GFDD에 基礎환 多値論理 디지탈시스템設計 = A Design of the Multiple-Valued Logic Digital System based on the GFDD

다국어 초록 (Multilingual Abstract)

This paper proposes the design method about constructing the Multiple-Valued Logic Digital Systems(MVLDS) over Galois Fields used by the Galois Field Decision Diagram(GFDD) that is based on the Graph Theory.
The proposed design method is as follows.
First of all, we discuss the mathematical properties of the Galois Fields and the basic properties of the Graph Theory.
After we discuss the operational domain and the functional domain, we obtain the transformation matrixes, Ψ?? and ζ??, in the case of one variable, that easily manipulate the relationship between two domains.
And we extend above transformation matrixes to n-variable case, we obtain Ψ?? and ζ??.
We discuss the Reed-Muller Expansion in order to obtain the multiple-valued logic switching functions of the P-valued single variable.
And for the purpose of extending above Reed-Muller Expansion to more two variables, we describe the Kronecker product arithmetic operation.
We discuss the method to extract final GFDD after proposing the concepts of the Operational Domain Truth Vector(ODTV) and Functional Domain Truth Vactor(FDTV).
Finally, we propose the basic module BM in order to design the circuit of the multiple-valued logic switching function.
Next we propose the method of the circuit design for the P-valued n-variables multiple-valued logic switching functions over Galois Field GF(P) based on the BM.
The proposed design method is more regular, extensibe and more smaller than the exixting earlier method.