The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. It is used for finding the truth table and the nature of the expression.
How to use the boolean calculator?
Follow the 2 steps guide to find the truth table using the boolean calculator.
- Enter the Expression.
- Click "Parse"
Take help from sample expressions in the input box or have a look at the boolean functions in the content to understand the mathematical operations used in expressions.
What is Boolean Algebra?
Mathematics has different branches e.g algebra, geometry e.t.c. These branches are further divided into sub-branches. Boolean algebra is one such sub-branch of algebra.
It has two logic values including true and false that are represented by 0 and 1. Where 1 is considered as true and 0 is considered as false.
Boolean expressions are simplified to build easy logic circuits.
Laws of Boolean Algebra
Boolean algebra has a set of laws or rules that make the Boolean expression easy for logic circuits. Through applying the laws, the function becomes easy to solve.
Here are the simplification rules:
According to this law;
A + B = B + A
A.B = B.A
This law states;
A + ( B + C ) = ( A + B ) + C
A(B.C) = (A.B)C
Using this law, we know;
A . ( B + C ) = ( A . B ) + ( A . C )
A + ( B . C ) = (A + B ) . (A + C )
By identity law:
A + 0 = A
A . 1 = A
A . 0 = 0
A + 1 = 1
By this law:
A + A = A
A . A = A
There are some other rules but these six are the most basic ones.
Application of Boolean Algebra
Boolean algebra can be used on any of the systems where the machine works in two states. For example, the machines that have the option of “On” or “Off”.
Here are some of the real-time applications in our daily life that are using the concept of Boolean algebra:
Elevator for two floors
Car (Starting and turning off the engine)
|AND||F = A.B|
|OR||F = A+B|
|NOT||F = A|
|NAND||F = (A.B)|
|NOR||F = (A+B)|
Table of Boolean Algebra
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