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Logic Gates: The NOR Gate

Document Reference: TN201009005 - Rev: 4.14 - Last Update: 14-11-2020 03:50 GMT - Downloaded: 26-Nov-2020 00:32 GMT

A NOR gate is a logic gate with two or more inputs and one output. All inputs states must be low to produce a high output.

NOR Gate Symbols

The inputs (A, B) of an NOR gate are on the left, and the output (X) is on the right of the logic NOR gate symbol.

Distinctive ShapeRectangular ShapeDIN Shape (Historic)
Distinctive Symbol of an NOR logic-gate.Rectangle Symbol of an NOR logic-gate.DIN40700 Symbol of an NOR logic-gate.

NOR Gate Truth Tables

Truth Table for NOR Gate with 2 Inputs

ABX
001
010
100
110

Truth Table for NOR Gate with 3 Inputs

ABCX
0001
0010
0100
0110
1000
1010
1100
1110

NOR Gate Test-It

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

...

NOR Gate Logical Expressions

Word Equation

X = NOT (A OR B)

Boolean Algebra

In boolean algebra the plus sign (+) combined with the overbar sign ( ) stands for the NOR operation, e.g.:

X = A + B

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

ABX = A + B
00X = 0 + 0 = 0 = 1
01X = 0 + 1 = 1 = 0
10X = 1 + 0 = 1 = 0
11X = 1 + 1 = 1 = 0
ABCX = A + B + C
000X = 0 + 0 + 0 = 0 = 1
001X = 0 + 0 + 1 = 1 = 0
010X = 0 + 1 + 0 = 1 = 0
011X = 0 + 1 + 1 = 1 = 0
100X = 1 + 0 + 0 = 1 = 0
101X = 1 + 0 + 1 = 1 = 0
110X = 1 + 1 + 0 = 1 = 0
111X = 1 + 1 + 1 = 1 = 0

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