Logical Operators

Logical operators are also called Boolean functions. Logical operators are part of Boolean algebra and are widely used in computer science, engineering, and mathematics. Various words and expressions are used for logical operators, such as Logic gates or bitwise operations, but the main principle is the same which is to perform logical operations on bits (values 0 and 1).

Electronics is a part of almost every technical field today, so it is very important for engineers to understand a minimum level of bitwise logical operators.

Boolean Algebra

Boolean algebra is an important part of mathematics which focuses on dealing with operations on specific binary variables. The application of Boolean algebra contributes to the analysis and interpretation of gates or digital circuits. Boolean algebra is commonly known as binary algebra or logical algebra. It plays a key role in the development process of various digital electronic devices and various programming languages. It is also commonly used in set theory and statistics.

Boolean Expression and Variables

A Boolean expression is an expression which creates a Boolean value when evaluated, true or false, the only way to define a Boolean value. While Boolean variables are variables which store Boolean numbers.

A+B=C is a Boolean phrase, where A, B, C are Boolean variables which can only store two values, that is, 0 and 1. The computer performs all operations on binary 0 and 1 because the computer understands only the machine language (0/ 1). Boolean logic is named after George Boole. Boolean logic is a type of algebra where all values reduce to one of two possibilities which is 1 or 0.

Truth Table

A truth table tabulates the full variety of combinations of input and output values. It shows all the possible inputs and outputs. Truth tables are often used in logic problems like Boolean algebra and electronic circuits. T or 1 means “True” and F or 0 means “False” in the truth table.

Logic Gates

The main structural element or part of a digital system are logic gates. A Logic gate is the fundamental building block of a digital circuit having two inputs and one output. The fundamental logic gates are divided into seven parts: AND, OR, XOR, NAND, NOR, XNOR, and NOT.

These are the important digital devices which are basically based on the logical operators or Boolean function. Logic gates carry the logical operations on single or multiple binary inputs and give one binary output.

Study material notes on Statements & Logical Operations

OR Logical Operator

The output of an OR logical operator is 1 when any of the inputs attain the state 1. When both inputs are 0 then output state is 0.

Boolean Expression of OR logical operator is

The expression is read as A ‘OR’ B.

The truth table of OR logical operator with two-input is given as

AND Logical Operator

The output of an AND logical operator is 1 when both of the inputs attain the state 1. Otherwise, it attains the state 0 (If any of the two inputs is 0 then output state will be 0).

Boolean Expression of AND logical operator is

Y=A.B 

The expression is read as A ‘AND’ B.

The truth table of AND logical operator with two-input is given as

NOT Logical Operation

The output of an AND logical operator is 1 when the input did not attain the state 1, that is, the input attains the state 0. Otherwise, it attains the state 0 (If the input is 1 then output state will be 0).

Boolean Expression of NOT logical operation is

The expression is read as Y is equal to NOT A.

The truth table of NOT logical operator is given as

XOR Logical Operator

The output of the XOR logical operator is 1 when only one of the inputs attain the state 1. When both inputs are 0 or 1 then the output state will be 0 (zero).

Boolean Expression of XOR logical operator is

Y=A++B

Y=A⊕B

Truth Table of XOR logical operator

Conclusion

Logical operators are also called Boolean functions. Logical operators are part of Boolean algebra and are widely used in computer science, engineering, and mathematics.

Boolean algebra is an important part of mathematics which focuses on dealing with operations on specific binary variables.

A+B=C is a Boolean phrase, where A, B, C are Boolean variables which can only store two values, that is, 0 and 1.

Boolean logic is a type of algebra where all values reduce to one of two possibilities which is 1 or 0.

A truth table tabulates the full variety of combinations of input and output values.

The main structural element or part of a digital system are logic gates.

The fundamental logic gates are divided into seven parts: AND, OR, XOR, NAND, NOR, XNOR, and NOT.