유한체 상에서 결정다이아그램에 기초한 다치논리 디지탈 시스템의 구성 방법

Abstract

This paper presents a method a constructing Multiple-Valued Logic Digital Systems(MVLDS) based on the Decision Diagram(DD) over Finite Fields(FF). First, we discuss a method of constructing Ordered Multiple-Valued Logic Decision Diagram (OMVLDD) by the multiple-valued Shannon's expansion theorem. Next, we define identity isomorphism, tautology isomorphism, and constant isomorphism in order to simplify OMVLDD, and then discuss a method of selecting the variable ordering that is applied to the proposed several isomorphism relationships. The simplification method applies the proposed isomorphism after decomposing OMVLDD into subgraph, and then the vertex exchange and vertex substitution is considered in order to apply effective isomorphism relationship. We also discuss the don't care term and the case of multiple-output for digital systems. Finally, we implement the logic circuit design using T-gate that is used to construct multiple-valued logic systems after obtaining Reduced OMVLDD(ROMVLDD) from OMVLDD.