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AND gate

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Input Output
A B A AND B
0 0 0
0 1 0
1 0 0
1 1 1

The AND gate is a basic digital logic gate that implements logical conjunction (∧) from mathematical logic – AND gate behaves according to the truth table. A HIGH output (1) results only if all the inputs to the AND gate are HIGH (1). If not all inputs to the AND gate are HIGH, LOW output results. The function can be extended to any number of inputs.

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Symbols

There are three symbols for AND gates: the American (ANSI or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated DIN symbol. Additional inputs can be added as needed. For more information see Logic gate symbols article. It can also be denoted as symbol "^" or "&".

AND ANSI.svg AND IEC.svg AND DIN.svg
MIL/ANSI symbol IEC symbol DIN symbol

The AND gate with inputs A and B and output C implements the logical expression . This expression also may be denoted as or .

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American National Standards Institute

American National Standards Institute

The American National Standards Institute 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 organization also coordinates U.S. standards with international standards so that American products can be used worldwide.

International Electrotechnical Commission

International Electrotechnical Commission

The International Electrotechnical Commission is an international standards organization that prepares and publishes international standards for all electrical, electronic and related technologies – collectively known as "electrotechnology". IEC standards cover a vast range of technologies from power generation, transmission and distribution to home appliances and office equipment, semiconductors, fibre optics, batteries, solar energy, nanotechnology and marine energy as well as many others. The IEC also manages four global conformity assessment systems that certify whether equipment, system or components conform to its international standards.

Deutsches Institut für Normung

Deutsches Institut für Normung

Deutsches Institut für Normung e.V. is the German national organization for standardization and is the German ISO member body. DIN is a German Registered Association (e.V.) headquartered in Berlin. There are currently around thirty thousand DIN Standards, covering nearly every field of technology.

Implementations

An AND gate can be designed using only N-channel (pictured) or P-channel MOSFETs, but is usually implemented with both (CMOS). The digital inputs a and b cause the output F to have the same result as the AND function. AND gates may be made from discrete components and are readily available as integrated circuits in several different logic families.

Analytical representation

is the analytical representation of AND gate:

Alternatives

If no specific AND gates are available, one can be made from NAND or NOR gates, because NAND and NOR gates are "universal gates" [1] meaning that they can be used to make all the others.

Desired gate NAND construction NOR construction
AND ANSI Labelled.svg AND from NAND.svg AND from NOR.svg

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Diode

Diode

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.

Transistor

Transistor

A transistor is a semiconductor device used to amplify or switch electrical signals and power. The transistor is one of the basic building blocks of modern electronics. It is composed of semiconductor material, usually with at least three terminals for connection to an electronic 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. Some transistors are packaged individually, but many more in miniature form are found embedded in integrated circuits.

NMOS logic

NMOS logic

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.

MOSFET

MOSFET

The metal–oxide–semiconductor field-effect transistor 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 determines the conductivity of the device. This ability to change conductivity with the amount of applied voltage can be used for amplifying or switching electronic signals. A metal-insulator-semiconductor field-effect transistor (MISFET) is a term almost synonymous with MOSFET. Another synonym is IGFET for insulated-gate field-effect transistor.

CMOS

CMOS

Complementary metal–oxide–semiconductor 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 MOSFETs for logic functions. CMOS technology is used for constructing integrated circuit (IC) chips, including microprocessors, microcontrollers, memory chips, and other digital logic circuits. CMOS technology is also used for analog circuits such as image sensors, data converters, RF circuits, and highly integrated transceivers for many types of communication.

Integrated circuit

Integrated circuit

An integrated circuit or monolithic integrated circuit is a set of electronic circuits on one small flat piece of semiconductor material, usually silicon. Large numbers of miniaturized transistors and other electronic components are integrated together on the chip. This results in circuits that are orders of magnitude smaller, faster, and less expensive than those constructed of discrete components. The IC's mass production capability, reliability, and building-block approach to integrated 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 home appliances are now inextricable parts of the structure of modern societies, made possible by the small size and low cost of ICs such as modern computer processors and microcontrollers.

Logic family

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 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 be 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.

NAND logic

NAND logic

The NAND Boolean function has the property of functional completeness. This means that any Boolean expression can be re-expressed by an equivalent expression utilizing only NAND operations. For example, the function NOT(x) may be equivalently expressed as NAND(x,x). In the field of digital electronic circuits, this implies that it is possible to implement any Boolean function using just NAND gates.

NOR logic

NOR logic

A NOR gate or a NOT OR gate is a logic gate which gives a positive output only when both inputs are negative.

NAND gate

NAND gate

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 laws, a two-input NAND gate's logic may be expressed as A • B=A+B, making a NAND gate equivalent to inverters followed by an OR gate.

NOR gate

NOR gate

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 in some senses be seen as the inverse of an AND gate. 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.

Source: "AND gate", Wikipedia, Wikimedia Foundation, (2023, January 26th), https://en.wikipedia.org/wiki/AND_gate.

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See also
References
  1. ^ Mano, M. Morris and Charles R. Kime. Logic and Computer Design Fundamentals, Third Edition. Prentice-Hall, 2004. p. 73.

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