Discover the Magic of XOR and XNOR Gates in Digital Electronics

Table of Contents:

1. Introduction
2. The Exclusive OR Gate (XOR Gate)
   • 2.1 Truth Table and Symbol
   • 2.2 Logic Expression
   • 2.3 Practical Applications
3. The Exclusive NOR Gate (XNOR Gate)
   • 3.1 Truth Table and Symbol
   • 3.2 Logic Expression
   • 3.3 Scaling to a 3-input XNOR Gate
4. Conclusion
5. Resources

Introduction

In digital electronics, there are various logic gates that form the building blocks of circuits. In this article, we will focus on the last two basic gates, namely the Exclusive OR (XOR) gate and the Exclusive NOR (XNOR) gate. These gates play a crucial role in performing binary computations and are widely used in various applications.

The Exclusive OR Gate (XOR Gate)

2.1 Truth Table and Symbol

The XOR gate is represented by a symbol similar to the OR gate, but with two curved lines on the left side. Its truth table shows that the output is asserted whenever the two inputs are different from each other.

2.2 Logic Expression

To express the XOR gate in terms of logic expressions, a new algebraic operator is defined. It is similar to the OR gate expression, but with a circle around it. The XOR gate is also known as a difference gate, as it asserts when A and B are different and is unassertive when A and B are equivalent.

2.3 Practical Applications

While a two-input XOR gate serves as a difference gate, its three-input version is not as useful. Instead, a cascade of two-input XOR gates is employed to achieve the desired functionality. This gate finds extensive application in addition and binary bit Patterns. Additionally, it is crucial in error code checking and parity checking to detect errors in data transmission.

The Exclusive NOR Gate (XNOR Gate)

3.1 Truth Table and Symbol

The XNOR gate is similar to the XOR gate, but with an inversion on the output. It asserts when A and B are equal and is unassertive when they are different.

3.2 Logic Expression

The logic expression for the XNOR gate is simply the inverted version of the XOR gate's logic expression. It can be represented as F = (A xor B)' or F = (A or B) and (A' or B').

3.3 Scaling to a 3-input XNOR Gate

Similar to the XOR gate, the three-input version of the XNOR gate can be implemented using a cascade of two-input XNOR gates. The outputs of the cascade are inverted to achieve the desired result.

Conclusion

In conclusion, the XOR gate and XNOR gate are essential components in digital electronics. They enable various computational operations and find application in arithmetic, error detection, and data transmission. By understanding these gates, one can delve deeper into the world of digital circuits and logic.

Resources

• XOR gate - Wikipedia
• XNOR gate - Wikipedia