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

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

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

Ternary full adder using multi-threshold voltage graphene barristors

Ternary logic circuit has been studied for several decades because it can provide simpler circuits and subsequently lower power consumption via succinct interconnects. We demonstrated a ternary full adder exhibiting a low power-delay-product of ~10-16 J, which is comparable with the binary equivalent circuit. The ternary full adder was modeled using device parameters extracted from the experimentally demonstrated multi-Vth ternary graphene barristors

Investigation of Multiple-valued Logic Technologies for Beyond-binary Era

Computing 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. In this review article, 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. This review of different technologies for the MVL system is intended to perform a comprehensive investigation of various MVL technologies and a comparative analysis of the feasible approaches to implement MVL devices, especially ternary logic

Technological Solution beyond MOSFET and Binary Logic Device

Title from PDF of title page viewed January 31, 2019Thesis advisor: Masud ChowdhuryVitaIncludes bibliographical references (pages 64-70)Thesis (M.S.)--School of Computing and Engineering, University of Missouri--Kansas City, 2018Today’s technology is based on the binary number system-based circuitry, which is the outcome of the simple on and off switching mechanism of the prevailing transistors. Consideration of higher radix number system can eradicate or lessen many limitations of binary number system such as the saturation of Moore’s law. The most substantial potential benefits of higher radix approaches are the decrease of wiring complexity. Excessive scaling of the technologies has led the researchers beyond Binary Logic and MOSFET technology. TFET considered as one of the most promising options for low-power application for beyond MOSFET technologies. Graphene Nano Ribbon, due to its high-carrier mobility, tunable bandgap and its outstanding electrostatic control of device gate becomes ideal choice for channel material of TFET. This paper proposes double gated ultra-thin body (UTB) TFET device model using Graphene nano ribbon as the channel material. In this paper evaluation of the model by performing the comparative analysis with InAs as the channel material in terms of Ec-Ev on and off state and Id-Vg characteristics is presented. The feasibility of multi valued logic system in real-world rests on two serious aspects, such as, the easiness of mathematical approach for implementing the multivalued logic into today’s technology and the sufficiency of synthesis techniques. In this paper, we have focused on the different technology available for implementing multivalued logic especially ternary logic. Ternary logic devices are expected to lead to an exponential increase of the information handling capability, which binary logic cannot support. Memory capacitor or memcapacitor is an emerging device that exhibits hysteresis behavior, which can be manipulated by external parameters, such as, the applied electric field or voltage. One of the unique properties of the memcapacitor is that by using the percolation approach, we can achieve Metal-Insulator-Transition (MIT) phenomenon, which can be utilized to obtain a staggered hysteresis loop. For multivalued logic devices staggered hysteresis behavior is the critical requirement. In this paper, we propose a new conceptual design of a ternary logic device by vertically stacking dielectric material interleaved with layers of graphene nanoribbon (GNR) between two external metal plates. The proposed device structure displays the memcapacitive behavior with the fast switching metal-to-insulator transition in picosecond scale. The device model is later extended into a vertical-cascaded version, which acts as a ternary device.Introduction -- Multi valued logic -- Overview of different MVL technologies -- Graphene memcapacitor based ternary logic device -- Graphene nano ribbon based TFET -- Conclusion and future wor

New Logic Synthesis As Nanotechnology Enabler (invited paper)

Nanoelectronics comprises a variety of devices whose electrical properties are more complex as compared to CMOS, thus enabling new computational paradigms. The potentially large space for innovation has to be explored in the search for technologies that can support large-scale and high- performance circuit design. Within this space, we analyze a set of emerging technologies characterized by a similar computational abstraction at the design level, i.e., a binary comparator or a majority voter. We demonstrate that new logic synthesis techniques, natively supporting this abstraction, are the technology enablers. We describe models and data-structures for logic design using emerging technologies and we show results of applying new synthesis algorithms and tools. We conclude that new logic synthesis methods are required to both evaluate emerging technologies and to achieve the best results in terms of area, power and performance

New Data Structures and Algorithms for Logic Synthesis and Verification

The strong interaction between Electronic Design Automation (EDA) tools and Complementary Metal-Oxide Semiconductor (CMOS) technology contributed substantially to the advancement of modern digital electronics. The continuous downscaling of CMOS Field Effect Transistor (FET) dimensions enabled the semiconductor industry to fabricate digital systems with higher circuit density at reduced costs. To keep pace with technology, EDA tools are challenged to handle both digital designs with growing functionality and device models of increasing complexity. Nevertheless, whereas the downscaling of CMOS technology is requiring more complex physical design models, the logic abstraction of a transistor as a switch has not changed even with the introduction of 3D FinFET technology. As a consequence, modern EDA tools are fine tuned for CMOS technology and the underlying design methodologies are based on CMOS logic primitives, i.e., negative unate logic functions. While it is clear that CMOS logic primitives will be the ultimate building blocks for digital systems in the next ten years, no evidence is provided that CMOS logic primitives are also the optimal basis for EDA software. In EDA, the efficiency of methods and tools is measured by different metrics such as (i) the result quality, for example the performance of a digital circuit, (ii) the runtime and (iii) the memory footprint on the host computer. With the aim to optimize these metrics, the accordance to a specific logic model is no longer important. Indeed, the key to the success of an EDA technique is the expressive power of the logic primitives handling and solving the problem, which determines the capability to reach better metrics. In this thesis, we investigate new logic primitives for electronic design automation tools. We improve the efficiency of logic representation, manipulation and optimization tasks by taking advantage of majority and biconditional logic primitives. We develop synthesis tools exploiting the majority and biconditional expressiveness. Our tools show strong results as compared to state-of-the-art academic and commercial synthesis tools. Indeed, we produce the best results for several public benchmarks. On top of the enhanced synthesis power, our methods are the natural and native logic abstraction for circuit design in emerging nanotechnologies, where majority and biconditional logic are the primitive gates for physical implementation. We accelerate formal methods by (i) studying properties of logic circuits and (ii) developing new frameworks for logic reasoning engines. We prove non-trivial dualities for the property checking problem in logic circuits. Our findings enable sensible speed-ups in solving circuit satisfiability. We develop an alternative Boolean satisfiability framework based on majority functions. We prove that the general problem is still intractable but we show practical restrictions that can be solved efficiently. Finally, we focus on reversible logic where we propose a new equivalence checking approach. We exploit the invertibility of computation and the functionality of reversible gates in the formulation of the problem. This enables one order of magnitude speed up, as compared to the state-of-the-art solution. We argue that new approaches to solve EDA problems are necessary, as we have reached a point of technology where keeping pace with design goals is tougher than ever

Challenges and solutions for large-scale integration of emerging technologies

Title from PDF of title page viewed June 15, 2021Dissertation advisor: Mostafizur RahmanVitaIncludes bibliographical references (pages 67-88)Thesis (Ph.D.)--School of Computing and Engineering and Department of Physics and Astronomy. University of Missouri--Kansas City, 2021The semiconductor revolution so far has been primarily driven by the ability to shrink devices and interconnects proportionally (Moore's law) while achieving incremental benefits. In sub-10nm nodes, device scaling reaches its fundamental limits, and the interconnect bottleneck is dominating power and performance. As the traditional way of CMOS scaling comes to an end, it is essential to find an alternative to continue this progress. However, an alternative technology for general-purpose computing remains elusive; currently pursued research directions face adoption challenges in all aspects from materials, devices to architecture, thermal management, integration, and manufacturing. Crosstalk Computing, a novel emerging computing technique, addresses some of the challenges and proposes a new paradigm for circuit design, scaling, and security. However, like other emerging technologies, Crosstalk Computing also faces challenges like designing large-scale circuits using existing CAD tools, scalability, evaluation and benchmarking of large-scale designs, experimentation through commercial foundry processes to compete/co-exist with CMOS for digital logic implementations. This dissertation addresses these issues by providing a methodology for circuit synthesis customizing the existing EDA tool flow, evaluating and benchmarking against state-of-the-art CMOS for large-scale circuits designed at 7nm from MCNC benchmark suits. This research also presents a study on Crosstalk technology's scalability aspects and shows how the circuits' properties evolve from 180nm to 7nm technology nodes. Some significant results are for primitive Crosstalk gate, designed in 180nm, 65nm, 32nm, and 7nm technology nodes, the average reduction in power is 42.5%, and an average improvement in performance is 34.5% comparing to CMOS for all mentioned nodes. For benchmarking large-scale circuits designed at 7nm, there are 48%, 57%, and 10% improvements against CMOS designs in terms of density, power, and performance, respectively. An experimental demonstration of a proof-of-concept prototype chip for Crosstalk Computing at TSMC 65nm technology is also presented in this dissertation, showing the Crosstalk gates can be realized using the existing manufacturing process. Additionally, the dissertation also provides a fine-grained thermal management approach for emerging technologies like transistor-level 3-D integration (Monolithic 3-D, Skybridge, SN3D), which holds the most promise beyond 2-D CMOS technology. However, such 3-D architectures within small form factors increase hotspots and demand careful consideration of thermal management at all integration levels. This research proposes a new direction for fine-grained thermal management approach for transistor-level 3-D integrated circuits through the insertion of architected heat extraction features that can be part of circuit design, and an integrated methodology for thermal evaluation of 3-D circuits combining different simulation outcomes at advanced nodes, which can be integrated to traditional CAD flow. The results show that the proposed heat extraction features effectively reduce the temperature from a heated location. Thus, the dissertation provides a new perspective to overcome the challenges faced by emerging technologies where the device, circuit, connectivity, heat management, and manufacturing are addressed in an integrated manner.Introduction and motivation -- Cross talk computing overview -- Logic simplification approach for Crosstalk circuit design -- Crostalk computing scalability study: from 180 nm to 7 nm -- Designing large*scale circuits in Crosstalk at 7 nm -- Comparison and benchmarking -- Experimental demonstration of Crosstalk computing -- Thermal management challenges and mitigation techniques for transistor-level- 3D integratio