AND gate

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.

AND gate truth table
Input		Output
A	B	A AND B
0	0	0
0	1	0
1	0	0
1	1	1

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 "&".


MIL/ANSI symbol	IEC symbol	DIN symbol

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

AND gate using diodes
AND gate using transistors
NMOS AND gate

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

$f(a,b)=a*b$ 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" [1] meaning that they can be used to make all the others.

Desired gate	NAND construction	NOR construction

References

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

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[1] Mano, M. Morris and Charles R. Kime. Logic and Computer Design Fundamentals, Third Edition. Prentice-Hall, 2004. p. 73.

Common logical connectives
Tautology/True $\top$
Alternative denial (NAND gate) $\uparrow$ Converse implication $\leftarrow$ Implication (IMPLY gate) $\rightarrow$ Disjunction (OR gate) $\lor$
Negation (NOT gate) $\neg$ Exclusive or (XOR gate) $\not \leftrightarrow$ Biconditional (XNOR gate) $\leftrightarrow$ Statement (Digital buffer)
Joint denial (NOR gate) $\downarrow$ Nonimplication (NIMPLY gate) $\nrightarrow$ Converse nonimplication $\nleftarrow$ Conjunction (AND gate) $\land$
Contradiction/False $\bot$
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