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### A multi-objective synthesis methodology for majority/minority logic networks [article]

2016 arXiv   pre-print
majority gates in the synthesis of Boolean functions using the proposed Majority Specification Matrix (MSM) concept.  ...  An important step in the generation of Boolean functions using the majority gate is reducing the number of involved gates.  ...  A QCA majority gate can perform a three-input majority gate. Equation (1) presents the logic function of a three-input majority gate where A, B, and C are the three inputs.  ...

### Digital Combinational Circuits Design By QCA Gates

Pijush Kanti Bhattacharjee
2010 International Journal of Computer and Electrical Engineering
Ultimately a general equation for the minimum number of gates required to an arbitrary number of input variables, causing synthesis of adder circuits, is achieved.  ...  The method is used in a classical logic. I use only 2-inputs and 2-outputs AND-NAND and OR-NOR cells designed on QCA technology. It admits a recursive construction.  ...  COMBINATIONAL CIRCUITS DESIGN A Combinational circuit consists of input variables, logic gates and output variables.  ...

### Three-Input Gates for Logic Synthesis

Dewmini Sudara Marakkalage, Eleonora Testa, Heinz Riener, Alan Mishchenko, Mathias Soeken, Giovanni De Micheli
2020 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
While recent multilevel logic synthesis efforts focused primarily on graphs with 2-input nodes such as AND and OR gates, the recently proposed paradigm of Majority-Inverter Graphs instead uses the 3-input  ...  Using SAT-based exact synthesis, we evaluate each 3-input gate using the minimum number of such gates (together with inverters) needed to synthesize all 4-input Boolean functions and a subset of frequent  ...  We show that the 3-input logic gate Dot is the most powerful in terms of expressibility and it uses a significantly fewer number of gates to represent 4-input functions as compared to And3 or Majority  ...

### A Comparative Study of Majority/Minority Logic Circuit Synthesis Methods for Post-CMOS Nanotechnologies

2017 Engineering
QCA Devices In QCA, a logic circuit is implemented using three primitive devices that are QCA wire, QCA inverter, and QCA majority logic gate.  ...  In these nanotechnologies, the basic logic units used to implement circuits are majority and/or minority gates. Several majority/minority logic circuit synthesis methods have been proposed.  ...  The function of a QCA majority gate is a three-input logic function given in (1) .  ...

### Integrating Nano-logic into an Undergraduate Logic Design Course

Saket Srivastava, Sanjukta Bhanja
2007 2007 IEEE International Conference on Microelectronic Systems Education (MSE'07)
The goal of this work is to motivate our students and enhance their ability to address newer logic blocks namely majority gates in the existing framework.  ...  Experiments with our students show that all the students were able to grasp the basic concept of majority logic synthesis and almost 63% of them had a deeper understanding of the synthesis algorithm demonstrated  ...  Akers, "Synthesis of combinational logic using three-input majority gates," in Proc. Third Annual Symp. Switching Circuit Theory & Logical Design, Oct. 1962, pp. 149-157.  ...

### Digital Combinational Circuits Design with the Help of Symmetric Functions Considering Heat Dissipation by Each QCA Gate

Pijush Kanti Bhattacharjee
2010 International Journal of Computer and Electrical Engineering
Ultimately a general equation for the minimum number of gates required to an arbitrary number of input variables causing synthesis of symmetric function is achieved.  ...  Index Terms-Majority Voter (MV) gate, And-Or-Inverter (AOI) gate, Nand-Nor-Inverter (NNI) gate, 2-Inputs and 2-Outputs AND-NAND (A-NA) gate, 2-Inputs and 2-Outputs OR-NOR (O-NO) gate, Symmetric Function  ...  studied the synthesis of symmetric Boolean functions using a simple recursive arrangement of 2-inputs, 2-outputs AND-NAND (A-NA) and OR-NOR (O-NO) logic gates realized with QCA (Quantum Dot Cellular Automata  ...

### A Logic Simplification Approach for Very Large Scale Crosstalk Circuit Designs [article]

Md Arif Iqbal, Naveen Kumar Macha, Bhavana Tejaswini Repalle, Mostafizur Rahman
2019 arXiv   pre-print
Our logic simplification approach first converts Cadence generated structured netlist to Boolean expressions and then uses the majority synthesis tool to obtain majority functions, which is further used  ...  We compare our approach of logic simplification to that of CMOS and majority logic-based approaches.  ...  This is mostly due to majority logic approaches are inefficient in logic reduction as they provide a very limited number of primitive gates (majority-three, majority-five, and inverter) and any logic function  ...

### Implementation of cascade logic gates and majority logic gate on a simple and universal molecular platform

Jinting Gao, Yaqing Liu, Xiaodong Lin, Jiankang Deng, Jinjin Yin, Shuo Wang
2017 Scientific Reports
In electronics, cascade logic gates can be easily made by physically connecting gates with a conductive wire to transfer the output of an up-stream logic gate as the input of a down-stream logic gate 10  ...  Interestingly, by only modulating the concentration of Cu 2+ , a majority logic gate with a single-vote veto function was realized following the same threshold value as that of the cascade logic gates.  ...  Acknowledgements This work is supported by the National Natural Science Foundation of China (No. 21575138 and No. 21775108). Author Contributions  ...

### Reversible Gates in Emerging Quantum-dot Cellular Automata Technology: An Innovative Approach to Design and Simulation [article]

2019 arXiv   pre-print
This comparison can be made on various parameters ranging from area, complexity (cell amount), delay (clocking zones), and to even logical levels including levels, Control inputs, the number of majority  ...  and NOT gates.  ...  Fig. 8 : 8 An algorithm of the synthesis of a reversible function One of the most frequently used reversible logic gates (RLGs) is Fredkin gate or controlled-SWAP gate. It is RG.  ...

### Study and Defect Characterization of a Universal QCA Gate

S. Ghosal, D. Biswas
2013 International Journal of Computer Applications
In this work we focus on a novel nanostructure (DPNNI) with double polarisation inputs which uses NAND/NOR gates as the basic building blocks, similar to conventional digital logic circuits.  ...  The first introduced logic element, the Majority Voter (MV) led to prohibitively large and complex circuits having both uncomplemented and complemented variables.  ...  Majority Voter The basic logic operation is the majority voter [3] [11] [12] of three inputs and the majority gate shown in Figure AND-OR-Inverter (AOI) This is a seven-cell gate with five input  ...

### Functional decomposition using majority

Zhufei Chu, Mathias Soeken, Yinshui Xia, Giovanni De Micheli
2018 2018 23rd Asia and South Pacific Design Automation Conference (ASP-DAC)
We propose a logic decomposition algorithm that uses the majority-of-three (MAJ) operation.  ...  Combined with disjoint-support decomposition, the algorithm can factorize XOR-Majority Graphs (XMGs), a recently proposed data structure which has XOR, MAJ, and inverters as only logic primitives.  ...  In contrast, datapath logic, especially when arithmetic functions are involved, makes extensive use of XOR and the majority-of-three function xyz = xy ∨ xz ∨ yz (MAJ, [1] ).  ...

### Use of Symmetric Functions Designed by QCA Gates for Next Generation IC

Pijush Kanti Bhattacharjee
2010 Journal of clean energy technologies
Ultimately I achieve a general equation for the minimum number of gates required to an arbitrary number of input variables, causing synthesis of symmetric function.  ...  The method is used in a classical logic. I use only 2-inputs and 2-outputs AND-NAND and OR-NOR cells designed on QCA technology. It admits a recursive construction.  ...  Fig. 4 . 4 QCA Majority Voter (MV) Gate The basic QCA logic elements [1]-[8] include a QCA wires are shown in Fig. 2, QCA inverter or NOT gate in Fig. 3 and Majority Voter (MV) or Majority Gate (Maj) in  ...

### Generalized Majority Voter Design Method for N-Modular Redundant Systems Used in Mission- and Safety-Critical Applications

2019 Computers
The issue is that the number of majority input clauses corresponding to an NMR system is governed by a mathematical combination, the complexity of which increases substantially with increases in the level  ...  This feature is additionally useful for any sharing of common logic with diverse degrees of redundancy in appropriate portions of an NMR implementation.  ...  logic [17] ; and (c) direct synthesis of the 3-input majority voter using one complex gate (AO222) [18] .The total number of majority clauses governing an NMR system increases substantially with increases  ...

### Power, Delay and Area Comparisons of Majority Voters relevant to TMR Architectures [article]

P Balasubramanian, N E Mastorakis
2016 arXiv   pre-print
The TMR scheme involves the two-times duplication of a simplex system hardware, with a majority voter ensuring correctness provided at least two out of three copies of the hardware remain operational.  ...  using a 32/28nm CMOS process.  ...  Single Complex Logic Gate Voters Thus far, majority voters designed using simple logic gates or using combinations of simplex and complex logic gates or utilizing just complex logic gates have been considered  ...