Logic gate
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A logic gate is a device that performs a Boolean function, a
logical operation In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a logical constant. Connectives can be used to connect logical formulas. For instance in the syntax of propositional logic, th ...
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). The primary way of building logic gates uses
diode A diode is a two-Terminal (electronics), terminal electronic component that conducts electric current primarily in One-way traffic, one direction (asymmetric electrical conductance, conductance). It has low (ideally zero) Electrical resistance ...
s or
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s acting as electronic switches. Today, most logic gates are made from
MOSFET upright=1.3, Two power MOSFETs in amperes">A in the ''on'' state, dissipating up to about 100 watt">W and controlling a load of over 2000 W. A matchstick is pictured for scale. In electronics, the metal–oxide–semiconductor field- ...
s (metal–oxide–semiconductor field-effect transistors). ''From
Integrated circuit An integrated circuit (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
''
They can also be constructed using
vacuum tube A vacuum tube, electron tube, thermionic 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 voltage, potential difference has been applied. It ...
s, electromagnetic relays with relay logic, 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 optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...
,
molecules A molecule is a group of two or more atoms that are held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemistry ...
, acoustics, or even mechanical or thermal elements. 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 variable (mathematics), variables are the truth values ''true'' and ''false'', usually denot ...
, and therefore, all of the algorithms and
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
that can be described with Boolean logic. Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and
computer memory Computer memory stores information, such as data and programs, for immediate use in the computer. The term ''memory'' is often synonymous with the terms ''RAM,'' ''main memory,'' or ''primary storage.'' Archaic synonyms for main memory include ...
, all the way up through complete
microprocessor A microprocessor is a computer processor (computing), processor for which the data processing logic and control is included on a single integrated circuit (IC), or a small number of ICs. The microprocessor contains the arithmetic, logic, a ...
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.


History and development

The binary number system was refined by
Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...
(published in 1705), influenced by the ancient '' I Ching''s binary system. Leibniz established that using the binary system combined the principles of arithmetic and
logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...
. The analytical engine devised by Charles Babbage in 1837 used mechanical logic gates based on gears. In an 1886 letter,
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...
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. 420–423. See Early Electromechanical computers were constructed from switches and relay logic rather than the later innovations of
vacuum tube A vacuum tube, electron tube, thermionic 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 voltage, potential difference has been applied. It ...
s (thermionic valves) or
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s (from which later electronic computers were constructed). Ludwig Wittgenstein introduced a version of the 16-row
truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arg ...
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 ( ; ; ) are awards administered by the Nobel Foundation and granted in accordance with the principle of "for the greatest benefit to humankind". The prizes were first awarded in 1901, marking the fifth anniversary of Alfred N ...
in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935 to 1938). From 1934 to 1936, NEC engineer Akira Nakashima, Claude Shannon and Victor Shestakov introduced switching circuit theory in a series of papers showing that two-valued Boolean algebra, which they discovered independently, can describe the operation of switching circuits. (3+207+1 pages
10:00 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 Computer programming, programmed to automatically Execution (computing), carry out sequences of arithmetic or logical operations (''computation''). Modern digital electronic computers can perform generic set ...
s. Switching circuit theory became the foundation of digital circuit 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 (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, with theoretical rigor superseding the ''ad hoc'' methods that had prevailed previously. In 1948, Bardeen and Brattain patented an insulated-gate transistor (IGFET) with an inversion layer. Their concept forms the basis of CMOS technology today. In 1957 Frosch and Derick were able to manufacture PMOS and NMOS planar gates. Later a team at Bell Labs demonstrated a working MOS with PMOS and NMOS gates. Both types were later combined and adapted into complementary MOS (CMOS) logic by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963.


Symbols

There are two sets of symbols for elementary logic gates in common use, both defined in
ANSI The American National Standards Institute (ANSI ) is a private nonprofit organization that oversees the development of voluntary consensus standards for products, services, processes, systems, and personnel in the United States. The organiz ...
/
IEEE The Institute of Electrical and Electronics Engineers (IEEE) is an American 501(c)(3) organization, 501(c)(3) public charity professional organization for electrical engineering, electronics engineering, and other related disciplines. The IEEE ...
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 United States Department of Defense. Standardization is beneficial ...
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 617-12 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 renumbered successor IEC 60617-12 do not explicitly show the "distinctive shape" symbols, but do not prohibit them. These are, however, shown in ANSI/IEEE Std 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. 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 semiconductor device fabrication, prefabricated chip with components that are later interconnected into logic devices (e.g. NAN ...
s. Today custom ICs and the field-programmable gate array 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, with the highest level of abstraction being at the re ...
or
VHDL VHDL (Very High Speed Integrated Circuit Program, VHSIC Hardware Description Language) is a hardware description language that can model the behavior and structure of Digital electronics, digital systems at multiple levels of abstraction, ran ...
.


De Morgan equivalent symbols

By use of De Morgan's laws, 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.


Truth tables

Output comparison of various logic gates:


Universal logic gates

Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American scientist, mathematician, logician, and philosopher who is sometimes known as "the father of pragmatism". According to philosopher Paul Weiss (philosopher), Paul ...
(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 called '' Sheffer stroke''; the logical NOR is sometimes called '' Peirce's arrow''. Consequently, these gates are sometimes called ''universal logic gates''.


Data storage and sequential logic

Logic gates can also be used to hold a state, allowing data storage. A storage element can be constructed by connecting several gates in a " latch" circuit. Latching circuitry is used in static random-access memory. More complicated designs that use clock signals and that change only on a rising or falling edge of the clock are called edge-triggered " flip-flops". 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 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 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 remembe ...
. They vary in performance, based on factors of speed, complexity, and reliability of storage, and many different types of designs are used based on the application.


Manufacturing


Electronic gates

A functionally complete logic system may be composed of relays, valves (vacuum tubes), or
transistor A transistor is a semiconductor device used to Electronic amplifier, amplify or electronic switch, switch electrical signals and electric power, power. It is one of the basic building blocks of modern electronics. It is composed of semicondu ...
s. 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 (electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points. In a Electrostatics, static electric field, it corresponds to the Work (electrical), ...
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 is a two-port electronic circuit that uses electric power from a power su ...
, 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. For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL
7400 series The 7400 series is a popular logic family of transistor–transistor logic (TTL) integrated circuits (ICs). In 1964, Texas Instruments introduced the SN5400 series of logic chips, in a ceramic semiconductor package. A low-cost plastic package ...
by Texas Instruments, the CMOS 4000 series by RCA, 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. An 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 of all the inputs and wiring and the finite amount of current that each output can provide.


Logic families

There are several logic families 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. 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 (IC), also known as a microchip or simply chip, is a set of electronic circuits, consisting of various electronic components (such as transistors, resistors, and capacitors) and their interconnections. These components a ...
s. For higher speed and better density, the resistors used in RTL were replaced by diodes resulting in diode–transistor logic (DTL). Transistor–transistor logic (TTL) then supplanted DTL. As integrated circuits became more complex, bipolar transistors were replaced with smaller field-effect transistors (
MOSFET upright=1.3, Two power MOSFETs in amperes">A in the ''on'' state, dissipating up to about 100 watt">W and controlling a load of over 2000 W. A matchstick is pictured for scale. In electronics, the metal–oxide–semiconductor field- ...
s); see PMOS and NMOS. To reduce power consumption still further, most contemporary chip implementations of digital systems now use CMOS logic. CMOS uses complementary (both n-channel and p-channel) MOSFET devices to achieve a high speed with low power dissipation. Other types of logic gates include, but are not limited to:


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 on buses of the CPU to allow multiple chips to send data. A group of three-state outputs driving a line with a suitable control circuit is basically equivalent to a multiplexer, 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.


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 from relay logic gates, using electro-mechanical relays. Logic gates can be made using pneumatic devices, such as the Sorteberg relay or mechanical logic gates, including on a molecular scale. Various types of fundamental logic gates have been constructed using molecules ( molecular logic gates), which are based on chemical inputs and spectroscopic outputs. Logic gates have been made out of DNA (see DNA nanotechnology) and used to create a computer called MAYA (see MAYA-II). Logic gates can be made from quantum mechanical 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).


See also

* And-inverter graph * Boolean algebra topics * Boolean function * Depletion-load NMOS logic * Digital circuit * Electronic symbol * Espresso heuristic logic minimizer * Emitter-coupled logic * Fan-out * Field-programmable gate array (FPGA) *
Flip-flop (electronics) In electronics, flip-flops and latches are electronic circuit, circuits that have two stable states that can store state information – a bistable multivibrator. The circuit can be made to change state by signals applied to one or more control ...
*
Functional completeness In Mathematical logic, logic, a functionally complete set of logical connectives or Boolean function, Boolean operators is one that can be used to express all possible truth tables by combining members of the Set (mathematics), set into a Boolean ...
* Integrated injection logic *
Karnaugh map A Karnaugh map (KM or K-map) is a diagram that can be used to simplify a Boolean algebra expression. Maurice Karnaugh introduced the technique in 1953 as a refinement of Edward W. Veitch's 1952 Veitch chart, which itself was a rediscovery of ...
* Combinational logic * List of 4000 series integrated circuits * List of 7400 series integrated circuits * Logic family * Logic level * Logical graph * Magnetic logic *
NMOS logic NMOS or nMOS logic (from N-type metal–oxide–semiconductor) uses n-type (-) MOSFETs (metal–oxide–semiconductor field-effect transistors) to implement logic gates and other digital circuits. NMOS transistors operate by creating an inv ...
* Parametron * Processor design * Programmable logic controller (PLC) * Programmable logic device (PLD) * Propositional calculus * Race hazard *
Reversible computing Reversible computing is any model of computation where every step of the process is time-reversible. This means that, given the output of a computation, it's possible to perfectly reconstruct the input. In systems that progress deterministica ...
* Superconducting computing *
Truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arg ...
* Unconventional computing


References


Further reading

* *


External links

* {{DEFAULTSORT:Logic Gate Charles Sanders Peirce