ELECTRONIC PRESENTATION

Introduction to Boolean Algebra and their Application

Logic Gates

START

Introduction

Logic Gates

INDEX

Types of Logic Gates

Truth Table and Its Importance

Boolean Algebra

Combination of Logic Gates

Applications of Logic Gates

Inrtroduction to Digital Logic

• Digital logic is the use of electronic devices and logic gates to process and control digital signals, which consist of only two discrete states, typically represented as 0 and 1.

• Example - Communications and Networking, Smartphones and Mobile Devices, Consumer Electronics, Industrial Automation, Transportation, Energy Management

Boolean Algebra

• Boolean algebra deals with binary values, they can be either ON (1) or OFF (0).

• There are three main operations: AND, OR, and NOT.
• AND means both conditions must be true for the result to be true.
• OR means at least one condition must be true for the result to be true.
• NOT means flipping the truth – true becomes false, and false becomes true.

• Boolean algebra has special sets of rules.

[2]S. Sarma and R. K. Bhuyan, “(PDF) boolean algebra and Logic Gates - Researchgate,”

Boolean Algebra

• Boolean Equation for Basic Logic Gates:
• AND - A.B
• OR - A+B
• NOT - A
• Basic Boolean Algebra Law:
• A+0=A
• A.1=A
• A+A=1
• A.A=0
• A+1=1
• A.0=0
• A+A=A
• A.A=A

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

[2]S. Sarma and R. K. Bhuyan, “(PDF) boolean algebra and Logic Gates - Researchgate,”

Truth Tables and Its importance

• A truth table is a tabular representation of all possible combinations of input values for a logical expression or a Boolean function, along with the resulting output.

• Importance of truth table- teaching and learning boolean algebra, Logical analysis, Error detection, Design and Verification.

[3] A. Dușa, “(PDF) the truth table - researchgate,”

Logic Gates

• Logic gates are fundamental electronic devices that perform logical operations on one or more binary inputs (0 and 1) to produce a singular binary output.

• Logic gates are essential in digital electronics, computer science, and various electronic systems.

Types of Logic Gates

OR

NOT

AND

XOR

XNOR

NOR

NAND

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

AND Gate

• Produces a high output (1) only if both inputs are high (1).

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

OR Gate

• Produces a high output (1) if at least one input is high (1).

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

NOT Gate

• Produces the opposite binary value of the input.

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

NAND Gate

• Produces a low output (0) only if both inputs are high (1).

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

NOR Gate

• Produces a low output (0) if at least one input is high (1).

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

XOR Gate

• Produces a high output (1) if the inputs are different.

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

XNOR Gate

• Produces a high output (1) if the inputs are the same.

Symbol

Truth Table

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

Combination of Logic Gates

• Combination of Logic Gates is combining multiple Logic Gates in various configuration to perform complex logical operations.

• For ex.

• AND-OR Combination: Combining an AND gate with an OR gate allows for more complex conditions. For example, outputting true if (A⋅B)+C.

• NAND-NAND Combination: Connecting two NAND gates creates a universal gate that can be used to construct any other logic gate.

• Arithmetic Logic Unit: ALU is a complex combination of various logic gates designed to perform arithmetic and logic operations in a computer's central processing unit (CPU).

Applications of Logic Gates

• We will discuss about the applications of Logic Gates in the paper attached in this

Link

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,”

References

[1] Mr. B. Garg and Ms. S. Kaur, “A review of logic gates and its applications,” JETIR, https://www.jetir.org/view?paper=JETIRCW06026 (accessed Dec. 3, 2023). [2] S. Sarma and R. K. Bhuyan, “(PDF) boolean algebra and Logic Gates - Researchgate,” Boolean Algebra and Logic Gates, https://www.researchgate.net/publication/334054812_Boolean_Algebra_and_Logic_Gates (accessed Dec. 3, 2023). [3] A. Dușa, “(PDF) the truth table - researchgate,” The truth table, https://www.researchgate.net/publication/325806607_The_Truth_Table (accessed Dec. 3, 2023).

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