Design and novel approach for ternary and quaternary logic circuits

Abstract

At beginning era of digital design, the binary logic is used in all industrial applications. The binary logic uses 2 states i.e. 0's and 1's to represent each state. Since the binary logic uses 2 states, it requires more number of bits to represent a number. For example, the number 25 is represented in (11001) 2 this format. So this number 25 requires 5 bits to represent it. And also occupies more area and more power is required in designing the circuit. Therefore ternary logic is introduced. Here the ternary logic uses less number of bits to represent a number compare to binary logic. It also reduces the area and also the power of the circuit. The ternary logic uses 3 states i.e. 0,1,2 where logic 0 is considered as low state and logic 1 is considered as middle state and logic 2 is considered as high state. The same number 25 to represent in ternary logic requires 3 bits. i.e. It is represented as (221) 3 in ternary logic. The further enhancement of ternary logic is quaternary logic. The quaternary logic uses 4 states i.e. 0,1,2,3 states. The quaternary logic further reduces number of bits and also enhances the power compare to binary and ternary logic. The number (25) in quaternary logic is represented as (121) 4 in this format.