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Logic Gates: The NAND Gate

Document Reference: TN201009004 - Rev: 4.14 - Last Update: 14-11-2020 03:46 GMT - Downloaded: 26-Nov-2020 00:20 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)
Distinctive Symbol of an NAND logic-gate.Rectangle Symbol of an NAND logic-gate.DIN40700 Symbol of an NAND logic-gate.

NAND Gate Truth Tables

Truth Table for NAND Gate with 2 Inputs

ABX
001
011
101
110

Truth Table for NAND Gate with 3 Inputs

ABCX
0001
0011
0101
0111
1001
1011
1101
1110

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 = AB     or     X = A | B

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

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