Boolean Algebra

ShareThis 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.

- Binary Number System
- Binary Constant
- Binary Variable
- Basic Logical Operation
- Boolean Function

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.

- OR operation (+)
- AND operation (.)
- NOT 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 0â€¨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.

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