Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate

Maoqun Yao,Jizhong Shen,Kai Yang,Congyuan Xu

doi:10.1155/2015/827572

Maoqun Yao, Jizhong Shen + Show 2 more

Open Access

https://doi.org/10.1155/2015/827572

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Abstract

The resonant tunneling device (RTD) has attracted much attention because of its unique negative differential resistance characteristic and its functional versatility and is more suitable for implementing the threshold logic gate. The universal logic gate has become an important unit circuit of digital circuit design because of its powerful logic function, while the threshold logic gate is a suitable unit to design the universal logic gate, but the function synthesis algorithm for then-variable logical function implemented by the RTD-based universal logic gate (UTLG) is relatively deficient. In this paper, three-variable threshold functions are divided into four categories; based on the Reed-Muller expansion, two categories of these are analyzed, and a new decomposition algorithm of the three-variable nonthreshold functions is proposed. The proposed algorithm is simple and the decomposition results can be obtained by looking up the decomposition table. Then, based on the Reed-Muller algebraic system, the arbitraryn-variable function can be decomposed into three-variable functions, and a function synthesis algorithm for then-variable logical function implemented by UTLG and XOR2 is proposed, which is a simple programmable implementation.

Highlights

With the improvement in integrated circuit integration, the complementary metal oxide semiconductor (CMOS) technology is gradually approaching its physical limitations
Based on the Reed-Muller algebraic system, the arbitrary n-variable function can be decomposed into three-variable functions, and a function synthesis algorithm for the n-variable logical function implemented by universal threshold logic gate (UTLG) and XOR2 is proposed, which is a simple programmable implementation
In our proposed decomposition algorithm of three-variable nonthreshold functions we introduced a bivariate XOR function, which cannot be implemented by a single UTLG, so according to the structure of MOBILE circuit [18], we design an resonant tunneling device (RTD)-based bivariate XOR gate (XOR2)

Summary

Introduction

With the improvement in integrated circuit integration, the complementary metal oxide semiconductor (CMOS) technology is gradually approaching its physical limitations. The universal logic gate, which has a powerful logic function, has become an important unit to implement n-variable logical functions [3], and the RTD is more suitable for implementing the universal logic gate because of its negative differential resistance characteristic [4,5,6]. 12], but these algorithms are not suitable for implementing an arbitrary n-variable function by the RTD-based universal threshold logic gate (UTLG) [13]. In this paper, based on the Reed-Muller expansion, the three-variable nonthreshold functions are classified Two categories of these are analyzed, and a new decomposition algorithm of the three-variable nonthreshold functions is proposed. A function synthesis algorithm which can implement an arbitrary n-variable logical function by UTLGs is proposed. The proposed function synthesis algorithm provides a new scheme for designing integrated circuits by RTD devices

Background

Decomposition Algorithm of Three-Variable

The Synthesis Algorithm of n-Variable

Conclusion