The alternative bases of Boolean functions as a means of improving the structure of digital blocks

TL;DR

This paper compares classical, algebraic, and Reed-Muller representations of Boolean functions, demonstrating that alternative forms can optimize digital logic design by reducing complexity and chip area.

Contribution

It introduces criteria for subset creation of Boolean function representations and shows that alternative forms outperform classical representation in efficiency and optimization.

Findings

Alternative representations can halve the number of PLA input buses.

Classical form is less optimal compared to algebraic and Reed-Muller forms.

Using alternative forms reduces device cost and chip area.

Abstract

This paper analyzes three forms of representation of Boolean functions, such as Classical, Algebraic and Reed-Muller. The concept of intersection and subsets of representation forms have been introduced, moreover suitable criteria for creating these subsets have been established. Later, these subsets have been quantitatively compared by the number of parameters, in order to assess the effectiveness of using each of the forms of representations proposed in the work. Definitions of the specific weight of subsets of priority forms of the representation of Boolean functions showed that the classical form is the least optimal, in comparison with the parameters of other forms Also, it has been shown that the use of alternative forms of representation of Boolean functions, in some cases, allows to reduce twice the number of incoming PLA buses. Estimating the average loss from the exclusive use of the Classical Form Representation also shows that the use of alternatives yields significant benefits in some parameters, this can be used to optimize devices in the logic design process and reduce the chip area, what also contributes to reductions in the cost of such devices.