A logic gate is an idealized or physical device implementing a

10:00 min

/ref> Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digital

Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

, a logical operation performed on one or more binary inputs that produces a single binary output. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fan-out, or it may refer to a non-ideal physical device (see Ideal and real op-amps for comparison).
Logic gates are primarily implemented using diode
A diode is a two- terminal electronic component that conducts current primarily in one direction (asymmetric conductance); it has low (ideally zero) resistance in one direction, and high (ideally infinite) resistance in the other.
A diode ...

s or transistor
file:MOSFET Structure.png, upright=1.4, Metal-oxide-semiconductor field-effect transistor (MOSFET), showing Metal gate, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink).
A ...

s acting as electronic switches, but can also be constructed using vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.
The type known as a ...

s, electromagnetic relay
A relay
Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts
An automotive-style miniature relay with the dust cover taken off
A relay is an electrically operated switch ...

s (relay logic
Relay logic is a method of implementing combinational logic in electrical control circuits by using several electrical relays wired in a particular configuration.
Ladder logic
The schematic diagrams for relay logic circuits are often calle ...

), fluidic logic, pneumatic logic, optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultraviol ...

, molecules, or even mechanical
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations of ...

elements. Now, most logic gates are made from MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...

s (metal–oxide–semiconductor field-effect transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs contro ...

s).
With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in e ...

, and therefore, all of the algorithms and mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

that can be described with Boolean logic.
Logic circuits include such devices as multiplexer
In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The se ...

s, registers, arithmetic logic unit
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numb ...

s (ALUs), and computer memory
In computing, memory is a device or system that is used to store information for immediate use in a computer or related computer hardware and digital electronic devices. The term ''memory'' is often synonymous with the term '' primary storage ...

, all the way up through complete microprocessor
A microprocessor is a computer processor where the data processing logic and control is included on a single integrated circuit, or a small number of integrated circuits. The microprocessor contains the arithmetic, logic, and control circ ...

s, which may contain more than 100 million logic gates.
Compound logic gates AND-OR-Invert (AOI) and OR-AND-Invert (OAI) are often employed in circuit design because their construction using MOSFETs is simpler and more efficient than the sum of the individual gates.
In reversible logic, Toffoli or Fredkin gates are used.
Electronic gates

A functionally complete logic system may be composed ofrelay
A relay
Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts
An automotive-style miniature relay with the dust cover taken off
A relay is an electrically operated switch ...

s, valves
A valve is a device or natural object that regulates, directs or controls the flow of a fluid (gases, liquids, fluidized solids, or slurries) by opening, closing, or partially obstructing various passageways. Valves are technically fitting ...

(vacuum tubes), or transistor
file:MOSFET Structure.png, upright=1.4, Metal-oxide-semiconductor field-effect transistor (MOSFET), showing Metal gate, gate (G), body (B), source (S) and drain (D) terminals. The gate is separated from the body by an insulating layer (pink).
A ...

s. The simplest family of logic gates uses bipolar transistors, and is called resistor–transistor logic (RTL). Unlike simple diode logic gates (which do not have a gain element), RTL gates can be cascaded indefinitely to produce more complex logic functions. RTL gates were used in early integrated circuit
An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tin ...

s. For higher speed and better density, the resistors used in RTL were replaced by diodes resulting in diode–transistor logic
Diode–transistor logic (DTL) is a class of digital circuits that is the direct ancestor of transistor–transistor logic. It is called so because the logic gating function (e.g., AND) is performed by a diode network and the amplifying functio ...

(DTL). Transistor–transistor logic (TTL) then supplanted DTL. As integrated circuits became more complex, bipolar transistors were replaced with smaller field-effect transistor
The field-effect transistor (FET) is a type of transistor that uses an electric field to control the flow of current in a semiconductor. FETs ( JFETs or MOSFETs) are devices with three terminals: ''source'', ''gate'', and ''drain''. FETs contro ...

s (MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a type of field-effect transistor (FET), most commonly fabricated by the controlled oxidation of silicon. It has an insulated gate, the voltage of which d ...

s); see PMOS and NMOS. To reduce power consumption still further, most contemporary chip implementations of digital systems now use CMOS
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSF ...

logic. CMOS uses complementary (both n-channel and p-channel) MOSFET devices to achieve a high speed with low power dissipation.
For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 series
The 7400 series of integrated circuits (ICs) are a popular logic family of transistor–transistor logic (TTL) logic chips.
In 1964, Texas Instruments introduced the SN5400 series of logic chips, in a ceramic semiconductor package. A low-co ...

by Texas Instruments
Texas Instruments Incorporated (TI) is an American technology company headquartered in Dallas, Texas, that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globall ...

, the CMOS
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSF ...

4000 series by RCA
The RCA Corporation was a major American electronics company, which was founded as the Radio Corporation of America in 1919. It was initially a patent trust owned by General Electric (GE), Westinghouse, AT&T Corporation and United Fruit Comp ...

, and their more recent descendants. Increasingly, these fixed-function logic gates are being replaced by programmable logic devices, which allow designers to pack many mixed logic gates into a single integrated circuit. The field-programmable nature of programmable logic devices such as FPGAs has reduced the 'hard' property of hardware; it is now possible to change the logic design of a hardware system by reprogramming some of its components, thus allowing the features or function of a hardware implementation of a logic system to be changed. Other types of logic gates include, but are not limited to:
Electronic logic gates differ significantly from their relay-and-switch equivalents. They are much faster, consume much less power, and are much smaller (all by a factor of a million or more in most cases). Also, there is a fundamental structural difference. The switch circuit creates a continuous metallic path for current to flow (in either direction) between its input and its output. The semiconductor logic gate, on the other hand, acts as a high- gain voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...

amplifier
An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the ...

, which sinks a tiny current at its input and produces a low-impedance voltage at its output. It is not possible for current to flow between the output and the input of a semiconductor logic gate.
Another important advantage of standardized integrated circuit logic families, such as the 7400 and 4000 families, is that they can be cascaded. This means that the output of one gate can be wired to the inputs of one or several other gates, and so on. Systems with varying degrees of complexity can be built without great concern of the designer for the internal workings of the gates, provided the limitations of each integrated circuit are considered.
The output of one gate can only drive a finite number of inputs to other gates, a number called the ' fan-out limit'. Also, there is always a delay, called the ' propagation delay', from a change in input of a gate to the corresponding change in its output. When gates are cascaded, the total propagation delay is approximately the sum of the individual delays, an effect which can become a problem in high-speed synchronous circuits. Additional delay can be caused when many inputs are connected to an output, due to the distributed capacitance
Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized a ...

of all the inputs and wiring and the finite amount of current that each output can provide.
History and development

The binary number system was refined byGottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz . ( – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat. He is one of the most prominent figures in both the history of philosophy and the history of mat ...

(published in 1705), influenced by the ancient ''I Ching
The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Zho ...

''s binary system. Leibniz established that using the binary system combined the principles of arithmetic
Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers— addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19t ...

and logic
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

.
In an 1886 letter, Charles Sanders Peirce described how logical operations could be carried out by electrical switching circuits.Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, '' Writings of Charles S. Peirce'', v. 5, 1993, pp. 421–423. See Eventually, vacuum tube
A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.
The type known as a ...

s replaced relays for logic operations. Lee De Forest
Lee de Forest (August 26, 1873 – June 30, 1961) was an American inventor and a fundamentally important early pioneer in electronics. He invented the first electronic device for controlling current flow; the three-element "Audion" triode v ...

's modification, in 1907, of the Fleming valve can be used as a logic gate. Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein ( ; ; 26 April 1889 – 29 April 1951) was an Austrians, Austrian-British people, British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy o ...

introduced a version of the 16-row truth table as proposition 5.101 of '' Tractatus Logico-Philosophicus'' (1921). Walther Bothe, inventor of the coincidence circuit, got part of the 1954 Nobel Prize
The Nobel Prizes ( ; sv, Nobelpriset ; no, Nobelprisen ) are five separate prizes that, according to Alfred Nobel's will of 1895, are awarded to "those who, during the preceding year, have conferred the greatest benefit to humankind." Alfre ...

in physics, for the first modern electronic AND gate in 1924. Konrad Zuse
Konrad Ernst Otto Zuse (; 22 June 1910 – 18 December 1995) was a German civil engineer, pioneering computer scientist, inventor and businessman. His greatest achievement was the world's first programmable computer; the functional program- ...

designed and built electromechanical logic gates for his computer Z1 (from 1935 to 1938).
From 1934 to 1936, NEC engineer Akira Nakashima, Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory".
As a 21-year-old master's degree student at the Massachusetts Ins ...

and Viktor Shestakov introduced switching circuit theory in a series of papers showing that two-valued Boolean algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in ...

, which they discovered independently, can describe the operation of switching circuits. (3+207+1 pages10:00 min

/ref> Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digital

computer
A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations ( computation) automatically. Modern digital electronic computers can perform generic sets of operations known as programs. These p ...

s. Switching circuit theory became the foundation of digital circuit In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical ...

design, as it became widely known in the electrical engineering community during and after World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposing ...

, with theoretical rigor superseding the ''ad hoc'' methods that had prevailed previously.
Metal-oxide-semiconductor (MOS) devices in the forms of PMOS and NMOS were demonstrated by Bell Labs
Nokia Bell Labs, originally named Bell Telephone Laboratories (1925–1984),
then AT&T Bell Laboratories (1984–1996)
and Bell Labs Innovations (1996–2007),
is an American industrial research and scientific development company owned by mul ...

engineers Mohamed M. Atalla and Dawon Kahng
Dawon Kahng ( ko, 강대원; May 4, 1931 – May 13, 1992) was a Korean-American electrical engineer and inventor, known for his work in solid-state electronics. He is best known for inventing the MOSFET (metal–oxide–semiconductor field-effe ...

in 1960. Both types were later combined and adapted into complementary MOS (CMOS) logic by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor
Fairchild Semiconductor International, Inc. was an American semiconductor company based in San Jose, California. Founded in 1957 as a division of Fairchild Camera and Instrument, it became a pioneer in the manufacturing of transistors and of int ...

in 1963.
Active research is taking place in molecular logic gates.
Symbols

There are two sets of symbols for elementary logic gates in common use, both defined inANSI
The American National Standards Institute (ANSI ) is a private non-profit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organ ...

/IEEE
The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operat ...

Std 91-1984 and its supplement ANSI/IEEE Std 91a-1991. The "distinctive shape" set, based on traditional schematics, is used for simple drawings and derives from United States Military Standard
A United States defense standard, often called a military standard, "MIL-STD", "MIL-SPEC", or (informally) "MilSpecs", is used to help achieve standardization objectives by the U.S. Department of Defense.
Standardization is beneficial in achievi ...

MIL-STD-806 of the 1950s and 1960s. It is sometimes unofficially described as "military", reflecting its origin. The "rectangular shape" set, based on ANSI Y32.14 and other early industry standards as later refined by IEEE and IEC, has rectangular outlines for all types of gate and allows representation of a much wider range of devices than is possible with the traditional symbols. The IEC standard, IEC 60617-12, has been adopted by other standards, such as EN 60617-12:1999 in Europe, BS EN 60617-12:1999 in the United Kingdom, and DIN EN 60617-12:1998 in Germany.
The mutual goal of IEEE Std 91-1984 and IEC 60617-12 was to provide a uniform method of describing the complex logic functions of digital circuits with schematic symbols. These functions were more complex than simple AND and OR gates. They could be medium scale circuits such as a 4-bit counter to a large scale circuit such as a microprocessor.
IEC 617-12 and its successor IEC 60617-12 do not explicitly show the "distinctive shape" symbols, but do not prohibit them. These are, however, shown in ANSI/IEEE 91 (and 91a) with this note: "The distinctive-shape symbol is, according to IEC Publication 617, Part 12, not preferred, but is not considered to be in contradiction to that standard." IEC 60617-12 correspondingly contains the note (Section 2.1) "Although non-preferred, the use of other symbols recognized by official national standards, that is distinctive shapes in place of symbols ist of basic gates shall not be considered to be in contradiction with this standard. Usage of these other symbols in combination to form complex symbols (for example, use as embedded symbols) is discouraged." This compromise was reached between the respective IEEE and IEC working groups to permit the IEEE and IEC standards to be in mutual compliance with one another.
A third style of symbols, DIN 40700 (1976), was in use in Europe and is still widely used in European academia, see the logic table in German Wikipedia
The German Wikipedia (german: Deutschsprachige Wikipedia) is the German-language edition of Wikipedia, a free and publicly editable online encyclopedia.
Founded on March 16, 2001, it is the second-oldest Wikipedia (after the English Wikipedia), ...

.
In the 1980s, schematics were the predominant method to design both circuit boards and custom ICs known as gate array
A gate array is an approach to the design and manufacture of application-specific integrated circuits (ASICs) using a prefabricated chip with components that are later interconnected into logic devices (e.g. NAND gates, flip-flops, etc.) accordin ...

s. Today custom ICs and the field-programmable gate array
A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturinghence the term '' field-programmable''. The FPGA configuration is generally specified using a hardware de ...

are typically designed with Hardware Description Languages (HDL) such as Verilog
Verilog, standardized as IEEE 1364, is a hardware description language (HDL) used to model electronic systems. It is most commonly used in the design and verification of digital circuits at the register-transfer level of abstraction. It is als ...

or VHDL
The VHSIC Hardware Description Language (VHDL) is a hardware description language (HDL) that can model the behavior and structure of digital systems at multiple levels of abstraction, ranging from the system level down to that of logic gate ...

.
Truth tables

Output comparison of 1-input logic gates. Output comparison of 2-input logic gates.Universal logic gates

Charles Sanders Peirce (during 1880–1881) showed that NOR gates alone (or alternatively NAND gates alone) can be used to reproduce the functions of all the other logic gates, but his work on it was unpublished until 1933. The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes calledSheffer stroke
In Boolean functions and propositional calculus, the Sheffer stroke denotes a logical operation that is equivalent to the negation of the conjunction operation, expressed in ordinary language as "not both". It is also called nand ("not and") o ...

; the logical NOR is sometimes called ''Peirce's arrow''. Consequently, these gates are sometimes called ''universal logic gates''.
De Morgan equivalent symbols

By use ofDe Morgan's laws
In propositional logic and Boolean algebra, De Morgan's laws, also known as De Morgan's theorem, are a pair of transformation rules that are both valid rules of inference. They are named after Augustus De Morgan, a 19th-century British mathem ...

, an ''AND'' function is identical to an ''OR'' function with negated inputs and outputs. Likewise, an ''OR'' function is identical to an ''AND'' function with negated inputs and outputs. A NAND gate is equivalent to an OR gate with negated inputs, and a NOR gate is equivalent to an AND gate with negated inputs.
This leads to an alternative set of symbols for basic gates that use the opposite core symbol (''AND'' or ''OR'') but with the inputs and outputs negated. Use of these alternative symbols can make logic circuit diagrams much clearer and help to show accidental connection of an active high output to an active low input or vice versa. Any connection that has logic negations at both ends can be replaced by a negationless connection and a suitable change of gate or vice versa. Any connection that has a negation at one end and no negation at the other can be made easier to interpret by instead using the De Morgan equivalent symbol at either of the two ends. When negation or polarity indicators on both ends of a connection match, there is no logic negation in that path (effectively, bubbles "cancel"), making it easier to follow logic states from one symbol to the next. This is commonly seen in real logic diagrams – thus the reader must not get into the habit of associating the shapes exclusively as OR or AND shapes, but also take into account the bubbles at both inputs and outputs in order to determine the "true" logic function indicated.
A De Morgan symbol can show more clearly a gate's primary logical purpose and the polarity of its nodes that are considered in the "signaled" (active, on) state. Consider the simplified case where a two-input NAND gate is used to drive a motor when either of its inputs are brought low by a switch. The "signaled" state (motor on) occurs when either one OR the other switch is on. Unlike a regular NAND symbol, which suggests AND logic, the De Morgan version, a two negative-input OR gate, correctly shows that OR is of interest. The regular NAND symbol has a bubble at the output and none at the inputs (the opposite of the states that will turn the motor on), but the De Morgan symbol shows both inputs and output in the polarity that will drive the motor.
De Morgan's theorem is most commonly used to implement logic gates as combinations of only NAND gates, or as combinations of only NOR gates, for economic reasons.
Data storage

Logic gates can also be used to store data. A storage element can be constructed by connecting several gates in a "latch
A latch or catch (called sneck in Northern England and Scotland) is a type of mechanical fastener that joins two (or more) objects or surfaces while allowing for their regular separation. A latch typically engages another piece of hardware on t ...

" circuit. Latching circuitry is used in static random-access memory
Static random-access memory (static RAM or SRAM) is a type of random-access memory (RAM) that uses latching circuitry (flip-flop) to store each bit. SRAM is volatile memory; data is lost when power is removed.
The term ''static'' differe ...

. More complicated designs that use clock signal
In electronics and especially synchronous digital circuits, a clock signal (historically also known as ''logic beat'') oscillates between a high and a low state and is used like a metronome to coordinate actions of digital circuits.
A clock sig ...

s and that change only on a rising or falling edge of the clock are called edge-triggered "flip-flops
Flip-flops are a type of light sandal, typically worn as a form of casual footwear. They consist of a flat sole held loosely on the foot by a Y-shaped strap known as a toe thong that passes between the first and second toes and around both side ...

". Formally, a flip-flop is called a bistable circuit, because it has two stable states which it can maintain indefinitely. The combination of multiple flip-flops in parallel, to store a multiple-bit value, is known as a register. When using any of these gate setups the overall system has memory; it is then called a sequential logic
In automata theory, sequential logic is a type of logic circuit whose output depends on the present value of its input signals and on the sequence of past inputs, the input history. This is in contrast to '' combinational logic'', whose output ...

system since its output can be influenced by its previous state(s), i.e. by the ''sequence'' of input states. In contrast, the output from combinational logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This i ...

is purely a combination of its present inputs, unaffected by the previous input and output states.
These logic circuits are used in computer memory
Memory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remember ...

. They vary in performance, based on factors of speed
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quanti ...

, complexity, and reliability of storage, and many different types of designs are used based on the application.
Three-state logic gates

A three-state logic gate is a type of logic gate that can have three different outputs: high (H), low (L) and high-impedance (Z). The high-impedance state plays no role in the logic, which is strictly binary. These devices are used onbuses
A bus (contracted from omnibus, with variants multibus, motorbus, autobus, etc.) is a road vehicle that carries significantly more passengers than an average car or van. It is most commonly used in public transport, but is also in use for ch ...

of the CPU
A central processing unit (CPU), also called a central processor, main processor or just processor, is the electronic circuitry that executes instructions comprising a computer program. The CPU performs basic arithmetic, logic, controlling, an ...

to allow multiple chips to send data. A group of three-states driving a line with a suitable control circuit is basically equivalent to a multiplexer
In electronics, a multiplexer (or mux; spelled sometimes as multiplexor), also known as a data selector, is a device that selects between several analog or digital input signals and forwards the selected input to a single output line. The se ...

, which may be physically distributed over separate devices or plug-in cards.
In electronics, a high output would mean the output is sourcing current from the positive power terminal (positive voltage). A low output would mean the output is sinking current to the negative power terminal (zero voltage). High impedance would mean that the output is effectively disconnected from the circuit.
Manufacturing

Since the 1990s, most logic gates are made inCMOS
Complementary metal–oxide–semiconductor (CMOS, pronounced "sea-moss", ) is a type of metal–oxide–semiconductor field-effect transistor (MOSFET) fabrication process that uses complementary and symmetrical pairs of p-type and n-type MOSF ...

(complementary metal oxide semiconductor) technology that uses both NMOS and PMOS transistors. Often millions of logic gates are packaged in a single integrated circuit
An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tin ...

.
Non-electronic logic gates

Non-electronic implementations are varied, though few of them are used in practical applications. Many early electromechanical digital computers, such as the Harvard Mark I, were built fromrelay logic
Relay logic is a method of implementing combinational logic in electrical control circuits by using several electrical relays wired in a particular configuration.
Ladder logic
The schematic diagrams for relay logic circuits are often calle ...

gates, using electro-mechanical relay
A relay
Electromechanical relay schematic showing a control coil, four pairs of normally open and one pair of normally closed contacts
An automotive-style miniature relay with the dust cover taken off
A relay is an electrically operated switch ...

s. Logic gates can be made using pneumatic
Pneumatics (from Greek ‘wind, breath’) is a branch of engineering that makes use of gas or pressurized air.
Pneumatic systems used in industry are commonly powered by compressed air or compressed inert gases. A centrally located and ele ...

devices, such as the Sorteberg relay or mechanical logic gates, including on a molecular scale. Logic gates have been made out of DNA (see DNA nanotechnology
DNA nanotechnology is the design and manufacture of artificial nucleic acid structures for technological uses. In this field, nucleic acids are used as non-biological engineering materials for nanotechnology rather than as the carriers of geneti ...

) and used to create a computer called MAYA (see MAYA-II). Logic gates can be made from quantum mechanical
Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, qu ...

effects, see quantum logic gate. Photonic logic gates use nonlinear optical effects.
In principle any method that leads to a gate that is functionally complete (for example, either a NOR or a NAND gate) can be used to make any kind of digital logic circuit. Note that the use of 3-state logic for bus systems is not needed, and can be replaced by digital multiplexers, which can be built using only simple logic gates (such as NAND gates, NOR gates, or AND and OR gates).
Logic families

There are severallogic families
In computer engineering, a logic family is one of two related concepts:
* A logic family of monolithic digital integrated circuit devices is a group of electronic logic gates constructed using one of several different designs, usually with compati ...

with different characteristics (power consumption, speed, cost, size) such as: RDL (resistor–diode logic), RTL (resistor-transistor logic), DTL (diode–transistor logic), TTL (transistor–transistor logic) and CMOS. There are also sub-variants, e.g. standard CMOS logic vs. advanced types using still CMOS technology, but with some optimizations for avoiding loss of speed due to slower PMOS transistors.
See also

* And-inverter graph * Boolean algebra topics *Boolean function
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually , or ). Alternative names are switching function, used especially in older computer science literature, and truth function ...

* Digital circuit In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes a function. Circuits of this kind provide a generalization of Boolean circuits and a mathematical ...

* Espresso heuristic logic minimizer
The ESPRESSO logic minimizer is a computer program using heuristic and specific algorithms for efficiently reducing the complexity of digital logic gate circuits. ESPRESSO-I was originally developed at IBM by Robert K. Brayton et al. in 1982. ...

* Fan-out
* Field-programmable gate array
A field-programmable gate array (FPGA) is an integrated circuit designed to be configured by a customer or a designer after manufacturinghence the term '' field-programmable''. The FPGA configuration is generally specified using a hardware de ...

(FPGA)
* Flip-flop (electronics)
In electronics, a flip-flop or latch is a circuit that has two stable states and can be used to store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control inputs and ...

* Functional completeness
* Karnaugh map
The Karnaugh map (KM or K-map) is a method of simplifying Boolean algebra expressions. Maurice Karnaugh introduced it in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which was a rediscovery of Allan Marquand's 1881 ''logic ...

* Combinational logic
In automata theory, combinational logic (also referred to as time-independent logic or combinatorial logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only. This i ...

* List of 4000 series integrated circuits
* List of 7400 series integrated circuits
* Logic family
In computer engineering, a logic family is one of two related concepts:
* A logic family of monolithic digital integrated circuit devices is a group of electronic logic gates constructed using one of several different designs, usually with compat ...

* Logic level
* Logical graph
* NMOS logic
* Processor design
Processor design is a subfield of computer engineering and electronics engineering (fabrication) that deals with creating a processor, a key component of computer hardware.
The design process involves choosing an instruction set and a certain ex ...

* Programmable logic controller
A programmable logic controller (PLC) or programmable controller is an industrial computer that has been ruggedized and adapted for the control of manufacturing processes, such as assembly lines, machines, robotic devices, or any activity tha ...

(PLC)
* Programmable Logic Device (PLD)
* Propositional calculus
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions (which can be true or false) and relations ...

* Quantum logic gate
* Race hazard
A race condition or race hazard is the condition of an electronics, software, or other system where the system's substantive behavior is dependent on the sequence or timing of other uncontrollable events. It becomes a bug when one or more of t ...

* Reversible computing
Reversible computing is any model of computation where the computational process, to some extent, is time-reversible. In a model of computation that uses deterministic transitions from one state of the abstract machine to another, a necessary ...

* Truth table
References

Further reading

* * *External links

* {{DEFAULTSORT:Logic Gate