Multiple-valued product-of-sums expression with truncated sum

Abstract

Truncated sum (TSUM for short) can be useful for MV-PLAs realization. This paper introduces multiple-valued product-of-sums expressions where sum refers to TSUM and product does MIN. We investigate the multiple-valued product-of-sums expressions and show the minimization method and the simulation results. We describe the minimization method based on binary Quine-McCluskey algorithm. It is proved that in the minimal product-of-sums expressions, the implicate number of the expressions with TSUM is equivalent to the number of those with MAX. Next, we propose multiple-valued product-of-sums expressions with variables. The expressions involve the TSUM of variables and nonzero constants as the coefficients of the implicates. The minimization method is also proposed. Finally, we show the simulation results for some multiple-valued arithmetic functions. In them, an efficiency of the product-of-sums expressions with variables is shown and some comparisons are made.