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Multiple Valued Logic: Concepts and Representations

Synthesis Lectures on Digital Circuits and Systems

D. Michael Miller​‌
University of Victoria, Canada
Mitchell A. Thornton​‌
Southern Methodist University


Multiple Valued Logic: Concepts and Representations begins with a survey of the use ofmultiple-valued logic in several modern application areas including electronic design automation algorithms and circuit design. The mathematical basis and concepts of various algebras and systems of multiple valued logic are provided including comparisons among various systems and examples of their application. The book also provides an examination of alternative representations of multiple-valued logic suitable for implementation as data structures in automated computer applications. Decision diagram structures for multiple valued applications are described in detail with particular emphasis on the recently developed quantum multiple valued decision diagram.

Table of Contents: Multiple Valued Logic Applications / MVL Concepts and Algebra / Functional Representations / Reversible andQuantum Circuits / Quantum Multiple-Valued Decision Diagrams / Summary / Bibliography

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Cited by

Abhay S Vidhyadharan, Sanjay Vidhyadharan​‌. (2022) Mux Based Ultra-Low-Power Ternary Adders and Multiplier implemented with CNFET and 45 nm MOSFETs. International Journal of Electronics 109:1, 58-82.
Online publication date: 20-Apr-2021.
Ramzi A. Jaber, Hiba Bazzi, Ali Haidar, Bilal Owaidat, Abdallah Kassem​‌. (2021) 1-trit Ternary Multiplier and Adder Designs Using Ternary Multiplexers and Unary Operators. 2021 International Conference on Innovation and Intelligence for Informatics, Computing, and Technologies (3ICT), 292-297.
Afsaneh Daraei, Seied Ali Hosseini​‌. (2021) Alternative design techniques of quaternary latch, flip-flops and counters in nanoelectronics. International Journal of Electronics 25, 1-30.
Online publication date: 24-Aug-2021.
Mohammad-Ali Asadi, Mohammad Mosleh, Majid Haghparast​‌. (2021) Towards designing quantum reversible ternary multipliers. Quantum Information Processing 20:7.
Online publication date: 3-Jul-2021.
Mansi Jhamb, Ratnesh Mohan​‌. (2021) Ultra low power design of multi-valued logic circuit for binary interfaces. Journal of King Saud University - Computer and Information Sciences 69.
Online publication date: 1-Feb-2021.
Abhay S. Vidhyadharan, Sanjay Vidhyadharan​‌. (2021) An ultra-low-power CNFET based dual V ternary dynamic Half Adder. Microelectronics Journal 107, 104961.
Online publication date: 1-Jan-2021.
Sanjay Vidhyadharan, Surya Shankar Dan​‌. (2021) An Efficient Ultra-Low-Power and Superior Performance Design of Ternary Half Adder Using CNFET and Gate-Overlap TFET Devices. IEEE Transactions on Nanotechnology 20, 365-376.
Online publication date: 1-Jan-2021.
Li Luo, Zhekang Dong, Xiaofang Hu, Lidan Wang, Shukai Duan​‌. (2020) MTL: Memristor Ternary Logic Design. International Journal of Bifurcation and Chaos 30:15, 2050222.
Online publication date: 9-Dec-2020.
Asma Taheri Monfared, Majid Haghparast​‌. (2020) Quantum Ternary Multiplication Gate (QTMG): Toward Quantum Ternary Multiplier and a New Realization for Ternary Toffoli Gate. Journal of Circuits, Systems and Computers 29:05, 2050071.
Online publication date: 3-Jul-2019.
Zeno Toffano, François Dubois​‌. (2020) Adapting Logic to Physics: The Quantum-Like Eigenlogic Program. Entropy 22:2, 139.
Online publication date: 24-Jan-2020.
Ahmad Towhidy, Reza Omidi, Karim Mohammadi​‌. (2019) An Efficient Current Mode MVL Residue Code Checker for Fault-Tolerant Arithmetic. Journal of Circuits, Systems and Computers 28:14, 1950244.
Online publication date: 26-Mar-2019.
Kaitlin N. Smith, Mitchell A. Thornton​‌. (2019) Entangled State Preparation for Non-Binary Quantum Computing. 2019 IEEE International Conference on Rebooting Computing (ICRC), 1-9.
Mingqiang Huang, Xingli Wang, Guangchao Zhao, Philippe Coquet, Bengkang Tay​‌. (2019) Design and Implementation of Ternary Logic Integrated Circuits by Using Novel Two-Dimensional Materials. Applied Sciences 9:20, 4212.
Online publication date: 9-Oct-2019.
Elena Zaitseva, Vitaly Levashenko, Igor Lukyanchuk, Miroslav Kvassay, Jan Rabcan, Patrik Rusnak​‌. (2019) Application of Generalised Reed-Muller Expansion in Development of Programmable Logic Array. 2019 10th IEEE International Conference on Intelligent Data Acquisition and Advanced Computing Systems: Technology and Applications (IDAACS), 769-774.
Rakshith Saligram, Abhilash P, Vasundhara Patel K S​‌. (2018) Realization of multi-valued logic combinational circuits on fully depleted silicon on insulator. 2018 International Conference on Networking, Embedded and Wireless Systems (ICNEWS), 1-5.
Amitava Aditya, Souvik Saha, Angshuman Khan​‌. (2018) Implement and Analysis of a 1-Bit Ternary SRAM Cell Using Tanner Tools. SSRN Electronic Journal.
Online publication date: 1-Jan-2018.
Majid Haghparast, Robert Wille, Asma Taheri Monfared​‌. (2017) Towards quantum reversible ternary coded decimal adder. Quantum Information Processing 16:11.
Online publication date: 14-Oct-2017.
Asma Taheri Monfared, Majid Haghparast​‌. (2017) Design of novel quantum/reversible ternary adder circuits. International Journal of Electronics Letters 5:2, 149-157.
Online publication date: 1-Feb-2016.
Zhengbing Hu, Vitaly Deibuk​‌. (2016) New design of reversible/quantum devices for ternary arithmetic. 2016 IEEE First International Conference on Data Stream Mining & Processing (DSMP), 80-84.
Vincent Gaudet​‌. (2016) A survey and tutorial on contemporary aspects of multiple-valued logic and its application to microelectronic circuits. IEEE Journal on Emerging and Selected Topics in Circuits and Systems 6:1, 5-12.
Online publication date: 1-Mar-2016.
Anindya Das, Ifat Jahangir, Masud Hasan​‌. (2014) Optimization of sum of product expressions in a novel quaternary algebra. 2014 International Conference on Informatics, Electronics & Vision (ICIEV), 1-6.
. (2014) Modeling Digital Switching Circuits with Linear Algebra. Synthesis Lectures on Digital Circuits and Systems 9:1, 1-159.
Online publication date: 14-May-2014.
Abstract | PDF (2446 KB) | PDF Plus (1806 KB) | Supplementary Material 
Khandakar Mohammad Ishtiak, Safayat-Al-Imam, Nahyan Al Mahmud​‌. (2014) Design and embodiment of larger quaternary multiplexer and demultiplexer. 2014 International Conference on Electrical Engineering and Information & Communication Technology, 1-5.
, , . (2012) Representation of Multiple-Valued Logic Functions. Synthesis Lectures on Digital Circuits and Systems 7:2, 1-168.
Online publication date: 24-Jun-2012.
Abstract | PDF (923 KB) | PDF Plus (926 KB) 
Ifat Jahangir, Anindya Das, Masud Hasan​‌. (2012) Design of novel quaternary encoders and decoders. 2012 International Conference on Informatics, Electronics & Vision (ICIEV), 1021-1026.
, . (2010) Digital System Verification: A Combined Formal Methods and Simulation Framework. Synthesis Lectures on Digital Circuits and Systems 5:1, 1-93.
Online publication date: 19-Feb-2010.
Abstract | PDF (940 KB) | PDF Plus (985 KB) 

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