Boolean Algebra Operations
There are various operations that are used in Boolean algebra but the basic operations that form the base of Boolean Algebra are.
- Negation or NOT Operation
- Conjunction or AND Operation
- Disjunction or OR Operation
Boolean Algebra Expression
These operations have their own symbols and precedence and the table added below shows the symbol and the precedence of these operators.
Operator | Symbol | Precedence |
|---|---|---|
NOT | ‘ (or) ⇁ | First |
AND | . (or) ∧ | Second |
OR | + (or) ∨ | Third |
We can easily define these operations using two boolean variables.
Let’s take two boolean variables A and B that can have any of the two values 0 or 1, i.e. they can be either OFF or ON. Then these operations are explained as,
Negation or NOT Operation
Using the NOT operation reverse the value of the Boolean variable from 0 to 1 or vice-versa. This can be understood as:
- If A = 1, then using NOT operation we have (A)’ = 0
- If A = 0, then using the NOT operation we have (A)’ = 1
- We also represent the negation operation as ~A, i.e if A = 1, ~A = 0
Conjunction or AND Operation
Using the AND operation satisfies the condition if both the value of the individual variables are true and if any of the value is false then this operation gives the negative result. This can be understood as,
- If A = True, B = True, then A . B = True
- If A = True, B = False, Or A = false, B = True, then A . B = False
- If A = False, B = False, then A . B = False
Check: Boolean Algebraic Theorems
Disjunction (OR) Operation
Using the OR operation satisfies the condition if any value of the individual variables is true, it only gives a negative result if both the values are false. This can be understood as,
- If A = True, B = True, then A + B = True
- If A = True, B = False, Or A = false, B = True, then A + B = True
- If A = False, B = False, then A + B = False
Boolean Algebra
Boolean algebra is a type of algebra that is created by operating the binary system. In the year 1854, George Boole, an English mathematician, proposed this algebra. This is a variant of Aristotle’s propositional logic that uses the symbols 0 and 1, or True and False. Boolean algebra is concerned with binary variables and logic operations.
Boolean Algebra is fundamental in the development of digital electronics systems as they all use the concept of Boolean Algebra to execute commands. Apart from digital electronics this algebra also finds its application in Set Theory, Statistics, and other branches of mathematics.
In this article, we will learn about, basic Boolean operations, Boolean expressions, Truth Tables, Boolean laws, and others in detail.
Table of Content
- Boolean Algebra Operations
- Table of Boolean Algbera
- Boolean Expression and Variables
- Boolean Algebra Terminologies
- Truth Tables in Boolean Algebra
- Boolean Algebra Rules
- Laws for Boolean Algebra
- Boolean Algebra Theorems
- Solved Examples on Boolean Algebra