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Logical Gates: The AND Gate

Document Reference: TN201009002 - Rev: 4.14 - Last Update: 14-11-2020 03:18 GMT - Downloaded: 26-Nov-2020 01:31 GMT

A AND gate is a logic gate with two or more inputs and one output. All input states must be high to produce a high output.

AND Gate Symbols

The inputs (A, B) of an AND gate are on the left, and the output (X) is on the right of the logic AND gate symbol.

Distinctive ShapeRectangular ShapeDIN Shape (Historic)
Distinctive Symbol of an AND logic-gate.Rectangle Symbol of an AND logic-gate.DIN40700 Symbol of an AND logic-gate.

AND Gate Truth Tables

Truth Table for AND Gate with 2 Inputs

ABX
000
010
100
111

Truth Table for AND Gate with 3 Inputs

ABCX
0000
0010
0100
0110
1000
1010
1100
1111

AND Gate Test-It

To test the gate, click the switch symbols in the image below.

...

AND Gate Logical Expressions

Word Equation

X = A AND B

Boolean Algebra

In boolean algebra the multiplication sign () stands for the AND operation, e.g.:

X = AB     or simplified:     X = AB

Alternative notations:     X = AB     or     X = A & B

ABX = AB
00X = 0 ⋅ 0 = 0
01X = 0 ⋅ 1 = 0
10X = 1 ⋅ 0 = 0
11X = 1 ⋅ 1 = 1
ABCX = ABC
000X = 0 ⋅ 0 ⋅ 0 = 0
001X = 0 ⋅ 0 ⋅ 1 = 0
010X = 0 ⋅ 1 ⋅ 0 = 0
011X = 0 ⋅ 1 ⋅ 1 = 0
100X = 1 ⋅ 0 ⋅ 0 = 0
101X = 1 ⋅ 0 ⋅ 1 = 0
110X = 1 ⋅ 1 ⋅ 0 = 0
111X = 1 ⋅ 1 ⋅ 1 = 1

AND Gate Circuit with Two Relays

AND logic-gate circuit with two relays.

By default, and without a signal on Input A and Input B, the Output X will be pulled to LOW (0) via R1.

A 12VDC (1/HIGH) signal on terminal Input A will light LEDA and energize RelayA. Energizing RelayA will allow 12VDC to pass via switched contact A from the terminal 12VDC IN to switched contact B.

A 12VDC (1/HIGH) signal on terminal Input B will light LEDB and energize RelayB. Energizing RelayB will allow 12VDC to pass via switched contact B and via DX from the switched contact A to the terminal Output X.

LEDX will light and Output X will be HIGH as soon as 12VDC is allowed to pass via switched contacts A and B.

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