Efficient Ternary Logic Circuits Optimized by Ternary Arithmetic Algorithms
Guangchao Zhao, Zhiwei Zeng, Xingli Wang, Abdelrahman G. Qoutb, Philippe Coquet, Eby G. Friedman, Beng Kang Tay, Mingqiang Huang
Abstract
Multi-valued logic (MVL) circuits, especially the ternary logic circuits, have attracted great attention in recent years due to their higher information density than binary logic systems. However, the basic construction method for MVL circuit standard cells and the CMOS fabrication possibility/compatibility issues are still to be addressed. In this work, we propose various ternary arithmetic circuits (adders and multipliers) with embedded ternary arithmetic algorithms to improve the efficiency. Firstly, ternary cycling gates are designed to optimize both the arithmetic algorithms and logic circuits of ternary adders. Secondly, optimized ternary Boolean truth table is used to simplify the circuit complexity. Thirdly, high-speed ternary Wallace tree multipliers are implemented with task dividing policy. Significant improvements in propagation delay and power-delay-product (PDP) have been achieved as compared with previous works. In particular, the ternary full adder shows 11 aJ PDP at 0.5 GHz, which is the best result among all the reported works using the same simulation platform. And an average PDP improvement of 36.8% in the ternary multiplier is also achieved. Furthermore, the proposed methods have been successfully explored using standard CMOS 180nm silicon devices, indicating its great potential for the practical application of ternary computing in the near future.