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The AND gate is a basic digital
logic gate A logic gate is an idealized or physical device implementing a Boolean 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 ga ...
that implements
logical conjunction In logic, mathematics and linguistics, And (\wedge) is the truth-functional operator of logical conjunction; the ''and'' of a set of operands is true if and only if ''all'' of its operands are true. The logical connective that represents thi ...
(∧) from
mathematical logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
AND gate behaves according to the
truth table A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra (logic), Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expression (mathematics) ...
. 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.


Symbols

There are three symbols for AND gates: the American (
ANSI 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 ...
or 'military') symbol and the IEC ('European' or 'rectangular') symbol, as well as the deprecated
DIN DIN or Din or din may refer to: People and language * Din (name), people with the name * Dīn, an Arabic word with three general senses: judgment, custom, and religion from which the name originates * Dinka language (ISO 639 code: din), spoken by ...
symbol. Additional inputs can be added as needed. For more information see Logic gate symbols article. It can also be denoted as symbol "^" or "&". The AND gate with inputs ''A'' and ''B'' and output ''C'' implements the logical expression C = A \cdot B. This expression also may be denoted as C=A \wedge B or C=A \And B.


Implementations

An AND gate can be designed using only N-channel (pictured) or P-channel
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, 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

f(a,b)=a*b is the analytical representation of AND gate: * f(0,0)=0*0=0 * f(0,1)=0*1=0 * f(1,0)=1*0=0 * f(1,1)=1*1=1


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" Mano, M. Morris and Charles R. Kime. ''Logic and Computer Design Fundamentals, Third Edition.'' Prentice-Hall, 2004. p. 73. meaning that they can be used to make all the others.


See also

*
OR gate The OR gate is a digital logic gate that implements logical disjunction. The OR gate returns true if either or both of its inputs are true; otherwise it returns false. The input and output states are normally represented by different voltage lev ...
* NOT 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 th ...
*
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 ...
* XOR gate * XNOR gate * IMPLY gate *
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 ...
*
Logic gate A logic gate is an idealized or physical device implementing a Boolean 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 ga ...


References

{{Logical connectives Logic gates