Ternary Half Adder Research Articles

CNTFET-based digital arithmetic circuit designs in ternary logic with improved performance

Ternary logics are more desirable than the binary logic because it offers high speed operations and large density of information in digital logic systems. The carbon nanotube field-effect transistors (CNTFETs) are considered as better option for designing the ternary circuits because it provides the multiple threshold voltages by changing nanotube diameter. The complex arithmetic schematics such as adders and multipliers are important circuits in many VLSI applications. The ternary half-adder (THA) and multiplier (TMUL) designed using the Stanford 32 nm CNTFET are proposed in this study. The proposed THA and TMUL uses 41 and 33 CNTFETs and that resulting in a 54.44 % and 45 % reduction in transistor count, which plays major role for delay and power optimization. As a result, the proposed THA shows 37.01 %, 14.07 %, and 45.87 % improvement in delay, power, and energy, whereas TMUL shows 30.48 %, 6.64 %, and 36.74 % improvement in delay, power and energy, respectively, compared to existing circuits. The proposed THA and TMUL are developed using HSPICE with 0.9 V as a supply voltage.

Design and Application of Memristive Balanced Ternary Univariate Logic Circuit.

This paper proposes a unique memristor-based design scheme for a balanced ternary digital logic circuit. First, a design method of a single-variable logic function circuit is proposed. Then, by combining with a balanced ternary multiplexer, some common application-type combinational logic circuits are proposed, including a balanced ternary half adder, multiplier and numerical comparator. The above circuits are all simulated and verified in LTSpice, which demonstrate the feasibility of the proposed scheme.

CNTFET and RRAM Based Low Power Design of Unbalanced Ternary Logic Gates and Arithmetic Circuits

The advent of multi-valued logic (MVL) systems provides considerable improvements in energy consumption and computational efficiency compared to binary logic systems. Using resistive random-access memory (RRAM) and carbon nanotube field effect transistors (CNTFETs), this manuscript presents a new design method for ternary logic gates (standard ternary inverter (STI), ternary NOR, and ternary NAND) and some arithmetic circuit applications are implemented based on the proposed ternary logic gates. The simulations of the proposed circuits are carried out in Synopsis HSPICE software by employing 32-nm Stanford CNTFET technology along with the Stanford RRAM model. The robustness of the designed CNTFET-RRAM STI circuit is investigated for variations in process parameters. Simulation results verify that the proposed designs outperform other CNTFET based ternary logic circuits in terms of number of components, power consumption, delay and power delay product (PDP). Furthermore, a reduced change is perceived with respect to power consumption and PDP of the presented logic gates with process deviation, and variations in supply voltage, temperature, capacitance and frequency. The presented STI, TNAND, TNOR, ternary half adder (THA) and ternary multiplier (TMUL) circuits exhibit an improvement in PDP with less transistor count as compared to the other existing designs in the literature.

An efficient GNRFET-based circuit design of ternary half-adder

Attaining low energy consumption in digital circuits design is a main task for designers because emerging applications are based on batteries and face limited-energy. Designing digital circuits with application to multiple-valued logic (MVL) and graphene nanoribbon field-effect transistor (GNRFET) provides a huge improvement in energy consumption. In this regard, this paper presents a novel ternary Half-Adder (THA) implemented with metal-oxide semiconductor (MOS)-type GNRFET. In the proposed THA, the Sum circuit is based on a combination of 3:1 ternary multiplexer, unary operators, and two supply voltages (dual-VDD), and the Carry circuit is based on unary operators, pass-transistor logic, and dual-VDD. The proposed THA is simulated using the 32-nm MOS-type GNRFET technology node at 0.9 V supply voltage in the HSPICE simulator. The proposed THA reduces the transistors count by 5.71–26.67% compared to the previously published THA circuits available in the literature, which are similar to the proposed THA from the design approach point of view. It is concluded from the simulation results that the proposed THA improves the power and energy consumptions by 83.33–91.41% and 66.38–82.27%, respectively. Moreover, the proposed THA is also designed and simulated using the Stanford 32-nm carbon nanotube field-effect transistor (CNTFET) technology. The proposed MOS-type GNRFET-based THA reduces the power and energy consumptions by 84.79% and 68.03%, respectively, and increases the delay by 2.12 × compared to its CNTFET-based counterpart. Moreover, the proposed CNTFET-based THA offers the second-lowest delay and power and the third-lowest energy compared to other existing CNTFET-based THA circuits.

An ultra‐low power and energy‐efficient ternary Half‐Adder based on unary operators and two ternary 3:1 multiplexers in 32‐nm GNRFET technology

SummaryInternet‐of‐Things (IoTs)‐based embedded systems require energy‐efficient designs for long‐term operation. To achieve energy‐efficient designs, multiple‐valued logic (MVL) circuits and graphene nanoribbon field‐effect transistors (GNRFETs) are used instead of binary logic circuits and complementary metal‐oxide‐semiconductor (CMOS), respectively. This paper presents a novel ultra‐low power and energy‐efficient ternary Half‐Adder (THA) circuit based on unary operators, two power supplies (dual‐VDD), VDD and VDD/2, and two ternary 3:1 multiplexers in 32 nm GNRFET technology. The superiority of the proposed design are improvements between 2.86% and 60% in transistor count, between 86.12% and 97.15% in power consumption, and between 58.14% and 98.39% in power‐delay‐product (PDP) compared to existing THA circuits. Moreover, the proposed THA circuit is also implemented with 32 nm carbon nanotube field‐effect transistors (CNTFETs). Simulation results indicate that the proposed GNRFET‐based THA circuit increases delay by 1.74 × and reduces power/PDP by 89.41%/81.63% compared to its CNTFET‐based counterpart.

Energy efficient design of unbalanced ternary logic gates and arithmetic circuits using CNTFET

The emergence of multi-valued logic (MVL) is a substitute to binary logic approaches for realizing high-information density logic systems and high-operating speed systems. In this paper, a design for standard ternary inverter (STI), ternary NAND (TNAND), ternary NOR (TNOR) using carbon nanotube field effect transistors (CNTFETs) is proposed in which a p-type dynamic diode is used with the goal of lowering the energy consumption expressed as power delay product (PDP) and thereby reducing battery usage. Additionally, the basic arithmetic operations are then performed using proposed ternary logic circuits, which can be extended to realize more complex operations. The proposed designs are simulated in HSPICE using a 32 nm Stanford CNTFET model. With respect to variation in process parameters, the reliability of the proposed STI circuit is examined. Simulation results verify that the proposed designs show improvement in terms of power consumption and power delay product (PDP) compared to the other CNTFET based ternary logic circuits. Moreover, less variations are observed in power and PDP of the proposed logic gates with variation in process parameters, capacitance, temperature, frequency and supply voltage. The proposed circuit designs of STI, TNAND, TNOR, ternary half adder (THA), ternary multiplier (TMUL) show 78 %, 98 %, 99 %, 99 %, 99 % improvement in PDP respectively, as compared to the conventional CNTFET based circuit designs and 99 % PDP improvement in all proposed circuits compared to CNTFET based logic circuits with resistive load.

Performance analysis of Ternary Adder and Ternary Multiplier without using Encoders and Decoders

This work presents comparison of ternary combinational digital circuits that reduce energy consumption in low-power VLSI (Very Large Scale Integration) design. CNTFET and GNRFET-based ternary half adder (THA) and multiplier (TMUL) circuits has been designed using ternary unary operator circuits at 32nm technology node and implement two power supplies Vdd and Vdd/2 without using any ternary decoders, basic logic gates, or encoders to minimize the number of used transistors and improve the energy efficiency. The effect of CNTFET and GNRFET parametric variation with threshold voltage on performance metrics namely delay and power has been analyzed. Dependence of threshold voltage on the geometry of carbon nanotube and graphene nanoribbon makes it feasible to be used for ternary logic design. It is analyzed that CNTFET based circuits are energy efficient than the GNRFET- based circuits. It is also concluded that the CNTFET-based circuitshas less power-delay product (PDP) when compared to GNRFET- based circuits. CNTFET-based THA is 23.5% more efficient than GNRFET-based THA and CNTFET-based Tmul is97.8% more efficient than GNRFET-based Tmul.All the digital circuits have been simulated using HSPICE tool.

Low power based ternary half adder using fin type field effect transistor technology

Low power based ternary half adder using fin type field effect transistor technology

Low-Variance Memristor-Based Multi-Level Ternary Combinational Logic

This paper presents a series of multi-stage hybrid memristor-CMOS ternary combinational logic stages that are optimized for reducing silicon area occupation. Prior demonstrations of memristive logic are typically constrained to single-stage logic due to the variety of challenges that affect device performance. Noise accumulation across subsequent stages can be amortized by integrating ternary logic gates, thus enabling higher density data transmission, where more complex computation can take place within a smaller number of stages when compared to single-bit computation. We present the design of a ternary half adder, a ternary full adder, a ternary multiplier, and a ternary magnitude comparator. These designs are simulated in SPICE using the broadly accessible Knowm memristor model, and we perform experimental validation of individual stages using an in-house fabricated Si-doped HfO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</sub> memristor which exhibits low cycle-to-cycle variation, and thus contributes to robust long-term performance. We ultimately show an improvement in data density in each logic block of between <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5.2\times - 17.3\times $ </tex-math></inline-formula> , which also accounts for intermediate voltage buffering to alleviate the memristive loading problem.

Modeling of molecular ternary logic gates and circuits based on diode structures

Modeling in molecular electronics is of great importance, and the use of semiconductor components for this type of modeling accelerates the development process in this field. In this work, a typical circuit model is proposed for modeling molecular components. Accordingly, an asymmetric oligo-phenylene vinylene (OPV) molecular diode and a bipyridine-biborinine molecular diode are modeled. A good agreement is observed between the current curves from the proposed circuit models and the atomic simulations of the molecules. Additionally, the electron density, the distribution of molecular orbitals, and the potential drop profile at + 1 and - 1V are obtained and analyzed for the bipyridine-biborinine molecular diode using the density functional theory (DFT) in combination with the non-equilibrium Green's function (NEGF). Using different molecular gates and circuits based on the molecular devices, we have modeled the ternary NOT logic gate, ternary NOR logic gate, ternary NAND logic gate, negative ternary inverter (NTI) logic gate, positive ternary inverter (PTI) logic gate, ternary buffer, ternary decoder, and ternary half adder.

Polarization rotation based all-optical ternary half-adder and full-adder: design and analysis using micro-ring resonator

Polarization rotation based all-optical ternary half-adder and full-adder: design and analysis using micro-ring resonator

Novel low-complexity and energy-efficient fuzzy min and max circuits in nanoelectronics

Ultra-efficient fundamental fuzzy Min and Max circuits are proposed in this paper using 3 CNTFETs. These are much energy-efficient compared to the state-of-the-art previous designs of Min and Max circuits, which are vastly superior to other models. This is due to the lack of a direct current path (between the inputs and GND /VDD) and the low output resistance. The superiority of the proposed Min and Max Circuits are technically described and proved. At the next step, an applied circuit, the ternary half-adder is developed based on the proposed Min and Max circuits. In these suggestions, all parts of half-adder, successor, and predecessor circuits are introduced based on ternary gates. The simulation results, as obtained through extensive simulations using Synopsys HSPICE and the 32 nm Stanford comprehensive CNTFET model, demonstrate that proposed Min and Max circuits are 22 times (%95.5) and 38 times (%97.39) more energy-efficient with a 0.5fF load compared to the best previous work, respectively. Furthermore, the proposed half-adder is %39 more energy-efficient with a 0.5fF load, compared to the previous work.

CNFET-based design of efficient ternary half adder and 1-trit multiplier circuits using dynamic logic

This paper presents a ternary half adder and a 1-trit multiplier using carbon nanotube transistors. The proposed circuits are designed using pass transistor logic and dynamic logic. Ternary logic uses less connections than binary logic, and less voltage changes are required for the same amount of data transmission. Carbon nanotube transistors have advantages over MOSFETs, such as the same mobility for electrons and holes, the ability to adjust the threshold voltage by changing the nanotube diameter, and less leakage power. The proposed half adder has lower power consumption, delay, and fewer transistors compared to recent ternary half adders that use similar design methods. The proposed 1-trit multiplier also has a lower delay than other designs. Moreover, these advantages are achieved over a wide supply voltage range, operating temperatures, and output loads. The design is also more robust to process variations than the nearest design in terms of PDP.

Mux Based Ultra-Low-Power Ternary Adders and Multiplier implemented with CNFET and 45 nm MOSFETs

ABSTRACT This paper presents improved multiplexer-based ultra-low-power ternary Half Adder (HA), ternary Full Adder (FA), and ternary 1-bit multiplier designs. The proposed circuits consume 61–91% lesser power and can be implemented with 10–40% lesser number of transistors, as compared to the other corresponding circuits available in the literature. The reduction in power and transistor count has been achieved through improved multiplexer designs and judicious use of pass transistor logic. CNFETs have low gate capacitance and hence are ideal devices for ultra-low-power VLSI applications; however, CMOS technology is presently the most preferred technology, because of the easy and low-cost fabrication option made available by the well-established CMOS fabrication labs. Keeping this in view, the proposed mux-based ternary half adder has been designed with both 45 nm MOSFETs and CNFETs. The performance of the proposed HA design has been benchmarked with other CNFET HA reported in the literature. The proposed mux-based CNFET ternary HA, FA and 1-bit multiplier have 10–30% lesser propagation delays than the other designs available in the literature. The reduction in the Power Delay Product (PDP) is 85–99% in the proposed mux-based CNFET ternary circuits as compared to the other benchmarked designs.

CNFET-Based Ultra-Low-Power Dual-$$V_{DD}$$ Ternary Half Adder

CNFET-Based Ultra-Low-Power Dual-$$V_{DD}$$ Ternary Half Adder

Carbon Nanotube Field Effect Transistor (CNTFET) and Resistive Random Access Memory (RRAM) Based Ternary Combinational Logic Circuits

The capability of multiple valued logic (MVL) circuits to achieve higher storage density when compared to that of existing binary circuits is highly impressive. Recently, MVL circuits have attracted significant attention for the design of digital systems. Carbon nanotube field effect transistors (CNTFETs) have shown great promise for design of MVL based circuits, due to the fact that the scalable threshold voltage of CNTFETs can be utilized easily for the multiple voltage designs. In addition, resistive random access memory (RRAM) is also a feasible option for the design of MVL circuits, owing to its multilevel cell capability that enables the storage of multiple resistance states within a single cell. In this manuscript, a design approach for ternary combinational logic circuits while using CNTFETs and RRAM is presented. The designs of ternary half adder, ternary half subtractor, ternary full adder, and ternary full subtractor are evaluated while using Synopsis HSPICE simulation software with standard 32 nm CNTFET technology under different operating conditions, including different supply voltages, output load variation, and different operating temperatures. Finally, the proposed designs are compared with the state-of-the-art ternary designs. Based on the obtained simulation results, the proposed designs show a significant reduction in the transistor count, decreased cell area, and lower power consumption. In addition, due to the participation of RRAM, the proposed designs have advantages in terms of non-volatility.

An Efficient Ultra-Low-Power and Superior Performance Design of Ternary Half Adder Using CNFET and Gate-Overlap TFET Devices

This paper presents a novel ultra-low power yet high-performance device and circuit design paradigm for implementing ternary logic based circuits using Gate-Overlap Tunnel FETs (GOTFETs) and Carbon Nanotube FETs (CNFETs). One of the distinguishing novelty reported in this work is the introduction of an innovative GOTFET device, which exhibits more than double the on-currents I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</sub> and less than 1/10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> the off-currents I <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</sub> of equivalent, equally-sized mosfets at the same technology node. Most of the ternary logic designs reported earlier in the literature encode ternary bits into binary for combinational functionality and then use an Encoder to get back ternary output. Unlike the earlier designs, this paper presents a novel and significantly more efficient approach of directly designing ternary logical functions with Low V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> Transistors (LVT) and High V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> Transistors (HVT) using CNFET and GOTFET technologies. The new approach simplifies the design and reduces the required transistor count & interconnects, thereby reducing the delays and power consumption. The proposed Ternary Half Adder (THA) circuit, designed using CMOS, enables a 52% reduction in transistor count compared to the conventional CMOS designs available in the literature. The THA implemented with CNFET exhibits 27 ps (87% lower delay than similar CMOS design and consumes 2.4 μW power (11% lower than CMOS). On the other hand, CGOT THA exhibits 101 ps (51% lower delay than similar CMOS design) and consumes merely 1.26 μW power (53% lower than CMOS, in ultra-low power regime). The overall decrease in the Power Delay Products (PDPs) are 88% and 77%, respectively, in the proposed CNFET and CGOT THA circuits compared to the CMOS THA.

Ultra-Low Energy CNFET-Based Ternary Combinational Circuits Designs

The embedded systems, IoT (Internet of Things) devices, and portable electronic devices spread very quickly recently. Most of them depend on batteries to operate. The target of this work is to decrease energy consumption by (1) using Multiple-valued logic (MVL) that shows notable enhancements regarding energy consumption over binary circuits and (2) using carbon nanotube field-effect transistors (CNFET) that show better performance than CMOS. This work proposes ternary combinational circuits using 32 nm CNFET: Ternary Half Adder (THA) with 36 transistors and Ternary Multiplier (TMUL) with 23 transistors. To reduce energy consumption by utilizing the unary operator of the ternary system and employing two voltage supplies ( $V_{dd}$ and $V_{dd}$ /2). The result of extensive HSPICE simulations regarding PVT (Process, Voltage, and Temperatures) variations and Noise Immunity Curve (NIC) show the improvements of the proposed designs up to 25% in transistors count and up to 98% in energy consumption reductions. Further, increasing the robustness of process variations and the noise tolerance compared to recent similar designs.

Novel Ternary Adder and Multiplier Designs Without Using Decoders or Encoders

Multiple-Valued Logic systems present significant improvements in terms of energy consumption over binary logic systems. This paper proposes new ternary combinational digital circuits that reduce energy consumption in low-power nano-scale embedded systems and Internet of Thing (IoT) devices to save their battery consumption. The 32 nm CNTFET-based ternary half adder (THA) and multiplier (TMUL) circuits use novel ternary unary operator circuits and implement two power supplies Vdd and Vdd/2 without using any ternary decoders, basic logic gates, or encoders to minimize the number of used transistors and improve the energy efficiency. Extensive simulations (over 160) of the proposed designs in terms of PVT (Process, Voltage, Temperature) variations, noise effect, and scalability studies, along with several benchmark designs using HSPICE simulator, prove the significance of the proposed circuits to decrease the power-delay product (PDP), improve the robustness to process variations, and the noise tolerance. The obtained results show the superiority of the designs in a reduction between 32% and 74% in transistors count and between 18% and 99% in PDP compared to the most recent works.

Toward novel designs of reversible ternary 6:2 Compressor using efficient reversible ternary full-adders

Integrated circuits always face with two major challenges including heat caused by energy losses and the area occupied. In recent years, different strategies have been presented to reduce these two major challenges. The implementations of circuits in a reversible manner as well as the use of multiple-valued logic are among the most successful strategies. Reversible circuits reduce energy loss and ultimately eliminate the problem of overheating in circuits. Preferring multiple-valued logic over binary logic can also greatly reduce area occupied of circuits. When switching from binary logic to multiple-valued logic, the dominant thought in binary logic is the basis of designing computational circuits in multiple-valued logic, and disregards the capabilities of multiple-valued logic. This can cause a minimal use of multiple-valued logic capabilities, increase complexity and delay in the multiple-valued computational circuits. In this paper, we first introduce an efficient reversible ternary half-adder. Afterward, using the reversible ternary half-adder, we introduce two reversible versions of traditional and comprehensive reversible ternary full-adders. Finally, using the introduced reversible ternary full-adders, we propose two novel designs of reversible ternary 6:2 Compressor. The results of the comparisons show that although the proposed circuits are similar to or better than previous corresponding designs in terms of criteria number of constant input and number of garbage outputs, they are superior in criterion quantum cost.