# Logic gate

Last updated

In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and 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). Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter.

In mathematics and logic, a (finitary) Boolean function is a function of the form ƒ : Bk → B, where B = {0, 1} is a Boolean domain and k is a non-negative integer called the arity of the function. In the case where k = 0, the "function" is essentially a constant element of B. In mathematics and digital electronics, a binary number is a number expressed in the base-2 numeral system or binary numeral system, which uses only two symbols: typically "0" (zero) and "1" (one).

## Contents

Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using vacuum tubes, electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. 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, and therefore, all of the algorithms and mathematics that can be described with Boolean logic. A diode is a two-terminal electronic component that conducts current primarily in one direction ; it has low resistance in one direction, and high resistance in the other. A diode vacuum tube or thermionic diode is a vacuum tube with two electrodes, a heated cathode and a plate, in which electrons can flow in only one direction, from cathode to plate. A semiconductor diode, the most commonly used type today, is a crystalline piece of semiconductor material with a p–n junction connected to two electrical terminals. Semiconductor diodes were the first semiconductor electronic devices. The discovery of asymmetric electrical conduction across the contact between a crystalline mineral and a metal was made by German physicist Ferdinand Braun in 1874. Today, most diodes are made of silicon, but other materials such as gallium arsenide and germanium are used. A transistor is a semiconductor device used to amplify or switch electronic signals and electrical power. It is composed of semiconductor material usually with at least three terminals for connection to an external circuit. A voltage or current applied to one pair of the transistor's terminals controls the current through another pair of terminals. Because the controlled (output) power can be higher than the controlling (input) power, a transistor can amplify a signal. Today, some transistors are packaged individually, but many more are found embedded in integrated circuits. In electronics, a vacuum tube, an electron tube, or valve or, colloquially, a tube, is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.

Logic circuits include such devices as multiplexers, registers, arithmetic logic units (ALUs), and computer memory, all the way up through complete microprocessors, which may contain more than 100 million gates. In modern practice, most gates are made from MOSFETs (metal–oxide–semiconductor field-effect transistors). In electronics, a multiplexer is a device that selects between several analog or digital input signals and forwards it to a single output line. A multiplexer of inputs has select lines, which are used to select which input line to send to the output. Multiplexers are mainly used to increase the amount of data that can be sent over the network within a certain amount of time and bandwidth. A multiplexer is also called a data selector. Multiplexers can also be used to implement Boolean functions of multiple variables.

In computer architecture, a processor register is a quickly accessible location available to a computer's central processing unit (CPU). Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only. Registers are typically addressed by mechanisms other than main memory, but may in some cases be assigned a memory address e.g. DEC PDP-10, ICT 1900. An arithmetic logic unit (ALU) is a combinational digital electronic 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 numbers. An ALU is a fundamental building block of many types of computing circuits, including the central processing unit (CPU) of computers, FPUs, and graphics processing units (GPUs). A single CPU, FPU or GPU may contain multiple ALUs.

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. AND-OR-Invert (AOI) logic and AOI gates are two-level compound logic functions constructed from the combination of one or more AND gates followed by a NOR gate. Construction of AOI cells is particularly efficient using CMOS technology where the total number of transistor gates can be compared to the same construction using NAND logic or NOR logic. The complement of AOI Logic is OR-AND-Invert (OAI) logic where the OR gates precede a NAND gate.

In reversible logic, Toffoli gates are used.

## Electronic gates

To build a functionally complete logic system, relays, valves (vacuum tubes), or transistors can be used. The simplest family of logic gates using bipolar transistors 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 circuits. 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 (MOSFETs); 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. A relay is an electrically operated switch. It consists of a set of input terminals for a single or multiple control signals, and a set of operating contact terminals. The switch may have any number of contacts in multiple contact forms, such as make contacts, break contacts, or combinations thereof.

Resistor–transistor logic (RTL) is a class of digital circuits built using resistors as the input network and bipolar junction transistors (BJTs) as switching devices. RTL is the earliest class of transistorized digital logic circuit used; other classes include diode–transistor logic (DTL) and transistor–transistor logic (TTL). RTL circuits were first constructed with discrete components, but in 1961 it became the first digital logic family to be produced as a monolithic integrated circuit. RTL integrated circuits were used in the Apollo Guidance Computer, whose design was begun in 1961 and which first flew in 1966. An integrated circuit or monolithic integrated circuit is a set of electronic circuits on one small flat piece of semiconductor material that is normally silicon. The integration of large numbers of tiny transistors into a small chip results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete electronic components. The IC's mass production capability, reliability, and building-block approach to circuit design has ensured the rapid adoption of standardized ICs in place of designs using discrete transistors. ICs are now used in virtually all electronic equipment and have revolutionized the world of electronics. Computers, mobile phones, and other digital home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs.

For small-scale logic, designers now use prefabricated logic gates from families of devices such as the TTL 7400 series 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 a large number of 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.

Transistor–transistor logic (TTL) is a logic family built from bipolar junction transistors. Its name signifies that transistors perform both the logic function and the amplifying function ; it is the same naming convention used in resistor–transistor logic (RTL) and diode–transistor logic (DTL). Texas Instruments Incorporated (TI) is an American technology company that designs and manufactures semiconductors and various integrated circuits, which it sells to electronics designers and manufacturers globally. Its headquarters are in Dallas, Texas, United States. TI is one of the top-10 semiconductor companies worldwide, based on sales volume. Texas Instruments's focus is on developing analog chips and embedded processors, which account for more than 80% of their revenue. TI also produces TI digital light processing technology and education technology products including calculators, microcontrollers and multi-core processors. To date, TI has more than 45,000 patents worldwide. Complementary metal–oxide–semiconductor (CMOS) is a type of MOSFET semiconductor device fabrication process. CMOS technology is used for constructing integrated circuits (ICs), including microprocessors, microcontrollers, memory chips, and other digital logic circuits. CMOS technology is also used for several analog circuits such as image sensors, data converters, and highly integrated transceivers for many types of communication. CMOS was invented by Chih-Tang Sah and Frank Wanlass at Fairchild Semiconductor in 1963, and was an adaptation of the PMOS and NMOS processes originally developed by MOSFET inventors Mohamed Atalla and Dawon Kahng in 1960. CMOS became the dominant MOSFET fabrication process for VLSI devices since it overtook NMOS in the 1980s.

Other types of logic gates include, but are not limited to: 

Logic familyAbbreviationDescription
Diode logic DL
Tunnel diode logicTDLExactly the same as diode logic but can perform at a higher speed.[ failed verification ]
Neon logicNLUses neon bulbs or 3 element neon trigger tubes to perform logic.
Core diode logicCDLPerformed by semiconductor diodes and small ferrite toroidal cores for moderate speed and moderate power level.
4Layer Device Logic4LDLUses thyristors and SCRs to perform logic operations where high current and or high voltages are required.
Direct-coupled transistor logic DCTLUses transistors switching between saturated and cutoff states to perform logic. The transistors require carefully controlled parameters. Economical because few other components are needed, but tends to be susceptible to noise because of the lower voltage levels employed. Often considered to be the father to modern TTL logic.
Current-mode logic CMLUses transistors to perform logic but biasing is from constant current sources to prevent saturation and allow extremely fast switching. Has high noise immunity despite fairly low logic levels.
Quantum-dot cellular automata QCAUses tunnelable q-bits for synthesizing the binary logic bits. The electrostatic repulsive force in between two electrons in the quantum dots assigns the electron configurations (that defines high-level logic state 1 or low-level logic state 0) under the suitably driven polarizations. This is a transistorless, currentless, junctionless binary logic synthesis technique allowing it to have very fast operation speeds.

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 amplifier, 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 circuits. Additional delay can be caused when a large number of 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.

## History and development

The binary number system was refined by Gottfried Wilhelm Leibniz (published in 1705), influenced by the ancient I Ching 's binary system.   Leibniz established that, by using the binary system, the principles of arithmetic and logic could be combined.

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, in 1907, of the Fleming valve can be used as a logic gate. Ludwig Wittgenstein 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 in physics, for the first modern electronic AND gate in 1924. Konrad Zuse designed and built electromechanical logic gates for his computer Z1 (from 1935–38).

From 1934 to 1936, NEC engineer Akira Nakashima introduced switching circuit theory in a series of papers showing that two-valued Boolean algebra, which he discovered independently, can describe the operation of switching circuits.     His work was later cited by Claude E. Shannon, who elaborated on the use of Boolean algebra in the analysis and design of switching circuits in 1937.  Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digital computers. 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, with theoretical rigor superseding the ad hoc methods that had prevailed previously. 

Active research is taking place in molecular logic gates.

## Symbols A synchronous 4-bit up/down decade counter symbol (74LS192) in accordance with ANSI/IEEE Std. 91-1984 and IEC Publication 60617-12.

There are two sets of symbols for elementary logic gates in common use, both defined in ANSI/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 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 [list 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 was in use in Europe and is still widely used in European academia. See the column "DIN 40700" in the table in the German Wikipedia.

In the 1980s, schematics were the predominant method to design both circuit boards and custom ICs known as gate arrays. Today custom ICs and the field-programmable gate array are typically designed with Hardware Description Languages (HDL) such as Verilog or VHDL.

TypeDistinctive shape
(IEEE Std 91/91a-1991)
Rectangular shape
(IEEE Std 91/91a-1991
IEC 60617-12 : 1997)
Boolean algebra between A & B Truth table
Negation
NOT  ${\overline {A}}$ or $\neg A$ INPUT OUTPUT A NOT A 0 1 1 0
In electronics a NOT gate is more commonly called an inverter. The circle on the symbol is called a bubble and is used in logic diagrams to indicate a logic negation between the external logic state and the internal logic state (1 to 0 or vice versa). On a circuit diagram it must be accompanied by a statement asserting that the positive logic convention or negative logic convention is being used (high voltage level = 1 or low voltage level = 1, respectively). The wedge is used in circuit diagrams to directly indicate an active-low (low voltage level = 1) input or output without requiring a uniform convention throughout the circuit diagram. This is called Direct Polarity Indication. See IEEE Std 91/91A and IEC 60617-12. Both the bubble and the wedge can be used on distinctive-shape and rectangular-shape symbols on circuit diagrams, depending on the logic convention used. On pure logic diagrams, only the bubble is meaningful.
Conjunction and Disjunction
AND  $A\cdot B$ or $A\land B$ INPUT OUTPUT A B A AND B 0 0 0 0 1 0 1 0 0 1 1 1
OR  $A+B$ or $A\lor B$ INPUT OUTPUT A B A OR B 0 0 0 0 1 1 1 0 1 1 1 1
Alternative denial and Joint denial
NAND  ${\overline {A\cdot B}}$ or $A\uparrow B$ INPUT OUTPUT A B A NAND B 0 0 1 0 1 1 1 0 1 1 1 0
NOR  ${\overline {A+B}}$ or $A\downarrow B$ INPUT OUTPUT A B A NOR B 0 0 1 0 1 0 1 0 0 1 1 0
Exclusive or and Biconditional
XOR  $A\oplus B$ or $A\veebar B$ INPUT OUTPUT A B A XOR B 0 0 0 0 1 1 1 0 1 1 1 0
The output of a two input exclusive-OR is true only when the two input values are different, and false if they are equal, regardless of the value. If there are more than two inputs, the output of the distinctive-shape symbol is undefined. The output of the rectangular-shaped symbol is true if the number of true inputs is exactly one or exactly the number following the "=" in the qualifying symbol.
XNOR  ${\overline {A\oplus B}}$ or ${A\odot B}$ INPUT OUTPUT A B A XNOR B 0 0 1 0 1 0 1 0 0 1 1 1

## Universal logic gates The 7400 chip, containing four NANDs. The two additional pins supply power (+5 V) and connect the ground.

Charles Sanders Peirce (during 1880–81) 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. 

## 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.

## Data storage

Logic gates can also be used to store data. A storage element can be constructed by connecting several gates in a "latch" circuit. 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 known as computer memory. 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.

## Three-state logic gates A tristate buffer can be thought of as a switch. If B is on, the switch is closed. If B is off, the switch is open.

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-states 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.

## Implementations

Since the 1990s, most logic gates are made in CMOS (complementary metal oxide semiconductor) technology that uses both NMOS and PMOS transistors. Often millions of logic gates are packaged in a single integrated circuit.

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.

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.  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 (though quantum computing usually diverges from boolean design; 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).

## Related Research Articles Digital electronics, digital technology or digital (electronic) circuits are electronics that operate on digital signals. In contrast, analog circuits manipulate analog signals whose performance is more subject to manufacturing tolerance, signal attenuation and noise. Digital techniques are helpful because it is a lot easier to get an electronic device to switch into one of a number of known states than to accurately reproduce a continuous range of values. N-type metal-oxide-semiconductor logic uses n-type MOSFETs to implement logic gates and other digital circuits. These nMOS transistors operate by creating an inversion layer in a p-type transistor body. This inversion layer, called the n-channel, can conduct electrons between n-type "source" and "drain" terminals. The n-channel is created by applying voltage to the third terminal, called the gate. Like other MOSFETs, nMOS transistors have four modes of operation: cut-off, triode, saturation, and velocity saturation. In digital logic, an inverter or NOT gate is a logic gate which implements logical negation. The truth table is shown on the right.

In computer engineering, a logic family may refer to 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 compatible logic levels and power supply characteristics within a family. Many logic families were produced as individual components, each containing one or a few related basic logical functions, which could be used as "building-blocks" to create systems or as so-called "glue" to interconnect more complex integrated circuits. A "logic family" may also refer to a set of techniques used to implement logic within VLSI integrated circuits such as central processors, memories, or other complex functions. Some such logic families use static techniques to minimize design complexity. Other such logic families, such as domino logic, use clocked dynamic techniques to minimize size, power consumption and delay.

The AND gate is a basic digital logic gate that implements logical conjunction - it behaves according to the truth table to the right. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If none or not all inputs to the AND gate are HIGH, a LOW output results. The function can be extended to any number of inputs.

The OR gate is a digital logic gate that implements logical disjunction – it behaves according to the truth table to the right. A HIGH output (1) results if one or both the inputs to the gate are HIGH (1). If neither input is high, a LOW output (0) results. In another sense, the function of OR effectively finds the maximum between two binary digits, just as the complementary AND function finds the minimum. In digital electronics, a NAND gate (NOT-AND) is a logic gate which produces an output which is false only if all its inputs are true; thus its output is complement to that of an AND gate. A LOW (0) output results only if all the inputs to the gate are HIGH (1); if any input is LOW (0), a HIGH (1) output results. A NAND gate is made using transistors and junction diodes. By De Morgan's theorem, a two-input NAND gate's logic may be expressed as AB=A+B, making a NAND gate equivalent to inverters followed by an OR gate. An electronic symbol is a pictogram used to represent various electrical and electronic devices or functions, such as wires, batteries, resistors, and transistors, in a schematic diagram of an electrical or electronic circuit. These symbols are largely standardized internationally today, but may vary from country to country, or engineering discipline, based on traditional conventions. XOR gate is a digital logic gate that gives a true output when the number of true inputs is odd. An XOR gate implements an exclusive or; that is, a true output results if one, and only one, of the inputs to the gate is true. If both inputs are false (0/LOW) or both are true, a false output results. XOR represents the inequality function, i.e., the output is true if the inputs are not alike otherwise the output is false. A way to remember XOR is "one or the other but not both".

The XNOR gate is a digital logic gate whose function is the logical complement of the exclusive OR (XOR) gate. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same. If one but not both inputs are high (1), a low output (0) results.

The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator. It can also be seen as an AND gate with all the inputs inverted. NOR is a functionally complete operation—NOR gates can be combined to generate any other logical function. It shares this property with the NAND gate. By contrast, the OR operator is monotonic as it can only change LOW to HIGH but not vice versa. Diode logic (DL), or diode-resistor logic (DRL), is the construction of Boolean logic gates from diodes. Diode logic was used extensively in the construction of early computers, where semiconductor diodes could replace bulky and costly active vacuum tube elements. The most common use for diode logic is in diode–transistor logic (DTL) integrated circuits that, in addition to diodes, include inverter logic for power gain and signal restoration.

The floating-gate MOSFET (FGMOS) is a type of MOSFET where the gate is electrically isolated, creating a floating node in DC, and a number of secondary gates or inputs are deposited above the floating gate (FG) and are electrically isolated from it. These inputs are only capacitively connected to the FG. Since the FG is completely surrounded by highly resistive material, the charge contained in it remains unchanged for long periods of time. Usually Fowler-Nordheim tunneling and hot-carrier injection mechanisms are used to modify the amount of charge stored in the FG. A solid-state relay (SSR) is an electronic switching device that switches on or off when a small external voltage is applied across its control terminals. SSRs consist of a sensor which responds to an appropriate input, a solid-state electronic switching device which switches power to the load circuitry, and a coupling mechanism to enable the control signal to activate this switch without mechanical parts. The relay may be designed to switch either AC or DC to the load. It serves the same function as an electromechanical relay, but has no moving parts. P-type metal-oxide-semiconductor logic uses p-channel metal-oxide-semiconductor field effect transistors (MOSFETs) to implement logic gates and other digital circuits. PMOS transistors operate by creating an inversion layer in an n-type transistor body. This inversion layer, called the p-channel, can conduct holes between p-type "source" and "drain" terminals.

The memory cell is the fundamental building block of computer memory. The memory cell is an electronic circuit that stores one bit of binary information and it must be set to store a logic 1 and reset to store a logic 0. Its value is maintained/stored until it is changed by the set/reset process. The value in the memory cell can be accessed by reading it.

1. Jaeger, Microelectronic Circuit Design, McGraw-Hill 1997, ISBN   0-07-032482-4, pp. 226–233
2. Tinder, Richard F. (2000). Engineering digital design: Revised Second Edition. pp. 317–319. ISBN   0-12-691295-5 . Retrieved 2008-07-04.
3. Rowe, Jim. "Circuit Logic – Why and How" (December 1966). Electronics Australia.
4. Nylan, Michael (2001). The Five "Confucian" Classics. Yale University Press. pp. 204–206. ISBN   978-0-300-08185-5 . Retrieved 8 June 2010.
5. Perkins, Franklin. Leibniz and China: A Commerce of Light. Cambridge: Cambridge University Press, 2004. p 117. Print.
6. Peirce, C. S., "Letter, Peirce to A. Marquand", dated 1886, Writings of Charles S. Peirce , v. 5, 1993, pp. 421–23. See Burks, Arthur W., "Review: Charles S. Peirce, The new elements of mathematics", Bulletin of the American Mathematical Society v. 84, n. 5 (1978), pp. 913–18, see 917. PDF Eprint.
7. History of Research on Switching Theory in Japan, IEEJ Transactions on Fundamentals and Materials, Vol. 124 (2004) No. 8, pp. 720–726, Institute of Electrical Engineers of Japan
8. Radomir S. Stanković (University of Niš), Jaakko T. Astola (Tampere University of Technology), Mark G. Karpovsky (Boston University), Some Historical Remarks on Switching Theory, 2007, DOI 10.1.1.66.1248
9. Radomir S. Stanković, Jaakko Astola (2008), Reprints from the Early Days of Information Sciences: TICSP Series On the Contributions of Akira Nakashima to Switching Theory, TICSP Series #40, Tampere International Center for Signal Processing, Tampere University of Technology
10. Overview of IEEE Standard 91-1984 Explanation of Logic Symbols , Doc. No. SDYZ001A, Texas Instruments Semiconductor Group, 1996
11. Peirce, C. S. (manuscript winter of 1880–81), "A Boolian Algebra with One Constant", published 1933 in Collected Papers v. 4, paragraphs 12–20. Reprinted 1989 in Writings of Charles S. Peirce v. 4, pp. 218–21, Google . See Roberts, Don D. (2009), The Existential Graphs of Charles S. Peirce, p. 131.
12. Hans Kleine Büning; Theodor Lettmann (1999). Propositional logic: deduction and algorithms. Cambridge University Press. p. 2. ISBN   978-0-521-63017-7.
13. John Bird (2007). Engineering mathematics. Newnes. p. 532. ISBN   978-0-7506-8555-9.
14. DNA Logic gates Archived 2010-06-18 at the Wayback Machine