This paper propose the design method of the constructing the digital logic systems over galois fields using by the galois field decision diagram(GFDD) that is based on the graph theory. The proposed design method is as following. 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, $psi$GF(P)(1) and $xi$GF(P)(1), 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 $psi$GF(P)(1) and $xi$GF(P)(1). We discuss the Reed-Muller expansion in order to obtain the digital switching functions of the P-valued single variable. And for the purpose of the extend above Reed-Muller expansion to more two variables, we describe the Kronecker product arithmetic operation.