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68-449: Digital electronic circuits are usually made from large assemblies of logic gates , often packaged in integrated circuits . Complex devices may have simple electronic representations of Boolean logic functions . The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705) and he also established that by using the binary system, the principles of arithmetic and logic could be joined. Digital logic as we know it

136-423: A bit only when the clock changes. The usual way to implement a synchronous sequential state machine is to divide it into a piece of combinational logic and a set of flip flops called a state register . The state register represents the state as a binary number. The combinational logic produces the binary representation for the next state. On each clock cycle, the state register captures the feedback generated from

204-694: A digital circuit , or a mixed-signal circuit (a combination of analog circuits and digital circuits). The most widely used semiconductor device in electronic circuits is the MOSFET (metal–oxide–semiconductor field-effect transistor ). Analog electronic circuits are those in which current or voltage may vary continuously with time to correspond to the information being represented. The basic components of analog circuits are wires, resistors, capacitors, inductors, diodes , and transistors . Analog circuits are very commonly represented in schematic diagrams , in which wires are shown as lines, and each component has

272-411: A field-effect transistor can be modeled as a current source from the source to the drain, with the current controlled by the gate-source voltage. When the circuit size is comparable to a wavelength of the relevant signal frequency, a more sophisticated approach must be used, the distributed-element model . Wires are treated as transmission lines, with nominally constant characteristic impedance , and

340-467: A printed circuit board which is a board which holds electrical components, and connects them together with copper traces. Engineers use many methods to minimize logic redundancy in order to reduce the circuit complexity. Reduced complexity reduces component count and potential errors and therefore typically reduces cost. Logic redundancy can be removed by several well-known techniques, such as binary decision diagrams , Boolean algebra , Karnaugh maps ,

408-409: A truth table . An equivalent high-level circuit uses logic gates , each represented by a different shape (standardized by IEEE / ANSI 91–1984). A low-level representation uses an equivalent circuit of electronic switches (usually transistors ). Most digital systems divide into combinational and sequential systems . The output of a combinational system depends only on the present inputs. However,

476-429: A bundle of wires called a bus that carries that number to other calculations. A calculation is simply a piece of combinational logic. Each calculation also has an output bus, and these may be connected to the inputs of several registers. Sometimes a register will have a multiplexer on its input so that it can store a number from any one of several buses. Asynchronous register-transfer systems (such as computers) have

544-437: A clock distribution network is not needed. An unexpected advantage is that asynchronous computers do not produce spectrally-pure radio noise. They are used in some radio-sensitive mobile-phone base-station controllers. They may be more secure in cryptographic applications because their electrical and radio emissions can be more difficult to decode. Computer architecture is a specialized engineering activity that tries to arrange

612-464: A collection of much simpler logic machines. Almost all computers are synchronous. However, asynchronous computers have also been built. One example is the ASPIDA DLX core. Another was offered by ARM Holdings . They do not, however, have any speed advantages because modern computer designs already run at the speed of their slowest component, usually memory. They do use somewhat less power because

680-543: A consequence, extremely complex digital circuits, with billions of logic elements integrated on a single silicon chip, can be fabricated at low cost. Such digital integrated circuits are ubiquitous in modern electronic devices, such as calculators, mobile phone handsets, and computers. As digital circuits become more complex, issues of time delay, logic races , power dissipation, non-ideal switching, on-chip and inter-chip loading, and leakage currents, become limitations to circuit density, speed and performance. Digital circuitry

748-437: A different clock, the digital system can be subject to metastability where a change to the input violates the setup time for a digital input latch. Since digital circuits are made from analog components, digital circuits calculate more slowly than low-precision analog circuits that use a similar amount of space and power. However, the digital circuit will calculate more repeatably, because of its high noise immunity. Much of

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816-406: A digital system, as long as the total noise is below a certain level, the information can be recovered perfectly. Even when more significant noise is present, the use of redundancy permits the recovery of the original data provided too many errors do not occur. In some cases, digital circuits use more energy than analog circuits to accomplish the same tasks, thus producing more heat which increases

884-404: A general solution. In the 1980s, some researchers discovered that almost all synchronous register-transfer machines could be converted to asynchronous designs by using first-in-first-out synchronization logic. In this scheme, the digital machine is characterized as a set of data flows. In each step of the flow, a synchronization circuit determines when the outputs of that step are valid and instructs

952-429: A logic gate can, in turn, control or feed into more logic gates. Another form of digital circuit is constructed from lookup tables, (many sold as " programmable logic devices ", though other kinds of PLDs exist). Lookup tables can perform the same functions as machines based on logic gates, but can be easily reprogrammed without changing the wiring. This means that a designer can often repair design errors without changing

1020-429: A receiver, analog circuitry is used to amplify and frequency-convert signals so that they reach a suitable state to be converted into digital values, after which further signal processing can be performed in the digital domain. In electronics , prototyping means building an actual circuit to a theoretical design to verify that it works, and to provide a physical platform for debugging it if it does not. The prototype

1088-421: A relatively compact space. In 1955, Carl Frosch and Lincoln Derick discovered silicon dioxide surface passivation effects. In 1957 Frosch and Derick, using masking and predeposition, were able to manufacture silicon dioxide field effect transistors; the first planar transistors, in which drain and source were adjacent at the same surface. At Bell Labs, the importance of Frosch and Derick technique and transistors

1156-481: A second version was completed there in April 1955. From 1955 and onwards, transistors replaced vacuum tubes in computer designs, giving rise to the "second generation" of computers. Compared to vacuum tubes, transistors were smaller, more reliable, had indefinite lifespans, and required less power than vacuum tubes - thereby giving off less heat, and allowing much denser concentrations of circuits, up to tens of thousands in

1224-596: A sequential system has some of its outputs fed back as inputs, so its output may depend on past inputs in addition to present inputs, to produce a sequence of operations. Simplified representations of their behavior called state machines facilitate design and test. Sequential systems divide into two further subcategories. "Synchronous" sequential systems change state all at once when a clock signal changes state. "Asynchronous" sequential systems propagate changes whenever inputs change. Synchronous sequential systems are made using flip flops that store inputted voltages as

1292-434: A single bit error may cause a much larger disruption. Because of the cliff effect , it can be difficult for users to tell if a particular system is right on the edge of failure, or if it can tolerate much more noise before failing. Digital fragility can be reduced by designing a digital system for robustness . For example, a parity bit or other error management method can be inserted into the signal path. These schemes help

1360-483: A unique symbol. Analog circuit analysis employs Kirchhoff's circuit laws : all the currents at a node (a place where wires meet), and the voltage around a closed loop of wires is 0. Wires are usually treated as ideal zero-voltage interconnections; any resistance or reactance is captured by explicitly adding a parasitic element, such as a discrete resistor or inductor. Active components such as transistors are often treated as controlled current or voltage sources: for example,

1428-481: Is a type of electrical circuit. For a circuit to be referred to as electronic , rather than electrical , generally at least one active component must be present. The combination of components and wires allows various simple and complex operations to be performed: signals can be amplified, computations can be performed, and data can be moved from one place to another. Circuits can be constructed of discrete components connected by individual pieces of wire, but today it

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1496-602: Is considered to be arguably the most important master's thesis ever written, winning the 1939 Alfred Noble Prize . The Z3 was an electromechanical computer designed by Konrad Zuse . Finished in 1941, it was the world's first working programmable , fully automatic digital computer. Its operation was facilitated by the invention of the vacuum tube in 1904 by John Ambrose Fleming . At the same time that digital calculation replaced analog, purely electronic circuit elements soon replaced their mechanical and electromechanical equivalents. John Bardeen and Walter Brattain invented

1564-449: Is known as static random-access memory (SRAM). Memory based on the storage of charge in a capacitor, dynamic random-access memory (DRAM), is also widely used.) The design process for digital circuits is fundamentally different from the process for analog circuits. Each logic gate regenerates the binary signal, so the designer need not account for distortion, gain control, offset voltages, and other concerns faced in an analog design. As

1632-495: Is much more common to create interconnections by photolithographic techniques on a laminated substrate (a printed circuit board or PCB) and solder the components to these interconnections to create a finished circuit. In an integrated circuit or IC, the components and interconnections are formed on the same substrate, typically a semiconductor such as doped silicon or (less commonly) gallium arsenide . An electronic circuit can usually be categorized as an analog circuit ,

1700-472: Is needed to accurately portray a given analog signal. If a single piece of digital data is lost or misinterpreted, in some systems only a small error may result, while in other systems the meaning of large blocks of related data can completely change. For example, a single-bit error in audio data stored directly as linear pulse-code modulation causes, at worst, a single audible click. But when using audio compression to save storage space and transmission time,

1768-450: Is often constructed using techniques such as wire wrapping or using a breadboard , stripboard or perfboard , with the result being a circuit that is electrically identical to the design but not physically identical to the final product. Open-source tools like Fritzing exist to document electronic prototypes (especially the breadboard-based ones) and move toward physical production. Prototyping platforms such as Arduino also simplify

1836-492: Is that signals represented digitally can be transmitted without degradation caused by noise . For example, a continuous audio signal transmitted as a sequence of 1s and 0s, can be reconstructed without error, provided the noise picked up in transmission is not enough to prevent identification of the 1s and 0s. In a digital system, a more precise representation of a signal can be obtained by using more binary digits to represent it. While this requires more digital circuits to process

1904-465: Is to construct a table of the minimum and maximum time that each such state can exist and then adjust the circuit to minimize the number of such states. The designer must force the circuit to periodically wait for all of its parts to enter a compatible state (this is called "self-resynchronization"). Without careful design, it is easy to accidentally produce asynchronous logic that is unstable—that is—real electronics will have unpredictable results because of

1972-665: Is used to create general purpose computing chips, such as microprocessors , and custom-designed logic circuits, known as application-specific integrated circuit (ASICs). Field-programmable gate arrays (FPGAs), chips with logic circuitry whose configuration can be modified after fabrication, are also widely used in prototyping and development. Mixed-signal or hybrid circuits contain elements of both analog and digital circuits. Examples include comparators , timers , phase-locked loops , analog-to-digital converters , and digital-to-analog converters . Most modern radio and communications circuitry uses mixed signal circuits. For example, in

2040-500: The Quine–McCluskey algorithm or binary decision diagrams . There are promising experiments with genetic algorithms and annealing optimizations . To automate costly engineering processes, some EDA can take state tables that describe state machines and automatically produce a truth table or a function table for the combinational logic of a state machine. The state table is a piece of text that lists each state, together with

2108-509: The Quine–McCluskey algorithm , and the heuristic computer method . These operations are typically performed within a computer-aided design system. Embedded systems with microcontrollers and programmable logic controllers are often used to implement digital logic for complex systems that do not require optimal performance. These systems are usually programmed by software engineers or by electricians, using ladder logic . A digital circuit's input-output relationship can be represented as

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2176-520: The impedances at the start and end determine transmitted and reflected waves on the line. Circuits designed according to this approach are distributed-element circuits . Such considerations typically become important for circuit boards at frequencies above a GHz; integrated circuits are smaller and can be treated as lumped elements for frequencies less than 10GHz or so. In digital electronic circuits , electric signals take on discrete values, to represent logical and numeric values. These values represent

2244-479: The point-contact transistor at Bell Labs in 1947, followed by William Shockley inventing the bipolar junction transistor at Bell Labs in 1948. At the University of Manchester , a team under the leadership of Tom Kilburn designed and built a machine using the newly developed transistors instead of vacuum tubes. Their " transistorised computer ", and the first in the world, was operational by 1953 , and

2312-519: The silicon integrated circuit. The basis for Noyce's silicon IC was Hoerni's planar process . The MOSFET's advantages include high scalability , affordability, low power consumption, and high transistor density . Its rapid on–off electronic switching speed also makes it ideal for generating pulse trains , the basis for electronic digital signals , in contrast to BJTs which, more slowly, generate analog signals resembling sine waves . Along with MOS large-scale integration (LSI), these factors make

2380-540: The 16-row truth table as proposition 5.101 of Tractatus Logico-Philosophicus (1921). Walther Bothe , inventor of the coincidence circuit , shared the 1954 Nobel Prize in physics, for creating the first modern electronic AND gate in 1924. Mechanical analog computers started appearing in the first century and were later used in the medieval era for astronomical calculations. In World War II , mechanical analog computers were used for specialized military applications such as calculating torpedo aiming. During this time

2448-437: The 1990s and was enabled by the wide adoption of MOSFET-based RF power amplifiers ( power MOSFET and LDMOS ) and RF circuits ( RF CMOS ). Wireless networks allowed for public digital transmission without the need for cables, leading to digital television , satellite and digital radio , GPS , wireless Internet and mobile phones through the 1990s–2000s. An advantage of digital circuits when compared to analog circuits

2516-479: The MOSFET an important switching device for digital circuits . The MOSFET revolutionized the electronics industry , and is the most common semiconductor device . In the early days of integrated circuits , each chip was limited to only a few transistors, and the low degree of integration meant the design process was relatively simple. Manufacturing yields were also quite low by today's standards. The wide adoption of

2584-699: The MOSFET transistor by the early 1970s led to the first large-scale integration (LSI) chips with more than 10,000 transistors on a single chip. Following the wide adoption of CMOS , a type of MOSFET logic, by the 1980s, millions and then billions of MOSFETs could be placed on one chip as the technology progressed, and good designs required thorough planning, giving rise to new design methods . The transistor count of devices and total production rose to unprecedented heights. The total amount of transistors produced until 2018 has been estimated to be 1.3 × 10 (13   sextillion ). The wireless revolution (the introduction and proliferation of wireless networks ) began in

2652-472: The analog nature of the components does not dominate the desired digital behavior. Digital systems must manage noise and timing margins, parasitic inductances and capacitances. Bad designs have intermittent problems such as glitches , vanishingly fast pulses that may trigger some logic but not others, runt pulses that do not reach valid threshold voltages . Additionally, where clocked digital systems interface to analog systems or systems that are driven from

2720-420: The arrangement of wires. Therefore, in small volume products, programmable logic devices are often the preferred solution. They are usually designed by engineers using electronic design automation software. Integrated circuits consist of multiple transistors on one silicon chip, and are the least expensive way to make large number of interconnected logic gates. Integrated circuits are usually interconnected on

2788-459: The complexity of the circuits such as the inclusion of heat sinks. In portable or battery-powered systems this can limit the use of digital systems. For example, battery-powered cellular phones often use a low-power analog front-end to amplify and tune the radio signals from the base station. However, a base station has grid power and can use power-hungry, but very flexible software radios . Such base stations can easily be reprogrammed to process

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2856-401: The computer. The sequencer then counts, and the count addresses the memory or combinational logic machine that contains the microprogram. The bits from the microprogram control the arithmetic logic unit , memory and other parts of the computer, including the microsequencer itself. In this way, the complex task of designing the controls of a computer is reduced to the simpler task of programming

2924-480: The conditions controlling the transitions between them and their associated output signals. Often, real logic systems are designed as a series of sub-projects, which are combined using a tool flow . The tool flow is usually controlled with the help of a scripting language , a simplified computer language that can invoke the software design tools in the right order. Tool flows for large logic systems such as microprocessors can be thousands of commands long, and combine

2992-512: The cumulative delays caused by small variations in the values of the electronic components. Many digital systems are data flow machines . These are usually designed using synchronous register transfer logic and written with hardware description languages such as VHDL or Verilog . In register transfer logic, binary numbers are stored in groups of flip flops called registers . A sequential state machine controls when each register accepts new data from its input. The outputs of each register are

3060-473: The diffusion processes, and H. K. Gummel and R. Lindner who characterized the device. While working at Texas Instruments in July 1958, Jack Kilby recorded his initial ideas concerning the integrated circuit (IC), then successfully demonstrated the first working integrated circuit on 12 September 1958. Kilby's chip was made of germanium . The following year, Robert Noyce at Fairchild Semiconductor invented

3128-527: The effort of designing large logic machines has been automated through the application of electronic design automation (EDA). Simple truth table-style descriptions of logic are often optimized with EDA that automatically produce reduced systems of logic gates or smaller lookup tables that still produce the desired outputs. The most common example of this kind of software is the Espresso heuristic logic minimizer . Optimizing large logic systems may be done using

3196-408: The factory by updating the product's software. This way, the product's design errors can be corrected even after the product is in a customer's hands. Information storage can be easier in digital systems than in analog ones. The noise immunity of digital systems permits data to be stored and retrieved without degradation. In an analog system, noise from aging and wear degrade the information stored. In

3264-448: The first MOSFET . Their transistors were the first in which drain and source were adjacent at the surface, showing that silicon dioxide surface passivation protected and insulated silicon wafers. At Bell Labs, the importance of Frosch's technique was immediately realized. Results of their work circulated around Bell Labs in the form of BTL memos before being published in 1957. At Shockley Semiconductor , William Shockley had circulated

3332-476: The first electronic digital computers were developed, with the term digital being proposed by George Stibitz in 1942 . Originally they were the size of a large room, consuming as much power as several hundred modern PCs . Claude Shannon , demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship, ultimately laid the foundations of digital computing and digital circuits in his master's thesis of 1937, which

3400-671: The first silicon dioxide field effect transistors. In 1955 they accidentally discovered that silicon could be protectively coated by silicon dioxide by the right exposure to oxygen when hot, and patented the method. Such protective coating overcame a problem of surface states found in active silicon circuit elements. The discovery also revealed the potential for the process of silicon etching . In 1957 Frosch and Derick published their discovery of silicon surface passivation by silicon dioxide, using selective SiO2 predeposition and masking to produce semiconductor surface patterns, to build silicon dioxide field effect transistors, thus devising

3468-820: The information that is being processed. In the vast majority of cases, binary encoding is used: one voltage (typically the more positive value) represents a binary '1' and another voltage (usually a value near the ground potential, 0 V) represents a binary '0'. Digital circuits make extensive use of transistors , interconnected to create logic gates that provide the functions of Boolean logic : AND, NAND, OR, NOR, XOR and combinations thereof. Transistors interconnected so as to provide positive feedback are used as latches and flip flops, circuits that have two or more metastable states, and remain in one of these states until changed by an external input. Digital circuits therefore can provide logic and memory, enabling them to perform arbitrary computational functions. (Memory based on flip-flops

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3536-473: The light used to expose the photoresist. Software that are designed for manufacturability add interference patterns to the exposure masks to eliminate open-circuits, and enhance the masks' contrast. Electronic circuit An electronic circuit is composed of individual electronic components , such as resistors , transistors , capacitors , inductors and diodes , connected by conductive wires or traces through which electric current can flow. It

3604-483: The maximum speed of its logic gates. Nevertheless, most systems need to accept external unsynchronized signals into their synchronous logic circuits. This interface is inherently asynchronous and must be analyzed as such. Examples of widely used asynchronous circuits include synchronizer flip-flops, switch debouncers and arbiters . Asynchronous logic components can be hard to design because all possible states, in all possible timings must be considered. The usual method

3672-465: The mechanism of thermally grown oxides, fabricated a high quality Si/ SiO 2 stack and published their results in 1960. Following this research at Bell Labs, Mohamed Atalla and Dawon Kahng proposed a silicon MOS transistor in 1959 and successfully demonstrated a working MOS device with their Bell Labs team in 1960. The team included E. E. LaBate and E. I. Povilonis who fabricated the device; M. O. Thurston, L. A. D’Asaro, and J. R. Ligenza who developed

3740-399: The next stage when to use these outputs. The most general-purpose register-transfer logic machine is a computer . This is basically an automatic binary abacus . The control unit of a computer is usually designed as a microprogram run by a microsequencer . A microprogram is much like a player-piano roll. Each table entry of the microprogram commands the state of every bit that controls

3808-435: The outputs of simulated logic against expected inputs. The test tools take computer files with sets of inputs and outputs and highlight discrepancies between the simulated behavior and the expected behavior. Once the input data is believed to be correct, the design itself must still be verified for correctness. Some tool flows verify designs by first producing a design, then scanning the design to produce compatible input data for

3876-572: The preprint of their article in December 1956 to all his senior staff, including Jean Hoerni . Taking advantage of silicon dioxide's passivating effect on the silicon surface, Hoerni proposed to make transistors that were protected by a layer of silicon dioxide. Later, Jean Hoerni, while working at Fairchild Semiconductor , had first patented the planar process in 1959. Frosch and Derrick build several silicon dioxide field effect transistors in 1957. One resembling modern MOSFETs and another with

3944-457: The previous state of the combinational logic and feeds it back as an unchanging input to the combinational part of the state machine. The clock rate is limited by the most time-consuming logic calculation in the combinational logic. Most digital logic is synchronous because it is easier to create and verify a synchronous design. However, asynchronous logic has the advantage of its speed not being constrained by an arbitrary clock; instead, it runs at

4012-505: The registers, calculation logic, buses and other parts of the computer in the best way possible for a specific purpose. Computer architects have put a lot of work into reducing the cost and increasing the speed of computers in addition to boosting their immunity to programming errors. An increasingly common goal of computer architects is to reduce the power used in battery-powered computer systems, such as smartphones . Digital circuits are made from analog components. The design must assure that

4080-418: The signals used in new cellular standards. Many useful digital systems must translate from continuous analog signals to discrete digital signals. This causes quantization errors . Quantization error can be reduced if the system stores enough digital data to represent the signal to the desired degree of fidelity . The Nyquist–Shannon sampling theorem provides an important guideline as to how much digital data

4148-429: The signals, each digit is handled by the same kind of hardware, resulting in an easily scalable system. In an analog system, additional resolution requires fundamental improvements in the linearity and noise characteristics of each step of the signal chain . With computer-controlled digital systems, new functions can be added through software revision and no hardware changes are needed. Often this can be done outside of

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4216-411: The structure of the logic and systematically generating tests targeting particular potential faults. This way the fault coverage can closely approach 100%, provided the design is properly made testable (see next section). Once a design exists, and is verified and testable, it often needs to be processed to be manufacturable as well. Modern integrated circuits have features smaller than the wavelength of

4284-517: The system detect errors, and then either correct the errors , or request retransmission of the data. A digital circuit is typically constructed from small electronic circuits called logic gates that can be used to create combinational logic . Each logic gate is designed to perform a function of Boolean logic when acting on logic signals. A logic gate is generally created from one or more electrically controlled switches, usually transistors but thermionic valves have seen historic use. The output of

4352-404: The task of programming and interacting with a microcontroller . The developer can choose to deploy their invention as-is using the prototyping platform, or replace it with only the microcontroller chip and the circuitry that is relevant to their product. Carl Frosch Carl John Frosch (September 6, 1908 – May 18, 1984) was a Bell Labs researcher who along Lincoln Derick build

4420-517: The tool flow. If the scanned data matches the input data, then the tool flow has probably not introduced errors. The functional verification data are usually called test vectors . The functional test vectors may be preserved and used in the factory to test whether newly constructed logic works correctly. However, functional test patterns do not discover all fabrication faults. Production tests are often designed by automatic test pattern generation software tools. These generate test vectors by examining

4488-460: The work of hundreds of engineers. Writing and debugging tool flows is an established engineering specialty in companies that produce digital designs. The tool flow usually terminates in a detailed computer file or set of files that describe how to physically construct the logic. Often it consists of instructions on how to draw the transistors and wires on an integrated circuit or a printed circuit board . Parts of tool flows are debugged by verifying

4556-421: Was immediately realized. Results of their work circulated around Bell Labs in the form of BTL memos before being published in 1957. At Shockley Semiconductor , Shockley had circulated the preprint of their article in December 1956 to all his senior staff, including Jean Hoerni , who would later invent the planar process in 1959 while at Fairchild Semiconductor .At Bell Labs, J.R. Ligenza and W.G. Spitzer studied

4624-453: Was the brain-child of George Boole in the mid 19th century. In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits. Eventually, vacuum tubes replaced relays for logic operations. Lee De Forest 's modification of the Fleming valve in 1907 could be used as an AND gate . Ludwig Wittgenstein introduced a version of

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