This is an introduction to Boolean algebra tutorial.
Mathematician George Boole invented the Boolean Algebra. This algebra deals with the rules by which logical operations are carried out. So, a digital circuit in this system is represented as input and output symbols and the function of the circuit is expressed as a Boolean relationship between the symbols.
It is a number system consisting of only two digits 0 and 1. It is also called the base 2 number system. All the numbers in this system is expressed in 0s and 1s.
Example: Decimal number (8)10 is written as (1000)2 in binary.
A binary value that will not change is called a binary constant.
A binary variable is a symbolic name assigned to a binary value.
Example: A = 1010
Here, A is a variable having binary value 1010.
Following are the basic logical operation.
Logical OR operation of two boolean variables A and B is written as X = A + B
It is also called logical addition.
The following table contains the input and output of the logical OR operation.
So, if any one of the input is 1 then the output is 1, otherwise it is 0.
Logical AND operation of two boolean variables A and B is written as X = A . B
It is also called logical multiplication.
The following table contains the input and output of the logical AND operation.
So, if both the input is 1 then the output is 1, otherwise it is 0.
Logical NOT operation performs inverse operation and converts 1 into 0 and 0 into 1.
The following table contains the input and output of the logical NOT operation.
So, if the input is 1 then the output is 0 and if the input is 0 then the output is 1.
A boolean function is an algebraic expression formed using binary constants, binary variables and basic logical operators.
Example: Boolean Function
F = A + 1
where, A is a binary variable
+ is a Basic Logical Operator (OR)
and, 1 is a binary constant.