Combinational Logic Circuit Design with the Buchberger Algorithm

TL;DR

This paper introduces a novel method for designing combinational logic circuits by applying the Buchberger algorithm to derive polynomial representations from truth tables, offering an alternative to traditional search-based methods.

Contribution

It presents a new approach using the Buchberger algorithm for polynomial computation in circuit design, which can be extended to multiple outputs.

Findings

Successfully designed a simple ALU using the proposed method

Demonstrated the feasibility of polynomial-based circuit synthesis

Compared favorably to traditional search algorithms in efficiency

Abstract

We detail a procedure for the computation of the polynomial form of an electronic combinational circuit from the design equations in a truth table. The method uses the Buchberger algorithm rather than current traditional methods based on search algorithms. We restrict the analysis to a single output, but the procedure can be generalized to multiple outputs. The procedure is illustrated with the design of a simple arithmetic and logic unit with two 3-bit operands and two control bits.