Ternary circuits: why R=3 is not the Optimal Radix for Computation

TL;DR

This paper challenges the notion that base 3 is optimal for computation by comparing ternary and binary circuits using CNTFET technology, showing binary circuits generally outperform ternary ones in efficiency and complexity.

Contribution

It provides a comparative analysis demonstrating that ternary circuits are not more efficient than binary circuits when implemented with CNTFET technology.

Findings

Binary circuits outperform ternary in adders and multipliers.

Ternary circuits have higher transistor count ratios than the information ratio.

Exceptions occur only with specific circuit approaches involving additional power supply and conflicts.

Abstract

A demonstration that e=2.718 rounded to 3 is the best radix for computation is disproved. The MOSFET-like CNTFET technology is used to compare inverters, Nand, adders, multipliers, D Flip-Flops and SRAM cells. The transistor count ratio between ternary and binary circuits is generally greater than the log(3)/log(2) information ratio. The only exceptions concern a circuit approach that combines two circuit drawbacks (an additional power supply and a circuit conflict between transistors) and only when it implements circuits based on the ternary inverter. For arithmetic circuits such as adders and multipliers, the ternary circuits are always outperformed by the binary ones using the same technology.