Synthesis of Ternary Logic Circuits Using 2:1 Multiplexers

Abstract

Traditionally, binary decision diagram (BDD)-based algorithms are used to synthesize binary logic functions. A BDD can be transformed into circuit implementation by replacing each node in the BDD with a 2:1 multiplexer. Similarly, a ternary decision diagram can be transformed into circuit implementation using 3:1 Multiplexers. In this paper, we present a novel synthesis technique to implement ternary logic circuits using 2:1 multiplexers. Initially a methodology, which transforms a ternary logic function into a ternary-transformed binary decision diagram, is presented. This methodology is the basis for the synthesis algorithm that is used to synthesize various ternary functions using 2:1 multiplexers. Results for various ternary benchmark functions indicate that the proposed algorithm results in circuits that have, on an average 79%, and up to 99% fewer transistors when compared with the most recent 3:1 multiplexer-based algorithm available in the literature. Synthesized circuits have been implemented using carbon-nanotube field-effect transistors and simulated in HSPICE.