Name 
Symbols and Equations 
Truth Table 
Description 
AND 


A 
B 
X 
All inputs must be present for output. 
1 
1 
1 
1 
0 
0 
0 
1 
0 
0 
0 
0 
OR 


A 
B 
X 
Any input must be present for output. 
1 
1 
1 
1 
0 
1 
0 
1 
1 
0 
0 
0 
NOT (inverter) 


A 
X 

Negates (inverts) input or output. 
1 
0 

0 
1 

NAND 


A 
B 
X 
All inputs must be absent for output. 
1 
1 
0 
1 
0 
1 
0 
1 
1 
0 
0 
1 
NOR 


A 
B 
X 
Any input must be absent for output. 
1 
1 
0 
1 
0 
1 
0 
1 
1 
0 
0 
1 
Exclusive OR (XOR) 


A 
B 
X 
Only one input must be present for output. 
1 
1 
0 
1 
0 
1 
0 
1 
1 
0 
0 
0 
Exclusive NOR (XNOR) 


A 
B 
X 
Neither or both inputs must be present for output. 
1 
1 
1 
1 
0 
0 
0 
1 
0 
0 
0 
1 