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 Shape | Rectangular Shape | DIN Shape (Historic) |
---|---|---|
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AND Gate Truth Tables
Truth Table for AND Gate with 2 Inputs
A | B | X |
---|---|---|
0 | 0 | 0 |
0 | 1 | 0 |
1 | 0 | 0 |
1 | 1 | 1 |
Truth Table for AND Gate with 3 Inputs
A | B | C | X |
---|---|---|---|
0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 |
1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 |
1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 |
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 = A ⋅ B
or simplified: X = AB
Alternative notations: X = A ∧ B
or X = A & B
A | B | X = AB |
---|---|---|
0 | 0 | X = 0 ⋅ 0 = 0 |
0 | 1 | X = 0 ⋅ 1 = 0 |
1 | 0 | X = 1 ⋅ 0 = 0 |
1 | 1 | X = 1 ⋅ 1 = 1 |
A | B | C | X = ABC |
---|---|---|---|
0 | 0 | 0 | X = 0 ⋅ 0 ⋅ 0 = 0 |
0 | 0 | 1 | X = 0 ⋅ 0 ⋅ 1 = 0 |
0 | 1 | 0 | X = 0 ⋅ 1 ⋅ 0 = 0 |
0 | 1 | 1 | X = 0 ⋅ 1 ⋅ 1 = 0 |
1 | 0 | 0 | X = 1 ⋅ 0 ⋅ 0 = 0 |
1 | 0 | 1 | X = 1 ⋅ 0 ⋅ 1 = 0 |
1 | 1 | 0 | X = 1 ⋅ 1 ⋅ 0 = 0 |
1 | 1 | 1 | X = 1 ⋅ 1 ⋅ 1 = 1 |
AND 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
.