An Optimal Gate Design for the Synthesis of Ternary Logic Circuits

Department of Electrical EngineeringOver the last few decades, CMOS-based digital circuits have been steadily developed. However, because of the power density limits, device scaling may soon come to an end, and new approaches for circuit designs are required. Multi-valued logic (MVL) is one of the new approaches, which increases the radix for computation to lower the complexity of the circuit. For the MVL implementation, ternary logic circuit designs have been proposed previously, though they could not show advantages over binary logic, because of unoptimized synthesis techniques. In this thesis, we propose a methodology to design ternary gates by modeling pull-up and pull-down operations of the gates. Our proposed methodology makes it possible to synthesize ternary gates with a minimum number of transistors. From HSPICE simulation results, our ternary designs show significant power-delay product reductions; 49 % in the ternary full adder and 62 % in the ternary multiplier compared to the existing methodology. We have also compared the number of transistors in CMOS-based binary logic circuits and ternary device-based logic circuits We propose a methodology for using ternary values effectively in sequential logic. Proposed ternary D flip-flop is designed to normally operate in four-edges of a ternary clock signal. A quad-edge-triggered ternary D flip-flop (QETDFF) is designed with static gates using CNTFET. From HSPICE simulation results, we have confirmed that power-delay-product (PDP) of QETDFF is reduced by 82.31 % compared to state of the art ternary D flip-flop. We synthesize a ternary serial adder using QETDFF. PDP of the proposed ternary serial adder is reduced by 98.23 % compared to state of the art design.ope

Performance Analysis of Montgomery Multiplier using 32nm CNTFET Technology

In VLSI design vacillating the parameters results in variation of critical factors like area, power and delay. The dominant sources of power dissipation in digital systems are the digital multipliers. A digital multiplier plays a major role in a mixture of arithmetic operations in digital signal processing applications hinge on add and shift algorithms. In order to accomplish high execution speed, parallel array multipliers are comprehensively put into application. The crucial drawback of these multipliers is that it exhausts more power than any other multiplier architectures. Montgomery Multiplication is the popularly used algorithm as it is the most efficient technique to perform arithmetic based calculations. A high-speed multiplier is greatly coveted for its extraordinary leverage. The primary blocks of a multiplier are basically comprised of adders. Thus, in order to attain a significant reduction in power consumption at the chip level the power utilization in adders can be decreased. To obtain desired results in performance parameters of the multiplier an efficient and dynamic adder is proposed and incorporated in the Montgomery multiplier. The Carbon Nanotube field effect transistor (CNTFET) is a promising new device that may supersede some of the fundamental limitations of a silicon based MOSFET. The architecture has been designed in 130nm and 32nm CMOS and CNTFET technology in Synopsys HSpice. The analysed parameters that are considered in determining the performance are power delay product, power and delay and comparison is made with both the technologies.The simulation results of this paper affirmed the CNTFET based Montgomery multiplier improved power consumption by 76.47% ,speed by 72.67% and overall energy by 67.76% as compared to MOSFET-based Montgomery multiplier

Novel Ternary Logic Gates Design in Nanoelectronics

In this paper, standard ternary logic gates are initially designed to considerably reduce static power consumption. This study proposes novel ternary gates based on two supply voltages in which the direct current is eliminated and the leakage current is reduced considerably. In addition, ST-OR and ST-AND are generated directly instead of ST-NAND and ST-NOR. The proposed gates have a high noise margin near V_(DD)/4. The simulation results indicated that the power consumption and PDP underwent a~sharp decrease and noise margin showed a considerable increase in comparison to both one supply and two supply based designs in previous works. PDP is improved in the proposed OR, as compared to one supply and two supply based previous works about 83% and 63%, respectively. Also, a memory cell is designed using the proposed STI logic gate, which has a considerably lower static power to store logic ‘1’ and the static noise margin, as compared to other designs

Multiple-valued logic: technology and circuit implementation

Title from PDF of title page, viewed March 1, 2023Dissertation advisors: Masud H. Chowdhury and Yugyung LeeVitaIncludes bibliographical references (pages 91-107)Dissertation (Ph.D.)--Department of Computer Science and Electrical Engineering. University of Missouri--Kansas City, 2021Computing technologies are currently based on the binary logic/number system, which is dependent on the simple on and off switching mechanism of the prevailing transistors. With the exponential increase of data processing and storage needs, there is a strong push to move to a higher radix logic/number system that can eradicate or lessen many limitations of the binary system. Anticipated saturation of Moore's law and the necessity to increase information density and processing speed in the future micro and nanoelectronic circuits and systems provide a strong background and motivation for the beyond-binary logic system. During this project, different technologies for Multiple-Valued-Logic (MVL) devices and the associated prospects and constraints are discussed. The feasibility of the MVL system in real-world applications rests on resolving two major challenges: (i) development of an efficient mathematical approach to implement the MVL logic using available technologies and (ii) availability of effective synthesis techniques. The main part of this project can be divided into two categories: (i) proposing different novel and efficient design for various logic and arithmetic circuits such as inverter, NAND, NOR, adder, multiplexer etc. (ii) proposing different fast and efficient design for various sequential and memory circuits. For the operation of the device, two of the very promising emerging technologies are used: Graphene Nanoribbon Field Effect Transistor (GNRFET) and Carbon Nano Tube Field Effect Transistor (CNTFET). A comparative analysis of the proposed designs and several state-of-the-art designs are also given in all the cases in terms of delay, total power, and power-delay-product (PDP). The simulation and analysis are performed using the H-SPICE tool with a GNRFET model available on the Nanohub website and CNTFET model available from Standford University website.Introduction -- Fundamentals and scope of multiple valued logic -- Technological aspect of multiple valued logic circuit -- Ternary logic gates using Graphene Nano Ribbon Field Effect Transistor (GNRFET) -- Ternary arithmetic circuits using Graphene Nano Ribbon Field Effect Transistor (GNRFET) -- Ternary sequential circuits using Graphene Nano Ribbon Field Effect Transistor (GNRFET) -- Ternary memory circuits using Carbon Nano Tube Field Effect Transistor (CNTFET) -- Conclusions & future wor

Implementation and Applications of a Ternary Threshold Logic Gate

Reducing delay, power consumption, and chip area of a logic circuit are the main targets of a designer. Most of the times, the designer sacrifices power consumption and chip area to improve delay for a given technology node. To overcome this problem, we propose a ternary threshold logic gate. We implement the proposed gate by combining threshold logic and ternary logic. Then, we construct basic building blocks of a ternary ALU (as logic gates, comparator, and arithmetic circuits) using the proposed gate. We show that the proposed ternary TLG improves delay, power consumption, and chip area of ternary circuits via simulations. Thus, the proposed gate can be used to improve delay, power consumption, and chip area of ternary circuits

High-Performance Ternary (4:2) Compressor Based on Capacitive Threshold Logic

This paper presents a ternary (4:2) compressor, which is an important component in multiplication. However, the structure differs from the binary counterpart since the ternary model does not require carry signals. The method of capacitive threshold logic (CTL) is used to achieve the output signals directly. Unlike the previously presented similar structure, the entire capacitor network is divided into two parts. This segregation results in higher reliability and robustness against unwanted process, voltage, and temperature (PVT) variations. Simulations are performed by HSPICE and 32nm CNFET technology. Simulation results demonstrate about 94% higher performance in terms of power-delay product (PDP) for the new design over the previous one

Design of Ternary Logic and Arithmetic Circuits Using GNRFET

Multiple valued logic (MVL) can represent an exponentially higher number of data/information compared to the binary logic for the same number of logic bits. Compared to the conventional and other emerging device technologies, Graphene Nano Ribbon Field Effect Transistor (GNRFET) appears to be very promising for designing MVL logic gates and arithmetic circuits due to some exceptional electrical properties of the GNRFET, e.g., the ability to control the threshold voltage by changing the width of the GNR. Variation of the threshold voltage is one of the prescribed techniques to achieve multiple voltage levels to implement the MVL circuit. This paper introduces a design approach for ternary logic gates and circuits using MOS-type GNRFET. The designs of basic ternary logic gates like inverters, NAND, NOR, and ternary arithmetic circuits like the ternary decoder, 3:1 multiplexer, and ternary half-adder are demonstrated using GNRFET. A comparative analysis of the GNRFET based ternary logic gates and circuits and those based on the conventional CMOS and CNTFET technologies is performed using delay, total power, and power-delay-product (PDP) as the metrics. The simulation and analysis are performed using the H-SPICE tool with a GNRFET model available on the Nanohub website

A balanced Memristor-CMOS ternary logic family and its application

The design of balanced ternary digital logic circuits based on memristors and conventional CMOS devices is proposed. First, balanced ternary minimum gate TMIN, maximum gate TMAX and ternary inverters are systematically designed and verified by simulation, and then logic circuits such as ternary encoders, decoders and multiplexers are designed on this basis. Two different schemes are then used to realize the design of functional combinational logic circuits such as a balanced ternary half adder, multiplier, and numerical comparator. Finally, we report a series of comparisons and analyses of the two design schemes, which provide a reference for subsequent research and development of three-valued logic circuits.Comment: 15 pages, 30 figure

Appropriateness of Imperfect CNFET Based Circuits for Error Resilient Computing Systems

With superior device performance consistently reported in extremely scaled dimensions, low dimensional materials (LDMs), including Carbon Nanotube Field Effect Transistor (CNFET) based technology, have shown the potential to outperform silicon for future transistors in advanced technology nodes. Studies have also demonstrated orders of magnitude improvement in energy efficiency possible with LDMs, in comparison to silicon at competing technology nodes. However, the current fabrication processes for these materials suffer from process imperfections and still appear to be inadequate to compete with silicon for the mainstream high volume manufacturing. Among the LDMs, CNFETs are the most widely studied and closest to high volume manufacturing. Recent works have shown a significant increase in the complexity of CNFET based systems, including demonstration of a 16-bit microprocessor. However, the design of such systems has involved significantly wider-than-usual transistors and avoidance of certain logic combinations. The resulting complexity of several thousand transistors in such systems is still far from the requirements of high-performance general-purpose computing systems having billions of transistors. With the current progress of the process to fabricate CNFETs, their introduction in mainstream manufacturing is expected to take several more years. For an earlier technology adoption, CNFETs appear to be suited for error-resilient computing systems where errors during computation can be tolerated to a certain degree. Such systems relax the need for precise circuits and a perfect process while leveraging the potential energy benefits of CNFET technology in comparison to conventional Si technology. In this thesis, we explore the potential applications using an imperfect CNFET process for error-resilient computing systems, including the impact of the process imperfections at the system level and methods to improve it. The current most widely adopted fabrication process for CNFETs (separation and placement of solution-based CNTs) still suffers from process imperfections, mainly from open CNTs due to missing of CNTs (in trenches connecting source and drain of CNFET). A fair evaluation of the performance of CNFET based circuits should thus take into consideration the effect of open CNTs, resulting in reduced drive currents. At the circuit level, this leads to failures in meeting 1) the minimum frequency requirement (due to an increase in critical path delay), and 2) the noise suppression requirement. We present a methodology to accurately capture the effect of open CNT imperfection in the state-of-the-art CNFET model, for circuit-level performance evaluation (both delay and glitch vulnerability) of CNFET based circuits using SPICE. A Monte Carlo simulation framework is also provided to investigate the statistical effect of open CNT imperfection on circuit-level performance. We introduce essential metrics to evaluate glitch vulnerability and also provide an effective link between glitch vulnerability and circuit topology. The past few years have observed significant growth of interest in approximate computing for a wide range of applications, including signal processing, data mining, machine learning, image, video processing, etc. In such applications, the result quality is not compromised appreciably, even in the presence of few errors during computation. The ability to tolerate few errors during computation relaxes the need to have precise circuits. Thus the approximate circuits can be designed, with lesser nodes, reduced stages, and reduced capacitance at few nodes. Consequently, the approximate circuits could reduce critical path delays and enhanced noise suppression in comparison to precise circuits. We present a systematic methodology utilizing Reduced Ordered Binary Decision Diagrams (ROBDD) for generating approximate circuits by taking an example of 16-bit parallel prefix CNFET adder. The approximate adder generated using the proposed algorithm has ~ 5x reduction in the average number of nodes failing glitch criteria (along paths to primary output) and 43.4% lesser Energy Delay Product (EDP) even at high open CNT imperfection, in comparison to the ideal case of no open CNT imperfection, at a mean relative error of 3.3%. The recent boom of deep learning has been made possible by VLSI technology advancement resulting in hardware systems, which can support deep learning algorithms. These hardware systems intend to satisfy the high-energy efficiency requirement of such algorithms. The hardware supporting such algorithms adopts neuromorphic-computing architectures with significantly less energy compared to traditional Von Neumann architectures. Deep Neural Networks (DNNs) belonging to deep learning domain find its use in a wide range of applications such as image classification, speech recognition, etc. Recent hardware systems have demonstrated the implementation of complex neural networks at significantly less power. However, the complexity of applications and depths of DNNs are expected to drastically increase in the future, imposing a demanding requirement in terms of scalability and energy efficiency of hardware technology. CNFET technology can be an excellent alternative to meet the aggressive energy efficiency requirement for future DNNs. However, degradation in circuit-level performance due to open CNT imperfection can result in timing failure, thus distorting the shape of non-linear activation function, leading to a significant degradation in classification accuracy. We present a framework to obtain sigmoid activation function considering the effect of open CNT imperfection. A digital neuron is explored to generate the sigmoid activation function, which deviates from the ideal case under imperfect process and reduced time period (increased clock frequency). The inherent error resilience of DNNs, on the other hand, can be utilized to mitigate the impact of imperfect process and maintain the shape of the activation function. We use pruning of synaptic weights, which, combined with the proposed approximate neuron, significantly reduces the chance of timing failures and helps to maintain the activation function shape even at high process imperfection and higher clock frequencies. We also provide a framework to obtain classification accuracy of Deep Belief Networks (class of DNNs based on unsupervised learning) using the activation functions obtained from SPICE simulations. By using both approximate neurons and pruning of synaptic weights, we achieve excellent system accuracy (only < 0.5% accuracy drop) with 25% improvement in speed, significant EDP advantage (56.7% less) even at high process imperfection, in comparison to a base configuration of the precise neuron and no pruning with the ideal process, at no area penalty. In conclusion, this thesis provides directions for the potential applicability of CNFET based technology for error-resilient computing systems. For this purpose, we present methodologies, which provide approaches to assess and design CNFET based circuits, considering process imperfections. We accomplish a DBN framework for digit recognition, considering activation functions from SPICE simulations incorporating process imperfections. We demonstrate the effectiveness of using approximate neuron and synaptic weight pruning to mitigate the impact of high process imperfection on system accuracy