## Journal of Applied Mathematics

### Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate

#### 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 the $n$-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 arbitrary $n$-variable function can be decomposed into three-variable functions, and a function synthesis algorithm for the $n$-variable logical function implemented by UTLG and XOR2 is proposed, which is a simple programmable implementation.

#### Article information

Source
J. Appl. Math., Volume 2015 (2015), Article ID 827572, 7 pages.

Dates
First available in Project Euclid: 17 August 2015

https://projecteuclid.org/euclid.jam/1439816408

Digital Object Identifier
doi:10.1155/2015/827572

Mathematical Reviews number (MathSciNet)
MR3358360

#### Citation

Yao, Maoqun; Yang, Kai; Xu, Congyuan; Shen, Jizhong. Function Synthesis Algorithm of RTD-Based Universal Threshold Logic Gate. J. Appl. Math. 2015 (2015), Article ID 827572, 7 pages. doi:10.1155/2015/827572. https://projecteuclid.org/euclid.jam/1439816408

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