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 algebra solver.
- 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.
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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 binary 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)
Boolean Expression and Functions
Here is a table with Boolean functions and expressions:
|AND||F = A.B|
|OR||F = A+B|
|NOT||F = A|
|NAND||F = (A.B)|
|NOR||F = (A+B)|
Table of Boolean Algebra
Truth Table for Binary Logical Operations
Here is a truth table for all binary logical operations:
Boolean Algebra Laws
Use the following rules and laws of boolean algebra to evaluate the boolean expressions:
|AND Form||OR Form|
|Commutative Law||A.B=B. A||A + B = B + A|
|Associate Law||(A. B) . C = A. (B C)||(A + B) + C = A + (B + C)|
|Distributive Law||(A+B)+ C = (A+C). (B+C)||(A + B) C = (A. C) + (B C)|
|Identity Law||A. 1 A||A- + 0 = A|
|Zero and One Law||A. 0 = 0||A+ 1 = 1|
|Inverse Law||A.A' = 0||A+ A' = 1|
|Idempotent Law||A.A= A||A+A = A|
|Absorption Law||A(A+B) = A||A + A.B = A A+ A'B = A+B|
|DeMorgan's Law||(A. B)'=(A)'+ (B)'||(A+B)' = (A)' . (B)'|
|Double Complement Law|| |
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