Three-valued Logic

List of accomplishments

• Basic ternary logic gates: T_NOT, T_OR, T_AND, T_NAND, T_NOR, T_XOR and more
• Synthesis, Minimization and Realization for Ternary Functions
• Ternary half adder, Ternary full adder, Ternary ripple carry adder
• Ternary full subtractor, comparator, multiplier, multiplexer/demultiplexer
• Ternary flip flap flops and latches
• A primitive Ternary Arithmetic and Logical Unit (ALU)

Conventions and used technologies

• Unbalanced Ternary (0, 1, 2) was used in implementation
• 1 Trit is expressed by 2 Bits: 0 ~ 00, 1 ~ 01, 2 ~10 (11 is undefined)
• ModelSim, Quartus prime, Logisim

Introduction

As first-year students of Innopolis University, we had the opportunity to realize projects throughout our computer architecture course. Our group was particularly interested in the ternary system and its functioning, so we decided to implement a simple ternary system with basic components (gates).

In logic, a three-valued logic (also trinary logic, trivalent, ternary) is one of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.

Ternary logic is MVL (Multi-valued logic) compliant. However, only three logic states are used, '0','1' and '2'. The optimum radix (r) of a fractional number is found to be the natural logarithm (e). Ternary logic uses number representation with r=3, compared to binary logic which uses r=2, hence the most economical integer radix which is the closest to the natural logarithm e, is base 3. This special property of base 3 inspired the early computer designers to build a ternary computer.

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