Fundamental Logic Gates Research Articles

Quantum computation with electrons trapped on liquid Helium by using the centimeter-wave manipulating techniques

Surface-state electrons floating on liquid Helium have been served as one of the great potential experimental platforms to implement quantum computation, wherein the qubits are usually encoded by either the lowest two levels of the vertical vibrations (i.e., Hydrogen-like atoms) or the electronic spins. Given the relevant operations require additional techniques, such as the corresponding millimeter-wave or magnetic field manipulations, here we investigate how to implement the scalable quantum computation with a trapped electron array by alternatively using the usual centimeter-wave manipulating techniques. This is because the eigenfrequency of the present qubit, encoded by the two lowest levels of the lateral vibration of the trapped electron, is limited in the centimeter-wave band. We show that, by biasing the electrodes properly and driving the coplanar waveguide transmission line resonator, the electrons can be individually trapped in a series of anharmonic potentials on liquid Helium. Therefore, the well-developed circuit quantum electrodynamics technique for the implementation of superconducting quantum computation can be conveniently utilized here in the present quantum computing platform (proposed firstly in Phys Rev Lett 105:040503, 2010, to implement the fundamental logic gates, typically such as the single-qubit rotations of the individually addressable trapped electrons, the switchable two-qubit manipulations between the electrons trapped in the distant traps, and also the high-fidelity readouts of the target qubits. The feasibility of the proposal is also discussed by numerical simulations.

Design and Implementation of a 2-input Arithmetic and Logic Unit using Quantum-dot Cellular Automata

Quantum-Dot-Cellular Automata (QCA), an emerging nanotechnology rooted in Coulomb repulsion, holds the ability to supplant orthodox complementary metal-oxide semiconductor (CMOS) technology. Its distinctive advantages lie in ultra-low power consumption, fast switching speed, and high-density structures. This study conducts an extensive literature review to introduce an Arithmetic and Logic Unit (ALU) based on QCA principles. The proposed QCA-based ALU incorporates fundamental logic gates, adders, and subtractors, leveraging the latest XOR gate. Utilizing simulation via QCA Designer 2.0.3, an in-depth performance evaluation of the model is conducted, comparing it with established ALUs based on metrics encompassing cell count, delay, and area. The findings showcase the efficiency of the proposed ALU, characterized by its minimal requirement of 277 cells, an area occupancy of 0.43 µm², and a delay of 2.75 clock cycles. This outcome highlights the favorable attributes of our design compared to existing alternatives, suggesting its potential contribution to the advancement of QCA-based digital circuitry. DUJASE Vol. 8 (1) 26-31, 2023 (January)

Ultraflexible, High-Performance Transistors and Logic Circuits on Biocompatible Polylactic Acid (PLA) Substrate.

Wearable and implantable devices have gained significant popularity, playing a crucial role in smart healthcare and human-machine interfaces, which necessitates the development of more complex electronic devices and circuits on biocompatible flexible materials. Polylactic acid (PLA) stands out due to its biodegradability, cost-effectiveness, and low immunogenicity. In this study, we utilize a solution-based spin-coating method to produce high-quality PLA thin films, serving as substrates for the fabrication of thin-film transistors (TFTs) in which the dielectric layer material is silicon dioxide, the channel layer material is IGZO, and the gate, drain, and source material is ITO at low temperatures (<40 °C) through a shadow masking technique. The resulting PLA-TFT devices exhibited remarkable flexibility, biocompatibility, and impressive electrical characteristics, including a charge carrier mobility of 27.81 cm2/(V s), a subthreshold swing of 162.8 mV/decade, and an ON/OFF current ratio of up to 1 × 106, and maintained performance under various deformations. We successfully constructed fundamental logic gate circuits using PLA-TFTs, including AND, OR, and NOT gates, which effectively performed logical functions and demonstrated stability under diverse bending conditions. These research findings provide valuable support for future endeavors in fabricating intricate logic circuits and realizing advanced functionalities on biocompatible flexible materials.

Multiplex-free physical reservoir computing with an adaptive oscillator.

Nonlinear oscillators can often be used as physical reservoir computers, in which the oscillator's dynamics simultaneously performs computation and stores information. Typically, the dynamic states are multiplexed in time, and then machine learning is used to unlock this stored information into a usable form. This time multiplexing is used to create virtual nodes, which are often necessary to capture enough information to perform different tasks, but this multiplexing procedure requires a relatively high sampling rate. Adaptive oscillators, which are a subset of nonlinear oscillators, have plastic states that learn and store information through their dynamics in a human readable form, without the need for machine learning. Highlighting this ability, adaptive oscillators have been used as analog frequency analyzers, robotic controllers, and energy harvesters. Here, adaptive oscillators are considered as a physical reservoir computer without the cumbersome time multiplexing procedure. With this multiplex-free physical reservoir computer architecture, the fundamental logic gates can be simultaneously calculated through dynamics without modifying the base oscillator.

Design and analysis of all-optical half and full adder/subtractor using nonlinear asymmetric directional couplers

The utilization of nonlinear asymmetric directional couplers has emerged as a viable alternative to conventional systems for the execution of arithmetic operations using optical signals. The present study explores the utilization of a coupler-based framework for the development of an all-optical half- and full-adder/subtractor circuit designed with the basic logic gates (AND, OR, XOR) and a soliton pulse as input signals. Nonlinear asymmetric directional couplers have been analysed theoretically and numerically, including the detailed mathematics of coupled wave theory. The switching characteristics of XPM effect based All-optical directional couplers have been examined for appropriate values of the phase shift (∆φ). Appropriate values of ∆φ, extinction ratio (dB), and corresponding controlled pump signal levels and other parameters are investigated for an efficient generation of fundamental logic gates. Further, the detailed analysis of layout generation and design aspects of an all-optical half- and full-adder/subtractor circuit along with the basic logic gates circuits has been carried out. Simulation results are validated with the standard result. The research findings demonstrate that soliton pulses might potentially be useful for optical computing applications when used as the input signal to nonlinear asymmetrical directional couplers.

All-optical logic gates using E-shaped silicon waveguides at 1.55 μm

Owing to the advanced fabrication technology of silicon, silicon waveguides are particularly attractive for implementing all-optical signal processing devices and switches. Therefore, in this paper, a silicon-on-silica waveguide that consists of four slots arranged in the shape of letter E is proposed to be employed as the building block for simulating fundamental all-optical logic gates (AOLGs), including XOR, AND, OR, NOT, NOR, NAND, and XNOR, at 1.55 μm telecommunications wavelength. The operation concept of these logic gates relies on the constructive and destructive interference that results from the phase difference induced by optical beams that are incident on the E-shaped waveguide. The performance of the target logic gates is assessed against the contrast ratio (CR) metric. Moreover, the dependence of the spectral transmission on the device's key operating parameters is investigated and assessed. Compared to other reported designs, the results obtained by conducting simulations using the finite-difference-time-domain in lumerical commercial software show that the proposed waveguide can operate at a higher speed of 80 Gb/s and attain higher CRs of 36, 39, 35.5, 28.8, 30, 38, and 36.7 dB for logic XOR, AND, OR, NOT, NOR, NAND, and XNOR, respectively. This suggests that by using the proposed scheme, AOLGs could be realized more feasibly with greater performance and faster operation toward satisfying the present and future needs of light wave circuits and systems.

Fundamental optical logic gate operations using optically controlled two surfaces plasmonic polariton mode coupler based on graphene clad waveguide

Here, an optical pulse controlled 2 × 2 surface–plasmon–polariton (SPP) mode interference coupler based on graphene clad is designed for the operation of optical fundamental gates. Exploiting the light–matter interactions on graphene–silicon interface and nonlinear optical property of graphene, coupling characteristics are obtained as a function of extra phase change between the excited SPP modes (fundamental and first order) modes with incidence of optical pulse. The device with a very small coupling length of ∼4.3 μm shows optical NOT, AND, and OR gate operation. Our compact design with high fabrication tolerance opens an avenue for the development of a complex optical processor.

Biogenic fluorescent carbon dots modulated fabrication of concatenate logic library and pattern-mediated molecular keypad lock for chemical sensing application

In recent years, molecular logic gates (MLGs) have gained much attention among researchers to replace conventional silicon-based electronic computers. MLGs are employed for various applications, including biological–chemical sensors, heavy metal ion detection, illness diagnosis, and therapy. In this work, we developed two different chemically functionalized forms of biogenic Carbon (C)-dots synthesized using F. religiose and applied as MLGs for multi-stimulus responsive computing. To mimic the operation of Boolean logic gates, we combined as-synthesized three different C-dot platforms (including bulk C-dots, thiol-functionalized (TC)-dots, and acid-functionalized (AC)-dots) with other analytes such as Fe3+, Hg2+, ascorbic acid (AA), glucose (Glu), dichlorvos (DV), and H2O2 and integrated to build a logic library that represents 15 fundamental logic gates (IMP, INH, NOT, NOR, YES, PASS0, and PASS1) and their combinational operations (IMP-OR, IMP-INH, INH-OR). Furthermore, we have developed a parity checker that distinguishes 0 to 9 natural integers as even or odd by using dual-source responsive C-dots and AC-dots platforms. Further, because of the lack of studies using C-dots in “On-Off-On” and “Off-On-Off” sensing to generate logic computation, we have developed a swiping pattern-mediated molecular keypad lock to promise the confidentiality, integrity, and availability of discrete information. A novel design idea for an advanced molecular keypad lock has been proposed based on the dynamic switching of C-dots photoluminescence emission (PLE) with 9 input keys and 6 input key combinations. The keypad lock can be potentially used in different fields, such as electronic gadgets, security systems, sensors, and therapeutics. This is an approach to replacing conventional silicon-based electronic systems with PLE-based nanoforms.

New Methodology for the Design of Nanostructured Integrated Circuits

Background: A metal oxide semiconductor field effect transistor (MOSFET) is widely used to make integrated circuits (ICs). MOSFET devices are reaching the practical limitations for further scaling in the nanoscale regime. It motivates the researchers to explore and develop new ways to advance the electronics industry. Quantum-dot cellular automata (QCA) is a potential way to replace the MOSFET devices in the nanoscale regime. QCA nanotechnology not only solves the issue of scalability but also degrades the leakage current. It has numerous benefits, such as a highly dense design, fast speed, and energy efficiency compared to complementary metal-oxide-semiconductor (CMOS) technology. Objective: An extensive study of QCA nanotechnology is needed to quickly understand the field. Optimizing the QCA designs is the mandatory requirement to minimize the occupied cell area, latency and quantum cost. The preliminary knowledge of QCA nanotechnology boosts the idea of generating different logic functions. This review paper presents the methodology for making the fundamental logic gates using QCA nanotechnology. XOR gate is commonly used to implement popular circuits such as adders, subtractors, comparators, code converters, reversible gates etc. The various available QCA-based 2-input XOR gate designs are discussed and compared for the different performance metrics. Methods: Columbic interaction causes logical operations, and data is transferred from one cell to another cell using cell-to-cell interaction. A specific arrangement of QCA cells produces a specific logic. QCA Designer tool using a Bi-stable simulation engine is used to design different digital circuits. Results: This review paper deals with the design of the 2-input XOR gate. The considered performance metrics for the comparison purpose are cell count, occupied area, clock cycle, and quantum cost. Existing works on 2-input XOR gates show that a minimum of 8 QCA cells are needed for a 2-input XOR gate using QCA nanotechnology. A single clock cycle-based 2-input XOR gate requires at least 9 QCA cells. The quantum cost can be minimized by reducing the number of QCA cells and clock cycles. Conclusion: This review paper helps the circuit designers to select the appropriate 2-input XOR gate for the design of complex circuits. Circuit designers can use the fundamental concepts detailed in the paper to implement any Boolean function and optimize it for the existing designs. A researcher had developed a 2-input XOR gate using only 8 QCA cells with 0.50 clock cycles. Therefore, designers can start from here to further optimize the 2-input XOR gate with a single clock cycle.

КЛАССИФИКАЦИЯ СПЕЦИАЛИЗИРОВАННЫХ ВЫЧИСЛИТЕЛЬНЫХ СИСТЕМ НА ТРАНСПОРТЕ

Relevance Today, the problem of increasing the speed of computing systems is quite acute. Until recently, the increase in the performance of computing systems was achieved by increasing the number of transistors on a chip according to Moore's law. However, at present, logic gates have already been invented, the dimensions of which are comparable to individual atoms and molecules. So already various types of fundamental logic gates have been built using molecules that are based on chemical inputs and spectroscopic outputs. This circumstance imposes a physical limitation on a further increase in the number of transistors on a chip. Thus, an increase in the speed of computing systems in modern conditions is possible only through parallelization. For the effective organization of a parallel computing process, it is necessary to have an idea of the functionality of specific computing systems. Aim of research The main aim of the research is to consider a number of specialized computing systems in transport and try to classify them on a number of grounds. The classification will allow structuring a number of developments in the field of specialized computing systems in transport, combining them into a single centralized and connected system. The goal is to find out what distinctive properties the existing specialized computing systems in transport have and to determine which of these properties prevail and which are rarer. Based on the results of the classification, the goal is to prepare generalized conclusions about the features of the computer systems under study. Research methods The article considers a number of specialized computing systems in transport. In the process of consideration, their distinctive properties and characteristics are highlighted. Based on the properties obtained, the basis for the classification is developed. The purpose of this classification is determined by the practical and theoretical needs associated with the simulation of parallel specialized computing systems. The Russian Science Citation Index will be used as a knowledge base for analyzing examples of specialized computing systems in transport. Results The article provides an overview of specialized computing systems used in the transport industry. In the process of review, characteristic properties are noted that determine their specialization and functional purpose. The key characteristics of these specialized computing systems that distinguish them from each other are reflected. On the basis of the obtained array of characteristics, the grounds for the classification of specialized computing systems in transport are determined. In conclusion, a table is constructed that reflects the dependencies between the selected bases, classes and the considered objects. The conclusions present the rationale and interpretation of the discovered dependencies.

A Space-Efficient Universal and Multi-Operative Reversible Gate Design Based on Quantum-Dots

Because of the high speed, low-power consumption, low latency and possible use at the atomic and molecular levels, Quantum-dot Cellular Automata (QCA) technology is one of the future nanoscale technologies that can replace the present transistor-based technology. For the purpose of creating QCA circuits, reversible logic can be regarded as an appropriate candidate. In this research, a new structure for multi-operative reversible designs is suggested. The Saeid Nima Gate (SNG), proposed in this research study, is a brand-new, incredibly effective, multi-operative, universal reversible gate implemented in QCA nanotechnology employing both majority and inverter gates. Reversible gates, also known as reversible logic gates, are gates that have n inputs and n outputs, which is an equal number of inputs and outputs. The amount of energy lost during computations will be reduced if the numbers of inputs and outputs are identical. The proposed gate is modified and reorganized to optimize further, employing exact QCA cell interaction. All fundamental logic gates are implemented using it to demonstrate the universality of the proposed SNG. Reversible logic has advanced, and as a result, our suggested solution has a lower quantum cost than previously reported systems. The suggested design is simulated using the QCADesigner-E tools.

All-electrical valley filtering in graphene systems (II): Numerical study of electron transport in valley valves

This work performs a numerical study of electron transport through the fundamental logic gate in valleytronics—a valley valve consisting of two or increasing number of valley filters. Various typical effects on the transport are investigated, such as those due to interface scattering, long- and short-range impurity scattering, edge roughness, strain, inter-filter spacing, or increasing number of valley filters. For illustration, we consider the class of specific valves built from graphene quantum wire valley filters in single layer or bilayer graphene, with the filters subject to separate control of in-plane, transverse electric fields. The nearest-neighbor tight-binding model of graphene is used to formulate the corresponding transport problem, and the algorithm of the recursive Green's function method is applied to solve for the corresponding transmission coefficient. In the case of two-filter valves, the result explicitly demonstrates the existence of a pronounced on-off contrast in electron transmission between the two configurations of valves, namely, one with identical and the other with opposite valley polarities in the two constituent filters. The contrast is shown to be enhanced when increasing the number of filters in valves. Signatures of Fano–Fabry–Pérot type resonances in association with interface scattering and inter-filter spacing are illustrated. Electron backscattering due to impurities is found to be sizably suppressed, with the valve performance showing considerable robustness against edge roughness scattering. On the other hand, the presence of a uniaxial strain modifies the electron transmission and results in an interesting quasi-periodic modulation of transmission as we vary the strain strength.

Tunable carbon nanotube diode with varying asymmetric geometry

We propose and demonstrate a carbon nanotube (CNT)-based field emission nanoscale diode to realize a fully integrated nanoscale system, namely, a true nanosystem. To the best of our knowledge, this is the first time a nanodiode simultaneously achieves ease of fabrication and individual tunability of multiple CNT diodes on the nanoscale on the same substrate in a one-time process. A nanodiode comprises a single-wall CNT cathode placed on a substrate, layered insulator, and metal anode. The proposed nanodiode allows us to adjust the turn-on voltage from 1 to 2.4 V by varying the surface area of the anode. Furthermore, as an example of a basic nano-electronic system, nanodiode-based fundamental logic gates (OR and NAND) are demonstrated on a CNT. We propose a theoretical model that derives the theoretical I–V characteristics based on the image-charge method to design the nanodiode quickly. The results in this study contribute to the development of carbon-based nanoelectronic systems.

Toward cascadable MEMS logic device based on mode localization

In line with the rising demand for smarter solutions and embedded systems, Microelectromechanical systems (MEMS) have gained increasing importance for the Internet of Things (IoT) applications, most notably for mobile wearable devices. This is driven by their simplicity, sensitivity, reliability, and low power consumption. Hence, they are being explored for ultra-low-power computing machines. However, the realization of energy-efficient complex logic functions and the cascadability of MEMS resonator-based computing devices have introduced new challenges, such as using the outputs of logic units as inputs into others, which is necessary for realistic implementations. This study demonstrates a complex logic function (half-adder) and fundamental logic gates (XOR and AND) based on selective modes activation. The concept is based on the activation and deactivation of the vibration modes of an F-shaped coupled resonators. The proposed approach requires power for actuation only, and this results in significant improvement in energy efficiency because it does not need DC-based frequency modulations. It shows promising low consumed energy in femtojoules per logic operations. The proposed scheme provides prospects for cascadable MEMS resonator logic devices since it enables both the logic inputs and outputs to be in the same AC signal mode at the same frequency.

Enhanced Functionality of Dual-Gate Organic Transistors Based on Semiconducting/Insulating Polyblend-Induced Asymmetric Charge Modulation Layers.

Dual-gate organic thin-film transistors (DG-OTFTs) with enhanced functionality, including large current enhancement behavior, highly efficient threshold voltage controllability, and self-contained dual-mode logic gate features, are reported. These DG-OTFTs are based on a semiconducting/insulating polyblend-based active layer with asymmetric top and bottom charge modulation layers (atb-CMLs). The atb-CMLs are automatically generated through the preparation of multilayer stacks of phase-separated semiconducting poly(3-hexylthiophene) (P3HT):insulating poly(methylmethacrylate) (PMMA) polyblend layer, poly(vinylidene fluoride) (PVDF) layer, and cross-linked-poly(4-vinylphenol) (cPVP) layer. They consist of a thin PMMA bottom layer and an uneven-shaped PMMA:PVDF miscible mixture-based top layer. The presence of the polarizable insulating PMMA, PVDF, and PMMA:PVDF mixture regions causes the bottom and top CMLs to experience electrical polarization, which induces the dipole field to achieve efficient charge modulation functions in DG-OTFTs. Owing to the presence of atb-CMLs, the DG-OTFTs exhibit unprecedented electrical characteristics, such as the easy depletion of the bottom channel by the top gate potential. However, the top channel can work properly only when given a bottom gate potential (either positive or negative). Given these unusual electrical features, the design of the fundamental dual-mode logic gates (e.g., AND and OR gates) can be achieved with just one DG transistor. This finding opens an interesting direction for the preparation of DG-OTFTs with diverse operating modes and increasing functionality, thereby widening the application potential of such transistors.

Atomic Silicon Quantum Dot: A New Designing Paradigm of an Atomic Logic Circuit

The recent fabrication progress in logic circuits using atomic-scale silicon dangling bond (DB) makes it a promising candidate for field coupled nanocomputing. Moreover, the use of silicon substrate opens the possibilities to integrate DB circuits with existing infrastructure for the complementary metal-oxide-semiconductors (CMOS) devices. However, this emerging technology is still in its initial stage. This paper presents a T-shape structure to realize logic circuits. In addition, fundamental logic gates, such as, two-input AND, NAND, OR, XOR, and XNOR gates, are reported using the T-shape structure. Besides, a novel three-input majority (Si-DBM3) gate and a three-input XOR (Si-DBX3) gate, based on DB pairs, have been presented. Using the proposed Si-DBX3 and Si-DBM3 logic gates, a Full-adder (FA) is designed. All the logic gates are designed and verified using the SiQAD simulation tool.

Multimode excitations for complex multifunctional logic device

The simplicity and prospect of energy efficiency of microelectromechanical systems (MEMS) resonator-based computing devices have captivated considerable research interest in recent years. Hence, they are being explored for ultra-low power computing machines, which are currently needed for internet-of-things (IoT) applications. Recently, there have been successful demonstrations of fundamental logic gates. However, the realization of complex multifunctional logic devices that involve multi-input and multi-output lines are facing challenges, such as the interconnections between multiple resonators and the limited controllability of the operating frequency. In this study, we demonstrate a 1:2 Demux combinational logic device with improved energy efficiency using the multi vibration modes of a single MEMS resonator. The MEMS device consists of three connected in-plane microbeams in the form of a U-shape structure. The actuation and modulation are based on electrostatic forces. The device shows actuation energy of 0.082 fJ and 0.91 fJ for output 1 and output 2, respectively, and switching energy per logic operation of 11.01 pJ for output 1 and 5.31 pJ for output 2. This indicates 75% decrease in switching energy per logic operation in comparison with the previously reported values for electrostatically actuated MEMS resonator-based computing devices.

End-Bonded Metal Contacts on WSe2 Field-Effect Transistors.

Contact engineering has been the central issue in the context of high-performance field-effect transistors (FETs) made of atomic thin transition metal dichalcogenides (TMDs). Conventional metal contacts on TMDs have been made on top via a lithography process, forming a top-bonded contact scheme with an appreciable contact barrier. To provide a more efficient pathway for charge injection, an end-bonded contact scheme has been proposed, in which covalent bonds are formed between the contact metal and channel edges. Yet, little efforts have been made to realize this contact configuration. Here, we bridge this gap and demonstrate seeded growth of end-bonded contact with different TMDs by means of chemical vapor deposition (CVD). Monolayer WSe2 FETs with a CVD-grown channel and end contacts exhibit improved performance metrics, including an on-current density of 30 μA/μm, a hole mobility of 90 cm2/V·s, and a subthreshold swing of 94 mV/dec, an order of magnitude superior than those of top-contact FET counterparts that share the same channel material. A fundamental NOT logic gate constructed using top-gated and end-bonded WSe2 and MoS2 FETs is also demonstrated. Calculations using density functional theory indicate that the superior device performance stems mainly from the stronger metal-TMD hybridization and substantial gap states in the end-contact configuration.

Implementation of Low Power Null Conventional Logic Function for Configuration Logic Block

Todays, transistor level design plays major impact in the power consumption of the VLSI based design. The various logic design models are used to reduce the power consumption that includes synchronous and asynchronous design model. The operation of synchronous circuit is limited by the in phase factor of the clock pulse signal which is used to control the synchronous circuit. In contrast, asynchronous circuits are used widely because it causes low noise, require less power. It affects the less electromagnetic interference that allows reuse of the components. These asynchronous circuits are being implemented by Null Conventional Logic (NCL) which is a delay insensitive logic model. The Configuration Logic Block is the power consuming model in Field Programmable Gate Array (FPGA). This block contains the lookup table (LUT) and 27 fundamental NCL logic gates. To reduce the power consumption of this module, we use the Differential Cascade Voltage Switch Logic (DVSL). The power reduction is achieved in LUT by means of DVSL and minimizes the number transistors. This NCL, DVSL, FPGA logic element is simulated using 90 nm TSMC CMOS processing technology.

Cascadable microelectromechanical resonator logic gate

Micro/nano-electromechanical resonator-based logic elements have emerged recently as an attractive potential alternative to semiconductor electronics. The next step for this technology platform to make it into practical applications and to build complex computing operations beyond the fundamental logic gates is to develop cascadable logic units. Such units should produce outputs that can be used as inputs for the next logic units. Despite the recent developments in electromechanical computing, this requirement has remained elusive. Here, we demonstrate for the first time a conceptual framework for cascadable logic units. Cascadability is experimentally demonstrated through two case studies; one by cascading two OR logic gates. The other case is the universal NOR logic gate realized by cascading an OR and a NOT gate. The logic operations are performed by on-demand activation and deactivation of the second mode of vibration of a clamped-clamped microbeam resonator. We show that the demonstrated approach significantly lowers the complexity and number of microresonator-based logic functions compared to the CMOS-based counterparts, which improves energy efficiency. This can potentially lead toward the realization of a novel technology platform for an alternative computing paradigm.