And Gate
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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 gate, ...
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 this ...
(∧) from
mathematical logic Mathematical logic is the study of logic, 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 for ...
AND gate behaves according to the
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 argumen ...
. 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 organi ...
or 'military') symbol and the
IEC The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
('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 "&". 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 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 MOSFE ...
). 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 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 tiny ...
s in several different
logic 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 ...
.


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 le ...
* 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 the ...
*
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 XOR gate (sometimes EOR, or EXOR and pronounced as Exclusive OR) is a digital logic gate that gives a true (1 or HIGH) output when the number of true inputs is odd. An XOR gate implements an exclusive or (\nleftrightarrow) from mathematical log ...
*
XNOR gate The XNOR gate (sometimes XORN'T, ENOR, EXNOR or NXOR and pronounced as Exclusive NOR. Alternatively XAND, pronounced Exclusive AND) is a digital logic gate whose function is the logical complement of the Exclusive OR ( XOR) gate. It is equival ...
*
IMPLY gate The IMPLY gate is a digital logic gate that implements a logical conditional pictured with a right-facing arrow (\rightarrow). F=A'+B ( Implication) Logic_gate_symbols. The_List_of_logic_symbols.html" ;"title="Logic_gate#Symbols.html" ;" ...
*
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 e ...
*
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 gate, ...


References

{{Logical connectives Logic gates