The design of combinatorial and sequential switching circuits. Topics include Boolean algebra, Boolean function minimization technique, combinatorial circuit analysis and synthesis, synchronous sequential circuit analysis and synthesis, algorithmic state machine design, asynchronous sequential circuit analysis and synthesis.

Grading Basis: Letter Grade

An introductory course in programming that provides a foundation for advanced system design. The objective of the course is to examine the design of programs using language concepts, data structures, algorithms, and software design techniques to solve fundamental engineering problems. Students develop skills to program, construct data structures, and test & debug solutions, while gaining knowledge of the fundamental elements and operation of computer systems.

Grading Basis: Letter Grade

Introduces circuit analysis: basic principles, operational amplifier circuits, first-order and second-order circuits, steady-state sinusoidal analysis with phasor mathematics.

Grading Basis: Letter Grade

Prereq: PHYS 2311 and MATH 2411 with a C- or higher

Sequential course after ELEC 2132. Topics include: Solution of circuits using Laplace transforms, frequency domain analysis, additional steady-state solutions, Bode plots, active filters, pulses, impluses, and computer-aided analysis. This course can be taken stand alone without a lab.

Grading Basis: Letter Grade

Prereq: ELEC 2132, MATH 2421 and PHYS 2331 with a C- or higher.

A second semester computer engineering course covering microcontroller based embedded system design including peripherals, development tools, constraints and interfacing between physical world and device.

Grading Basis: Letter Grade

Prereq: ELEC 1520 with a C- or higher.

Experiments in digital logic utilizing both computer simulation and actual analysis using integrated circuits. Initially, combinational logic circuits are studied, including circuits such as binary adders and multipliers, followed by sequential circuits, including counters. Meters and oscilloscopes are introduced. Use of computer-aided design tools facilitating design, simulation, and implementation of digital systems using field-programmable logic devices are an integral part of the entire course.

Grading Basis: Letter Grade

Coreq: ELEC 1510.

Introduction to discrete-time signal processing and frequency domain analysis. Sampling and interpolation, discrete Fourier transform, effects of filtering and modulation of signals. Concepts are explored in the context of multimedia, communications, and data analysis applications. Emphasizes computer-based signal processing using MATLAB.

Grading Basis: Letter Grade

Prereq: ELEC 1520 with a C- or better. Coreq: MATH 3195 or MATH 3191.

This basic electrical engineering course is for non-majors (does not apply to BSEE degree). Students study circuit analysis, transformers, electric motors, and simple electronic circuits (diodes and transistors). Cross-listed with MECH 3030.

Grading Basis: Letter Grade

Prereq: MATH 2421 and PHYS 2331 with a C- or higher Restriction: Restricted to majors within the College of Engineering, Design and Computing

Fundamental physics and applications of electric and magnetic fields are covered. Topics include: vector analysis in multiple coordinate systems, Maxwell's equations in free space and material regions including boundary conditions, static and quasi-static electric and magnetic fields, uniform plane waves for free space and for materials.

Grading Basis: Letter Grade

Prereq: ELEC 2132, MATH 2421, MATH 3195 (or MATH 3191 and MATH 3200), and PHYS 2331 all with a grade of C- or higher. Restriction: Restricted to students within the College of Engineering, Design and Computing

Explores various energy resources and modern conversion systems utilized to generate, store, process, and deliver electric power. Topics include electromechanical, electrochemical, and renewable energy systems, as well as switch-mode power processing and power networks.

Grading Basis: Letter Grade

Prereq: ELEC 2142 with a C- or higher, and ENGR 1130 with a C- or higher.

BJT and FET transistor models at high frequencies, multistage amplifiers, frequency response of amplifiers. Feedback, operational amplifiers, oscillators, power amplifiers, and introduction to power electronics.

Grading Basis: Letter Grade

Prereq: ELEC 2142 with a C- or better, PHYS 2331 with a C- or better and ENGR 1130 with a C- or better. Restriction: Restricted to students within the College of Engineering, Design and Computing.

Introduces the fundamentals of signals and systems analysis. Topics include: time domain analysis of continuous and discrete time systems, frequency domain (Laplace and z-transform) analysis, applications to filters and feedback systems, Fourier transform for both continuous and discrete time signals, sampling and signal reconstruction, applications to communication systems and state space representation. Learning experience is enhanced by using MATLAB-based examples and experiments.

Grading Basis: Letter Grade

Prereq: ELEC 2142 with a C- or higher, ELEC 2531 with a C- or higher, ELEC 2651 with a C- or higher, MATH 3195 with a C- or higher or MATH 3191 and MATH 3200 with a C- or higher.

A computer engineering course covering intelligent systems that include applications with connected Internet-of-Things (IoT) devices and cyber-physical elements. An intelligent system consists of a collection of computing devices communicating with one another and capable of interacting with the physical world. The course explores the system design and software development process to deploy real-time embedded applications in real-world scenarios. Topics include multiple hardware and software systems necessary to perform sensing, actuation, processing, and communication with connected computing devices.

Grading Basis: Letter Grade

Prereq: ELEC 2520 with a C- or better, ELEC 2531 with A C- or better and ELEC 2651 with a C- or better.

The course introduces the mathematical formalism and software for machine learning approaches in electrical engineering problems. Selected applications include signal detection, signal classification, remote sensing, imaging, and model optimization. Topics include: linear and logistic regression, support vector machines, clustering, artificial neural networks, hypothesis testing, and Bayesian analysis.

Grading Basis: Letter Grade

Requires prerequisite courses of (ELEC 3817 or BIOE 3060 or CVEN 3611 or MECH 3027 or MATH 3382 or MATH 3810 with a C- or better) AND (MATH 3195 or (MATH 3191 and MATH 3200 with a C- or better)).

Typically Offered: Spring.

Provides hands-on experience on electromechanical, electrochemical, and semiconductor-based energy conversion systems. Sessions include operation of induction motor and generator, energy storage, and renewable energy experiments.

Grading Basis: Letter Grade

Prereq: ELEC 2142 with a C- or better. Prereq or Coreq: ELEC 3164.

Topics include: definition of probability, conditional probability, independence, combined experiments and Bernoulli trials, random variables, joint distribution and density functions, correlations, sample mean and variance. Also, introduction to random processes, auto and cross correlation functions, spectral density of random signals, responses of a linear system to random inputs.

Grading Basis: Letter Grade

Prereq: MATH 3195 with a C- or better and Math 2421 with a C- or better.

Course with Hands-on content that involves electrical measurement and diagnosis in the context of electrical circuit design, fabrication, and validation. Standard benchtop tools of oscilloscope, signal generator, digital multi-meter, DC power supply are introduced. Final project involves layout and fabrication of a printed circuit board (PCB).

Grading Basis: Letter Grade

Prereq: ELEC 3225 with a C- or better and ELEC 2142 with a C- or better.

Students gain engineering design experience involving application of specific technical concepts and skills in a supervised industrial environment. (Must have approval from ELEC faculty.) Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Prereq: ELEC 2142

Explores digital integrated circuit design including MOS processing steps, physical operation, building blocks of digital circuits, advanced nMOS, pMOS and CMOS circuit design, silicon VLSI technology and circuit and chip level. Spice and lay-out Editor are used. The physical relationship between circuit design and actual silicon layout and structure and technology are emphasized. Cross-listed with ELEC 5005.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3225 (minimum grade C-).

A course relating performance and limitations of solid state devices to their structures and technology. For both advanced circuit and device engineers. Semiconductor physics and technology, pn-junction and MOS devices used in modern integrated circuits. Cross-listed with ELEC 5025.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3225 (minimum grade C-). Restricted to students with senior standing.

A course focused on electromagnetic waves. Topics include: electromagnetic power, reflection and transmission of uniform plane waves in layered media, rectangular wave guides, two-conductor transmission lines, Smith Chart representation of wave impedance and reflection. Cross-listed with ELEC 5033.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3133 (minimum grade C-).

This course provides the basic principles of microwave circuit design, including transmission line theory, network parameters, signal flow graphs, design of high frequency matching networks, filters, hybrids and couplers using waveguide elements, high frequency amplifier and mixer design. Cross-listed with ELEC 5134.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3133 (minimum grade C-).

Introduces students to the fundamentals of analysis and design of feedback systems. Topics include: mathematical models of linear continuous-time systems applied to modeling physical systems in the time and frequency domain, control system characteristics, Routh's stability and transient response analysis, Nyquist stability and polar plots, analysis and design of linear control systems by root locus and frequency response, methods, compensator implementation, finite-precision numerical effects, round-off errors, and computer-based design applications.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3316 (minimum grade C-). Requires corequisite course of ELEC 3817. Restricted to students within the College of Engineering, Design and Computing.

This course provides a comprehensive introduction to Intelligent Transportation Systems (ITS), addressing modern transportation challenges and exploring emerging research areas. Students will study traffic flow modeling, roadway network design, and the integration of Geographic Information Systems (GIS) with transportation applications. Key topics include communication and control systems, computer vision, machine learning in ITS, and technologies for electric and hydrogen vehicles. Practical applications cover intelligent charging strategies, safety systems, and sustainability considerations. The course emphasizes real-world problem solving using sensors, advanced algorithms, and data-driven methods to design and optimize next-generation transportation networks. Open to senior undergraduates and graduate students in Electrical Engineering and related fields. Cross-listed with NEW course proposal ELEC 5152

Grading Basis: Letter Grade

Restriction: Restricted to Junior standing or higher.

Covers the fundamental components and operation of electric and hybrid vehicles’ drivetrain. Topics include electric vehicle history, major vehicle components, fundamental vehicle dynamics, electric and hybrid drivetrain configurations, electric motors and drives, energy storage, and power electronics chargers. Cross-listed with ELEC 5154.

Grading Basis: Letter Grade

Restriction: Restricted to undergraduate students at a junior standing or higher

Typically Offered: Fall.

Covers power electronics drives for rotating electric machinery. Topics include power electronics elements for drives, load characteristics, dynamic modeling of AC machines, fundamental control algorithms, simulation and practical commercial drives. Cross-listed with ELEC 5164. Repeatable.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3164 (minimum grade C-). Restricted to students within the College of Engineering, Design, and Computing.

Offers hands-on experience on rotating electric machine drive simulations and commercial systems. Sessions include pulse-width modulation (PWM) inverter, induction, DC, and synchronous machine drives. Matlab/Simulink and a commercial inverter will be utilized. Cross-listed with ELEC 5170.

Grading Basis: Letter Grade

Prereq or Coreq: ELEC 4164 or ELEC 5164

Typically Offered: Fall.

Topics to be covered include: power electronics fundamentals and applications in power systems; uncontrolled, semi-controlled and fully controlled power semiconductors; converters design and control. Cross-listed with ELEC 5174.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3164 (minimum grade C-). Restricted to students within the College of Engineering, Design, and Computing.

Topics to be covered include: complex power; per-unit quantities; modeling of generators, transformers and transmission lines; power flow problem; economic dispatch; faults and sequence networks; and an introduction to power system protection and dynamics. Cross-listed with ELEC 5184.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3164 (minimum grade C-). Restricted to students within the College of Engineering, Design, and Computing.

Reliability Engineering is a critical part of systems engineering and sustainability design. There are four objectives of this course: 1) to introduce systems and controls in the design process, 2) to apply reliability fundamentals to civil, computer science, bio-engineering, mechanical, and electrical engineering projects and systems , 3) to employ and explore sustainability design in engineering projects, and 4) to prepare for the American Society of Quality Control (ASQC) test: the Certified Reliability Engineer Certification (CRE). Cross-listed with ELEC 5212.

Grading Basis: Letter Grade

Prereq: ELEC 3817.

Typically Offered: Summer.

Switching state models of discrete components and integrated circuits, including logic gates, comparators, and operational amplifiers. Input, output, and transfer characteristics. Non-ideal properties. Analog-digital and digital-analog conversion. MOS-integrated circuits.

Grading Basis: Letter Grade

Prereq: ELEC 3225 and Coreq: ELEC 3900. Restriction: Restricted to students within the College of Engineering, Design and Computing.

Introduces digital communication systems covering elements of information theory; mathematical representation of signals and systems; modulation and demodulation for the additive Gaussian noise channel; performance analysis of various transmission formats; synchronization; coded waveforms; decoding algorithms; and other related topics. Cross-listed with ELEC 5248.

Grading Basis: Letter Grade

Pre-req: ELEC 3316 and 3817

Fundamentals of wireless communication from a physical-layer perspective. Multipath signal propagation and fading channel models. Design of constellations to exploit time, frequency, and spatial diversity. Reliable communication and single-user capacity. Interference management, multiple-access protocols, and multi-user capacity. Cellular uplink and downlink. Multiple-antenna systems and architectures. Communications with Intelligent Reflecting Surfaces. mmWave and THz communications. Connections to modern standards. Cross-listed with ELEC 5249.

Grading Basis: Letter Grade

Prereq: ELEC 3316 and ELEC 3817

We indulge in a journey from the theory of information to the world of applications. We talk about what information means and provide the means to measure it. We then investigate various methods for extracting what matters from the available data. We bring in topics such as Bayesian data modeling, clustering algorithms, and neural networks to name a few. Cross-listed with ELEC 5250.

Grading Basis: Letter Grade

Prereq: ELEC 3316 and ELEC 3817 with a C- or higher.

Typically Offered: Fall.

Topics to be covered include: discrete-time systems and the z-transform, characteristics of open-loop and closed-loop discrete-time systems, time-response characteristics and stability analysis, design of digital and hybrid control systems using z-transform, root locus, frequency domain, and state variable compensation techniques, compensator on, implementation, and computer-based design applications. Cross-listed with ELEC 5276.

Grading Basis: Letter Grade

Prereq: ELEC 3316

Design methodology and tools, project planning and team building, ethics in engineering and research, career planning and portfolio building. Project designs are completed and presented to the class. ELEC 4309 and ELEC 4319 must be completed in subsequent academic semesters.

Grading Basis: Letter Grade

Prereq: ELEC 2531. Coreq: ELEC 3133, 3164, 3225, 3316, 3724, 3900, and 3817. Restricted to undergraduate majors within the College of Engineering, Design, and Computing. ELEC 4309 and ELEC 4319 must be completed in subsequent academic semesters.

Project designs completed in ELEC 4309 are constructed and tested. Oral and written presentations of the completed project performance are required.

Grading Basis: Letter Grade

Prereq: ELEC 4309 with a C- or higher. Coreq: ELEC 3701 and ELEC 3520/

Typically Offered: Spring.

An intro to computational electromagnetics based on the Finite Difference Time-Domain (FDTD) covering, finite difference methods, the Yee algorithm, numerical error, stability, boundary conditions, source excitations, hands-on programming experience and application of FDTD to real problems. Cross-listed with ELEC 5333.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3133 (minimum grade C-).

This course introduces some of the most important concepts in optical engineering and prepares students a solid foundation to apply them to applications in the industry and academic research. Cross-listed with ELEC 5373.

Grading Basis: Letter Grade

Prereq: ELEC 3133

In this course, students will be introduced to the principles of brain signal processing, neural instrumentation, and brain data analysis techniques. These principles will equip students with the necessary knowledge to apply engineering concepts to neural engineering applications. Cross-listed with ELEC 5375.

Grading Basis: Letter Grade

Prereq: ELEC 3316 or Graduate Standing

This lab includes system identification, design of velocity control systems, design of PID controllers and control systems using state variable feedback.

Grading Basis: Letter Grade

Prereq or Coreq: ELEC 4136 or 4276.

Projects involve modern RF analyzers, wave-guide devices, time-domain techniques, characterization of filters/amplifiers, signal propagation and scattering, harmonic mixing, and radio frequency identification. Students will gain experience using MATLAB for data acquisition and processing. Cross-listed with ELEC 5423.

Grading Basis: Letter Grade

Requires prerequisite courses of ELEC 3133 and ELEC 3225 (all minimum grade C-).

Projects related to digital logic, analog and digital switches, A/D and D/A converters, and design of signal filters.

Grading Basis: Letter Grade

Prereq: ELEC 3225. Coreq: ELEC 3900 and ELEC 4225.

This lab introduces the student to modern computational tools used in power system analysis. Algorithms to solve the "power flow problem," the "economic dispatch problem," and the "optimal power flow problem" are discussed and implemented in the Matlab-Simulink mathematical analysis software package. Cross-listed with ELEC 5444.

Grading Basis: Letter Grade

Requires corequisite course of ELEC 4184 or ELEC 4154 or ELEC 4164 or ELEC 4755 or ELEC 4174.

Introduction to semiconductors, introductory numerical analysis of semiconductor devices, use of software programs for electron devices, junction devices, numerical modeling and simulation of MOS transistors. Cross-listed with ELEC 5455.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3225 (minimum grade C-).

Typically Offered: Spring.

The power electronics laboratory introduces students to seven fundamental switchmode power conversion topologies, along with voltage and current feedback control, assembled on a reconfigurable power pole circuit board with external power supplies and laboratory. Cross-listed with ELEC 5474.

Grading Basis: Letter Grade

Coreq: ELEC 4174 Restriction: Restricted to students within the College of Engineering, Design and Computing

Covers advanced treatment of embedded system design using microprocessors. Analog input circuitry is interfaced to a microprocessor, and a PC board layout is created to develop a complete system design. Software/Operating System is implemented for realtime I/O. Cross-listed with ELEC 5501.

Grading Basis: Letter Grade

Prereq/Coreq: ELEC 3520.

Computer engineering methods in hardware and software design applied to problems drawn from the mini- and micro-computer systems field. Hardware and software techniques for the design of combined hardware or software are developed. Interface and real-time programming techniques are considered. Graduate level requires additional projects and homework. Cross-listed with ELEC 5511.

Grading Basis: Letter Grade

Prereq: ELEC 3520.

Provides support for the projects assigned in ELEC 4501 - a complete embedded system is designed, built and tested.

Grading Basis: Letter Grade

Coreq: ELEC 4501

This course introduces the fundamentals of deep learning through hands-on projects using PyTorch. Students will learn to build and train neural networks, explore key architectures like CNNs and transformers, and apply them to real-world tasks. By the end, students will be able to apply and experiment with advanced neural network architectures. Cross-listed with ELEC 5531

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3701 (minimum grade C-).

Typically Offered: Spring, Summer.

This course introduces the state-of-the-art deep learning research work. Students will gain both theoretical and practical understanding of deep learning in computer vision area. Cross-listed with ELEC 5541.

Grading Basis: Letter Grade

Prereq: ELEC 3520.

Typically Offered: Spring, Summer.

Computer methods for large integrated circuits. Theory and practice of VLSI circuit simulation. Nodal formulations of networks. Computer generation of sensitivities. Modeling active devices. DC solution of nonlinear networks. Cross-listed with ELEC 5555.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3225 (minimum grade C-).

Projects related to the software interface of a processor to external devices. Topics include A/D converters, serial and parallel interfaces.

Grading Basis: Letter Grade

Prereq: ELEC 3520 and Coreq: ELEC 4511.

The course Graph Signal Processing is designed to provide the students with tools to perform convolutional information processing on graphs. The tools introduced are a formal extension of the tools learned in previous signal processing courses. Consequently, the student will learn the basics about how to perform filtering, frequency decompositions, sampling, and representation of signals on a graph. The course also emphasizes how these tools are formally consistent with concepts from previous courses when framed in the theory of algebraic signal processing. Cross-listed with ELEC 5627

Grading Basis: Letter Grade

Discrete-time signals and systems in the time and frequency domain. Digital filter structures, design of FIR filters by windowing, optimum approximations of FIR filters. Design of digital IIR filters from continuous time domain. Computer-aided design of digital filters. The discrete Fourier transform and DSP algorithm implementation. Analysis of finite word length effects. Application of digital signal processing. Cross-listed with ELEC 5637.

Grading Basis: Letter Grade

Prereq: ELEC 3316 and ELEC 3817

This course will introduce students to the basic physics, technologies, and clinical methodologies underlying Ultrasound, MRI,CT, PET and SPECT imaging systems. The course will include lectures, and visits to campus hospital and research imaging systems as well as hands on ultrasound labs. Cross-listed with ELEC 5644.

Grading Basis: Letter Grade

Prereq: ELEC 2651 or graduate standing.

The course teaches students the principles, the algorithms and the programming methods of quantum computing, and also discusses the associated physics and mathematics background required. Other related topics such as quantum communication and quantum entanglement will also be discussed. Cross-listed with ELEC 5678, PHYS 4678, and PHYS 5678.

Grading Basis: Letter Grade

Prereq: ELEC 3817 or CSCI 3560/4650/4110 with a C- or better.

Typically Offered: Fall.

The course discusses several seminal quantum algorithms, including the quantum Fourier transforms, Grover’s and Shor’s algorithms, followed by explaining several advanced quantum computing algorithms, including quantum error correction, sparse linear systems, and variational eigensolver. Google Cirq quantum programming library will be used for actual quantum programming implementations of the algorithms discussed. Cross-listed with ELEC 5679, PHYS 4679, and PHYS 5679.

Grading Basis: Letter Grade

Prereq: ELEC 4678 or ELEC 3817 or CSCI 3560/4650/4110 with a C- or better.

Typically Offered: Fall.

Students will explore some of the concepts and experimental practices for realizing quantum computers and related quantum information technologies. They will engage in laboratory practice of relevant skills including high-performance analog electronics; optics-based quantum encryption and eraser implementations; and RF electronics. Cross-listed with ELEC 5680, PHYS 4680, PHYS 5680

Grading Basis: Letter Grade

Prereq: ELEC 3900 with a C- or higher.

Typically Offered: Fall.

Students will explore a systems approach toward experimental practices for realizing quantum information science and engineering (QISE), with a focus on vacuum and cryogenic techniques and integration of electronics subsystems into a "dry" cryostat. They will engage in laboratory practice of relevant skills including creation and measurement of high vacuum, methods for reaching ultra-low temperatures, concerns in the design and construction of cryogenic apparatuses, and operation of a "dry" cryogenic system at 4 K, including measurements on superconducting quantum interference devices. Cross-listed with PHYS 4681, PHYS 5681 and ELEC 5681.

Grading Basis: Letter Grade

Prereq: PHYS 4680 OR PHYS 5680 OR ELEC 4680 OR ELEC 5680 with a C- or higher.

High Performance Computer Architecture covers the design of advanced computing systems. In particular, the course includes the design of modern microprocessors, characteristics of the memory hierarchy, and issues involved in multithreading and multicore architectures. Cross-listed with ELEC 5723.

Grading Basis: Letter Grade

Prereq: ELEC 3520.

This course provides an introduction to machine vision systems regarding concepts, algorithms, and applications, especially revealing how the latest vision systems can mimic and even outperform humans in specific tasks. Through practical assignments and projects, students will learn to develop vision systems that can see, interpret, and act on visual data. Key topics include image/video formation and transformation, feature extraction, object recognition, and evaluating vision system performance. By the end of the course, students will have a solid background in machine vision algorithms and be able to advance their knowledge in solving real-world problems. Cross-listed with ELEC 5727.

Grading Basis: Letter Grade

Requires prerequisite course of ELEC 3817 (minimum grade C-).

Typically Offered: Fall.

This course focuses on the modeling, analysis and control of grid-connected wind and photovoltaic energy systems. Cross-listed with ELEC 5755. Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Prereq: ELEC 3164 Restriction: Restricted to students within the College of Engineering, Design and Computing

Typically Offered: Spring.

Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Cross-listed with ELEC 5802. Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Restricted to undergraduate ELEC students.

Cross-listed with ELEC 5810. Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

An opportunity for independent creative work. Repeatable.

Grading Basis: Letter Grade

Repeatable. Max Credits: 9.

Restrictions: Restricted to majors within the College of Engineering, Design and Computing.