Extended regular ternary logic functions and majority functions capable of synthesizing any ternary logic function

2003 ◽  
Vol 35 (1) ◽  
pp. 79-90 ◽  
Author(s):  
Yoshinori Yamamoto
Keyword(s):  
Ternary Logic ◽  
Logic Function ◽  
Logic Functions

scholarly journals Implementation of Unbalanced Ternary Logic Gates with the Combination of Spintronic Memristor and CMOS

Electronics ◽  
2020 ◽  
Vol 9 (4) ◽  
pp. 542 ◽  
Author(s):  
Haifeng Zhang ◽  
Zhaowei Zhang ◽  
Mingyu Gao ◽  
Li Luo ◽  
Shukai Duan ◽  
...  
Keyword(s):  
High Efficiency ◽  
Load Capacity ◽  
Complementary Metal Oxide Semiconductor ◽  
Logic Gates ◽  
Logic Circuit ◽  
Oxide Semiconductor ◽  
Ternary Logic ◽  
Logic Operations ◽  
Almost All ◽  
Logic Functions

A memristor is a nanoscale electronic element that displays a threshold property, non-volatility, and variable conductivity. Its composite circuits are promising for the implementation of intelligence computation, especially for logic operations. In this paper, a flexible logic circuit composed of a spintronic memristor and complementary metal-oxide-semiconductor (CMOS) switches is proposed for the implementation of the basic unbalanced ternary logic gates, including the NAND, NOR, AND, and OR gates. Meanwhile, due to the participation of the memristor and CMOS, the proposed circuit has advantages in terms of non-volatility and load capacity. Furthermore, the input and output of the proposed logic are both constant voltages without signal degradation. All these three merits make the proposed circuit capable of realizing the cascaded logic functions. In order to demonstrate the validity and effectiveness of the entire work, series circuit simulations were carried out. The experimental results indicated that the proposed logic circuit has the potential to realize almost all basic ternary logic gates, and even some more complicated cascaded logic functions with a compact circuit construction, high efficiency, and good robustness.

DESIGN AND APPLICATION OF AN INTERACTIVE WHEELCHAIR TRAINING SYSTEM

2008 ◽  
Vol 20 (06) ◽  
pp. 377-385 ◽  
Author(s):  
Chern-Sheng Lin ◽  
Chia-Chang Chang ◽  
Wei-Lung Chen
Keyword(s):  
Control Function ◽  
Training System ◽  
Digital Logic ◽  
3D Simulation ◽  
Initial Time ◽  
Logic Function ◽  
Wheelchair Users ◽  
Rehabilitation Training ◽  
Direction Control ◽  
Logic Functions

In this paper we constructed an interactive wheelchair rehabilitation training platform. The roller wheel on the platform is driven mainly by turning the wheelchair, and then the relative position of wheelchair on the screen can be adjusted based on the rotation speed of left and right wheels on the platform. Comparing the digital logic function when two wheels rotate at the same time and judging the variance in digital logic, the steering direction of wheels can be known and be controlled forward or backward. Additionally, the standard digital logic function could be individually judged when left wheel rotates and vice versa, so as to control the steering. Through judging three digital logic functions, the initial time of left wheel, next signal selecting time of left wheel, initial time of right wheel, and next signal selecting time of right wheel could be obtained, then the system can achieve the required direction control function through the judgment formula. The direction control function is indicated by standard digital logic function, so that the user can operate smoothly in the interactive situation software and make an interaction with the computer 3D simulation scene, the patient would have rehabilitation training through various 3D simulation real exteriors. This study not only provides basic trainings but also records the service behavior of wheelchair users, so that the rehabilitation consultant would have reference for the future diagnosis.

3D Visualization Model and Sample Implementation of 0-1 Function on Variant Logic

2013 ◽  
Vol 718-720 ◽  
pp. 480-483
Author(s):  
Huan Wang ◽  
Jie Ao Zhu ◽  
Xue Liu ◽  
Jeffrey Zheng
Keyword(s):  
Data Visualization ◽  
3D Visualization ◽  
Random Sequence ◽  
Relevant Logic ◽  
Complex Data ◽  
Paper Sample ◽  
Logic Function ◽  
Visual Model ◽  
Logic Functions ◽  
Visual Results

Random sequences generated by different logic functions play an important role in cryptography. The structure and the special properties of the logic function has been one of the most active areas of research. In order to study the random sequence and its related logic functions, many models have been established, and different advanced tools are applied to make complex data visualization. In this paper, sample logic functions are transferred into variant logic expressions to form a set of measurements. Using selected measurements, a 3D visual model is proposed. Selected 3D visual results are shown their intrinsic 3D spatial characteristics of relevant logic functions respectively.

scholarly journals Energy Efficient Tri-State CNFET Ternary Logic Gates

2018 ◽  
Author(s):  
Sepher Tabrizchi ◽  
Fazel Sharifi ◽  
Abdel-Hameed A. Badawy
Keyword(s):  
Carbon Nanotube ◽  
Field Effect Transistors ◽  
Logic Gates ◽  
Logic Circuits ◽  
Ternary Logic ◽  
Large Area ◽  
Logic Function ◽  
Correct Operation ◽  
Power Efficient ◽  
Simulation Results

Traditional silicon binary circuits continue to face challenges such as high leakage power dissipation and large area of interconnections. Multiple-Valued Logic (MVL) and nano-devices are two feasible solutions to overcome these problems. In this paper, we present a novel method to design ternary logic circuits based on Carbon Nanotube Field Effect Transistors (CNFETs). The proposed designs use the unique properties of CNFETs, e.g., adjusting the Carbon Nanotube (CNT) diameters to have the desired threshold voltage and have the same mobility of P-FET and N-FET transistors. Each of our designed logic circuits implements a logic function and its complementary via a control signal. Also, these circuits have a high impedance state which saves power while the circuits are not in use. We show a more detailed application of our approach by designing a two-digit adder-subtractor circuit. We simulate the proposed ternary circuits using HSPICE via standard 32nm CNFET technology. The simulation results indicate the correct operation of the designs under different process, voltage and temperature (PVT) variations. Moreover, we designed a two-digit adder/subtractor and a power efficient ternary logic ALU based on the proposed gates. Simulation results show that the two-digit adder/subtractor using our proposed gates has 12X and 5X lower power consumption and PDP (power delay product) respectively, compared to previous designs.

scholarly journals Study of T-norms and Quantum Logic Functions on BL-algebra and Their Relationships to the Classical Probability Structures

2020 ◽  
pp. 591-599
Author(s):  
Ahmed AL-Adilee ◽  
Habeeb Kareem Abdullah ◽  
Hawraa A. AL-Challabi
Keyword(s):  
Quantum Logic ◽  
Probability Space ◽  
Binary Operation ◽  
The Other ◽  
Symmetric Difference ◽  
Logic Function ◽  
Classical Probability ◽  
Binary Operations ◽  
Basic Probability ◽  
Logic Functions

This paper is concerned with the study of the T-norms and the quantum logic functions on BL-algebra, respectively, along with their association with the classical probability space. The proposed constructions depend on demonstrating each type of the T-norms with respect to the basic probability of binary operation. On the other hand, we showed each quantum logic function with respect to some binary operations in probability space, such as intersection, union, and symmetric difference. Finally, we demonstrated the main results that explain the relationships among the T-norms and quantum logic functions. In order to show those relations and their related properties, different examples were built.

scholarly journals Foundations for Applications of Gibbs Derivatives in Logic Design and VLSI

VLSI Design ◽  
2002 ◽  
Vol 14 (1) ◽  
pp. 65-81 ◽  
Author(s):  
Radomir S. Stanković ◽  
Milena Stanković ◽  
Reiner Creutzburg
Keyword(s):  
New Technologies ◽  
Differential Operators ◽  
Rate Of Change ◽  
Logic Design ◽  
Logic Function ◽  
Spectral Techniques ◽  
Cad Systems ◽  
Vlsi Cad ◽  
Efficient Calculation ◽  
Logic Functions

New technologies and increased requirements for performances of digital systems require new mathematical theories and tools as a basis for future VLSI CAD systems. New or alternative mathematical approaches and concepts must be suitable to solve some concrete problems in VLSI and efficient algorithms for their efficient application should be provided. This paper is an attempt in this direction and relates with the recently renewed interest in arithmetic expressions for switching functions, instead representations in Boolean structures, and spectral techniques and differential operators in switching theory and applications. Logic derivatives are efficiently used in solving different tasks in logic design, as for example, fault detection, functional decomposition, detection of symmetries and co-symmetries of logic functions, etc. Their application is based on the property that by differential operators, we can measure the rate of change of a logic function. However, by logic derivatives, we can hardly distinguish the direction of the change of the function, since they are defined in finite algebraic structures. Gibbs derivatives are a class of differential operators on groups, which applied to logic functions, permit to overcome this disadvantage of logic derivatives. Therefore, they may be useful in logic design in the same areas where the logic derivatives have been already using. For such applications, it is important to provide fast algorithms for calculation of Gibbs derivatives on finite groups efficiently in terms of space and time. In this paper, we discuss the methods for efficient calculation of Gibbs derivatives. These methods should represent a basis for further applications of these and related operators in VLSI CAD systems.

scholarly journals Synthetic metabolic computation in a bioluminescence-sensing system

2019 ◽  
Vol 47 (19) ◽  
pp. 10464-10474 ◽  
Author(s):  
Natalia Barger ◽  
Phyana Litovco ◽  
Ximing Li ◽  
Mouna Habib ◽  
Ramez Daniel
Keyword(s):  
Protein Interactions ◽  
Detection Threshold ◽  
Living Cells ◽  
Genetic Circuit ◽  
Biological Research ◽  
Protein Protein Interactions ◽  
Genetic Circuits ◽  
Logic Function ◽  
Single Input ◽  
Logic Functions

Abstract Bioluminescence is visible light produced and emitted by living cells using various biological systems (e.g. luxCDABE cassette). Today, this phenomenon is widely exploited in biological research, biotechnology and medical applications as a quantitative technique for the detection of biological signals. However, this technique has mostly been used to detect a single input only. In this work, we re-engineered the complex genetic structure of luxCDABE cassette to build a biological unit that can detect multi-inputs, process the cellular information and report the computation results. We first split the luxCDABE operon into several parts to create a genetic circuit that can compute a soft minimum in living cells. Then, we used the new design to implement an AND logic function with better performance as compared to AND logic functions based on protein-protein interactions. Furthermore, by controlling the reverse reaction of the luxCDABE cassette independently from the forward reaction, we built a comparator with a programmable detection threshold. Finally, we applied the redesigned cassette to build an incoherent feedforward loop that reduced the unwanted crosstalk between stress-responsive promoters (recA, katG). This work demonstrates the construction of genetic circuits that combine regulations of gene expression with metabolic pathways, for sensing and computing in living cells.

scholarly journals The evolvability of programmable hardware

2010 ◽  
Vol 8 (55) ◽  
pp. 269-281 ◽  
Author(s):  
Karthik Raman ◽  
Andreas Wagner
Keyword(s):  
Fault Tolerant ◽  
Biological Systems ◽  
Neutral Network ◽  
Logic Function ◽  
Vast Number ◽  
Functional Flexibility ◽  
Neutral Networks ◽  
Electronic Circuitry ◽  
Genotype Space ◽  
Logic Functions

In biological systems, individual phenotypes are typically adopted by multiple genotypes. Examples include protein structure phenotypes, where each structure can be adopted by a myriad individual amino acid sequence genotypes. These genotypes form vast connected ‘neutral networks’ in genotype space. The size of such neutral networks endows biological systems not only with robustness to genetic change, but also with the ability to evolve a vast number of novel phenotypes that occur near any one neutral network. Whether technological systems can be designed to have similar properties is poorly understood. Here we ask this question for a class of programmable electronic circuits that compute digital logic functions. The functional flexibility of such circuits is important in many applications, including applications of evolutionary principles to circuit design. The functions they compute are at the heart of all digital computation. We explore a vast space of 10 45 logic circuits (‘genotypes’) and 10 19 logic functions (‘phenotypes’). We demonstrate that circuits that compute the same logic function are connected in large neutral networks that span circuit space. Their robustness or fault-tolerance varies very widely. The vicinity of each neutral network contains circuits with a broad range of novel functions. Two circuits computing different functions can usually be converted into one another via few changes in their architecture. These observations show that properties important for the evolvability of biological systems exist in a commercially important class of electronic circuitry. They also point to generic ways to generate fault-tolerant, adaptable and evolvable electronic circuitry.

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