Document Reference: TN201009004 - Rev: 4.14 - Last Update: 14-11-2020 03:46 GMT - Downloaded: 07-Jun-2023 07:56 GMT
A NAND gate is a logic gate with two or more inputs and one output. All input states must be high to produce a low output.
NAND Gate Symbols
The inputs (A, B) of an NAND gate are on the left, and the output (X) is on the right of the logic NAND gate symbol.
| Distinctive Shape | Rectangular Shape | DIN Shape (Historic) |
|---|---|---|
 |  |  |
NAND Gate Truth Tables
Truth Table for NAND Gate with 2 Inputs
A | B | X |
|---|---|---|
0 | 0 | 1 |
0 | 1 | 1 |
1 | 0 | 1 |
1 | 1 | 0 |
Truth Table for NAND Gate with 3 Inputs
A | B | C | X |
|---|---|---|---|
0 | 0 | 0 | 1 |
0 | 0 | 1 | 1 |
0 | 1 | 0 | 1 |
0 | 1 | 1 | 1 |
1 | 0 | 0 | 1 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 |
1 | 1 | 1 | 0 |
NAND Gate Test-It
To test the gate, click the switch symbols in the image below.
NAND Gate Logical Expressions
Word Equation
X = NOT (A AND B)
Boolean Algebra
In boolean algebra the multiplication sign (⋅) combined with the overbar sign ( ) stands for the NAND operation, e.g.:
X = A ⋅ B or simplified: X = AB
Alternative notations: X = A ∧ B or X = A ∧ B or X = A ↑ B or X = A | B
A | B | X = AB |
|---|---|---|
0 | 0 | X = 0 ⋅ 0 = 0 = 1 |
0 | 1 | X = 0 ⋅ 1 = 0 = 1 |
1 | 0 | X = 1 ⋅ 0 = 0 = 1 |
1 | 1 | X = 1 ⋅ 1 = 1 = 0 |
A | B | C | X = ABC |
|---|---|---|---|
0 | 0 | 0 | X = 0 ⋅ 0 ⋅ 0 = 0 = 1 |
0 | 0 | 1 | X = 0 ⋅ 0 ⋅ 1 = 0 = 1 |
0 | 1 | 0 | X = 0 ⋅ 1 ⋅ 0 = 0 = 1 |
0 | 1 | 1 | X = 0 ⋅ 1 ⋅ 1 = 0 = 1 |
1 | 0 | 0 | X = 1 ⋅ 0 ⋅ 0 = 0 = 1 |
1 | 0 | 1 | X = 1 ⋅ 0 ⋅ 1 = 0 = 1 |
1 | 1 | 0 | X = 1 ⋅ 1 ⋅ 0 = 0 = 1 |
1 | 1 | 1 | X = 1 ⋅ 1 ⋅ 1 = 1 = 0 |