Member Login:

# Logic Gates: The NAND Gate

Document Reference: TN201009004 - Rev: 4.14 - Last Update: 14-11-2020 03:46 GMT - Downloaded: 22-Jun-2024 15:47 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 ShapeRectangular ShapeDIN 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

This website uses cookies to give you the best experience on our website, to personalise content and to analyse our website traffic. Some cookies may have been set already. To find out more about our use of cookies you can visit our Privacy Statement. By browsing this website, you agree to our use of cookies.

Hide this message