Boolean logic is a form of algebra where the value of variables is expressed in truth values instead of elementary algebra. This algebra form involves three terms: AND, OR, and NOT. Boolean logic was introduced by George Boole, from where it gets its name. This form of algebra is used to simplify and help decision-making. It is applied in simple calculators, computers, electronics, and programming languages. This type of algebra can help make clear and black and white decisions.  

Overview of Boolean Logic

  • Boolean logic is a form of algebra where variables are truth values and lie between 0 and 1. 
  • It implies that all values are either true or false.
  • There are certain logical operations in Boolean algebra, such as conjunction and disjunction.
  • It is aimed at simple decision-making. 
  • Boolean variable refers to the variables representing the logical quantities between 0 and 1.
  • Literal is a term used to denote variables or their complements, where complement refers to the inverse. 
  • The truth table is a table that contains all possible combinations of logical variables.
  • Boolean algebra only involves the use of variables that are binary or have only two values.
  • An example of Boolean logic could be Red AND Shoes to find red shoes. 
  • There are three main Boolean operators: AND, OR, and NOT.

Boolean Operators

There are three major operators in Boolean logic:  AND, OR, and NOT:

  • Conjunction or AND operation
  • Negation or NOT negation
  • Disjunction or OR operation

Boolean Expression 

A Boolean expression is a logical statement that produces a Boolean value, either True or False. Synonyms such as ‘Yes’ for ‘True’ and ‘No’ for ‘False’ are sometimes used to express the statement. In addition, digital circuits for True and False use the numbers 1 and 0.

Statements that use logical operators, such as AND, OR, XOR, and NOT, are Boolean expressions. As a result, writing X AND Y = True is a Boolean expression.

Terminologies

Some of the critical terms in Boolean algebra are as follows:

Boolean Algebra: Boolean algebra is the branch of mathematics concerned with logical operations and binary variables.

Boolean Variable: A Boolean variable is a variable or a symbol, usually an alphabet, that represents logical quantities like 0 or 1.

Boolean Function: Binary variables, logical operators, constants like 0 and 1, equal to the operator, and parenthesis symbols make up a Boolean function.

Literal: A literal is a variable or a variable’s complement.

Complement: The inverse of a variable is represented by a bar over the variable.

Truth Table: The truth table is a table that lists all of the possible values and combinations of logical variables. A truth table can be created by converting the Boolean equation. The truth table should have 2n rows, with “n” denoting the number of variables in the equation. The number of rows in the truth table is 8. For example, if a Boolean equation has three variables. 23 = 8 (i.e.

Laws of Boolean Logic :-

1) Law of Commutation

A commutative operation is any binary operation that satisfies the following expression. The commutative law states that changing the order of the variables does not affect the logic circuit’s output.

  1. B = B. A. B = A. B = A. B = A. B

B + A = A + B

2) Law of Association

It claims that the order in which the logic operations are carried out makes no difference because the result is the same.

(A.B.) A = C. ( B . C )

A + (B + C) = (A + B + C).

3) The Law of Distribution

The following conditions are stated in distributive law:

(A. B + C) = (A. B) + (A. B) + (A. B) + (A. B) + (A. (A. C)

(A + B) = A + (B. C). (A + C)

AND THE LAW

The AND operation is used in these laws. As a result, they’re known as AND laws.

.0 = 0 A.0 = 0 A.0 = 0 A.0

  1. A. A. A. A. A. A. A. A. A

A = A.1

OR the law

The OR operation is used in these laws. As a result, they are known as OR laws.

A + 0 equals A

1 = A + 1

A + A equals A

4) The Law of Inversion

The NOT operation is used in this law. According to the inversion law, double inversion of a variable results in the original variable.