In the previous example we used statements as propositions. Computer logic is accomplished by using logic gates as building blocks. A logic gate is a physical circuit which has electrical inputs and usually a single output.
Used in truth tables, we label each input and use truth values to represent weather or not an input is on or off.
We use the value true , T , 1 to represent on and false , F , 0 to represent off.
Sometimes, On is refered to as a high voltage and off is referred to as a low or no voltage.
The most common gates are shown in the table below:
Gate 
AND 
OR 
NOT 
NAND 
NOR 
XOR 

Symbol 







Inputs 


A 
B 
Q=AB 
Q=A+B 
Q = A 
Q= AB 
Q= A+B 
Q= A ⊕ B 
0 
0 
0 
0 
1 
1 
1 
0 
0 
1 
0 
1 
1 
0 
1 

1 
0 
0 
1 
0 
1 
0 
1 
1 
1 
1 
1 
0 
0 
0 



Description 
Outputs 1 when all inputs are 1 
Outputs 1 when ANY input is a 1 
Inverts the input 
Outputs 0 where all inputs are 1 
Outputs 1 then both inputs are 0 
Outputs 1 when exactly one input is 1 

Outputs 0 otherwise 
Outputs 0 otherwise 

Outputs 1 otherwise 
Outputs 0 otherwise 
Outputs 0 otherwise 
Typing the mathematical notation into most word processors can be challenging. Sometimes these worded expressions or symbols are used :
Gate  Worded expression  Symbol Expression 

AND  A AND B  A^B 
OR  A OR B  A v B 
NOT  NOT A  ~A 
NAND  NOT( A AND B)  ~(A^B) 
NOR  NOT (A OR B)  ~(A v B) 
XOR  A XOR B  A ∨ B 
© 2021 Vedesh Kungebeharry. All rights reserved.