Table of Contents

1. Introduction to Logic Gates and Truth Tables
2. Fundamental Logic Gates
   • 2.1 Inverter (NOT Gate)
   • 2.2 OR Gate
   • 2.3 AND Gate
   • 2.4 NOR Gate
   • 2.5 NAND Gate
   • 2.6 Universal Gates
3. De Morgan’s Theorem
4. Conclusion
5. FAQs

1. Introduction to Logic Gates and Truth Tables

Logic gates are the fundamental building blocks of digital electronics. These gates process binary inputs (0s and 1s) and produce a logical output based on predefined rules. They are widely used in computing, digital circuits, and automation systems.

What is a Truth Table?

A truth table represents the input-output relationship of a logic gate. It lists all possible combinations of inputs and their corresponding outputs, providing a clear understanding of how a gate functions.

For example, here’s a simple truth table for an OR gate:

Now, let’s explore different types of logic gates in detail.

2. Fundamental Logic Gates

2.1 Inverter (NOT Gate)

• The NOT gate, also known as an inverter, is the simplest logic gate. It has only one input and produces an output that is the logical complement of the input.
• The symbol of the NOT gate is shown in the below diagram.
• it includes one input  A , and produces out put Y= A’

• The boolean expression of NOT gate is given as Y= A̅

Truth Table for NOT Gate

Working Principle

• If the input is 0, the output is 1.
• If the input is 1, the output is 0.

2.2 OR Gate

• OR  gate is a basic electronic gate that gives an output of 1 (true) if at least one of its inputs is 1. If both inputs are 0, the output is 0 (false).
• The OR gate produces an output of 1 if at least one input is 1. It follows the Boolean equation:

$Y=A+B$

• The symbol of the OR gate is shown in the below diagram.

Truth Table for OR Gate

2.3 AND Gate

• The AND gate produces an output of 1 only if both inputs are 1. Its Boolean expression is:

                           Y=A⋅B

• The symbol of the AND gate and its truth table are explained below.

Truth Table for AND Gate

2.4 NOR Gate

• The NOR gate is the combination of an OR gate followed by a NOT gate.
• It produces an output of 1 only when all inputs are 0.
• The symbol of the NOR gate is shown below the diagram, it includes two inputs input A and input B, and produces out put Y= (A+B)’

Truth Table for NOR Gate

2.5 NAND Gate

• The NAND gate is an AND gate followed by a NOT gate. It produces an output of 0 only when both inputs are 1.
• The symbol of the  NAND gate is shown below the diagram.
• it includes two inputs input A, and input B, and produces output Y= (A.B)’
• The boolean expression of the NAND gate is given as

Y= (AB)’

Truth Table for NAND Gate

2.6 Universal Gates

• NAND and NOR gates are called universal gates because they can implement any Boolean function.
• These universal gates play a crucial role in circuit design and optimization.

Special Purpose Gate:

• Exclusive OR (Ex-OR)and Exclusive NOR (X-NOR) gates are called special-purpose gates due to their unique behavior and specific use cases in digital circuits. Unlike basic gates such as AND, OR, or NOT, which are used for general-purpose logic operations, the XOR gate has specialized applications that make it particularly useful in certain scenarios. Let’s break down why it’s called a special-purpose gate.

3.1 EX-OR Gate

• An Exclusive OR (XOR) gate, also known as an E-OR gate, is a digital logic gate that outputs true (or 1) only when the inputs to it are different.
• If both inputs are the same (either both 0 or both 1), the output is false (or 0).
• The symbol of the Ex-OR gate is shown in the below diagram.

3.2 EX-NOR Gate

• An Ex-NOR gate, also known as the Exclusive NOR gate or XNOR gate, is a type of digital logic gate that is the complement (inversion) of the Exclusive OR (XOR) gate.
• It produces a high output (1) only when the number of true inputs is even. In simpler terms, it outputs 1 if both inputs are the same, and 0 if the inputs are different.
• The symbol of EX-NOR gate is shown in the below diagram.
• The boolean expression of the E-NOR gate is given as

            Y = A ⊙ B = (A AND B) OR (NOT A AND NOT B)  

4. Conclusion

Logic gates form the backbone of digital electronics. Understanding truth tables, universal gates, and De Morgan’s theorem helps in designing efficient circuits. Whether you’re a student or a professional, mastering these concepts is crucial in the digital world.

compile by Er.Basant kumar yadav

5. FAQs

Q1: Why are NAND and NOR gates called universal gates?
A1: Because they can be used to construct any other logic gate.

Q2: What is the purpose of De Morgan’s theorem?
A2: It helps simplify Boolean expressions and logic circuits.

Q3: Where are logic gates used in real life?
A3: In computers, smartphones, calculators, and automation systems.

Q4: What is the main difference between AND and OR gates?
A4: AND requires all inputs to be 1 for 1 output, while OR requires only one.

Q5: Can NOT gate be created using NAND or NOR gates?
A5: Yes, by connecting both inputs together (NAND(A, A) or NOR(A, A)).