A design of ternary logic circuits using M-NAND and NOT gates.

We have proposed the canonical form for the p‐valued logical function (p is a natural number, p > 2), using M‐AND, M‐OR and NOT operations. However, the relations among those operations have been discussed only briefly. This paper discusses in detail the properties of M‐NAND, M‐OR and NOT operations for the ternary case (p = 3), deriving another new canonical form called M‐disjunctive canonical form. Then M‐NAND operation is defined, and a realization of the operation by electronic circuit is presented. The proposed circuit is the circuit by MOSFET, and can realize, in addition to M‐NAND operation, two other logical functions. By using these three kinds of logical functions, the logical circuit can be simplified. The circuit is called M‐NAND gate in this paper. It is possible to construct any ternary logical circuit using only M‐NAND gates. However, the total number of elements can be reduced by combining the proposed circuit with NOT gates by Mouftah and Jordan. Based on these properties and the canonical form, the construction of the logical circuit using M‐NAND and NOT gates is discussed. The circuit has properties which are similar to the well‐known operations such as AND, OR, NOT and NAND, and the construction will be easy for those familiar with such operations.