, for example, current-mode CMOS. Synthesis with a PLA involves expressing a target function in a sum-of-products form. The role of prime and non-prime implicants in minimizing sum-of-products expressions for MVL functions is investigated. It is seen that when the combining operation is MAX, prime implicants are sufficient; however, with the SUM operation, all implicants must be considered to guarantee minimality. Heuristic algorithms have been proposed to produce near minimal expressions for MVL functions. Algorithms that produce minimal expressions using all implicants, and using only prime implicants are presented. These algorithms require a search. The constrained implicant set is introduced to significantly reduce this search. The algorithms are compared based on two sets of 2-variable, 4-valued functions. The results show that none of the heuristic algorithms is clearly much superior to the others. There is surprisingly little overlap in the set of functions where the best realization is achieved. Thus, there is a benefit to applying different heuristics to a given function and then choosing the best realization. Another interesting result is that the algorithm that look only at prime implicants found the minimal solution for the majority of the functions analyzed.