Computer Architecture: Practicals

Practical No. 5

Title: To Verify the Truth Table of Special Purpose Logic Gates

Aim

To understand the specific operational characteristics of Exclusive-OR (XOR) and Exclusive-NOR (XNOR) logic gates and verify their corresponding truth tables.

Introduction

While basic and universal gates form the core of digital logic, certain tasks in digital design require gates with unique logical behaviors.

· Exclusive-OR (XOR) Gate: Outputs ‘1’ only when inputs are different. Applications include digital comparison, parity checking, and basic arithmetic.

· Exclusive-NOR (XNOR) Gate: Outputs ‘1’ only when inputs are the same. Ideal for equality detection.

Understanding their truth tables is fundamental for utilizing these gates effectively in digital circuits. These concepts align with Chapter 2.4 Exclusive Gates from the course material.

Procedure / Example

Example: Verifying the Truth Table of a 2-Input XOR Gate

1. Inputs: A and B; Output: Q.

2. With 2 inputs, there are 2² = 4 possible input combinations.

3. Apply inputs and record outputs:

o A = 0, B = 0 → Q = 0

o A = 0, B = 1 → Q = 1

o A = 1, B = 0 → Q = 1

o A = 1, B = 1 → Q = 0

4. Logical expression: Q = A ⊕ B

Truth Table (XOR Gate):

A	B	Q
0	0	0
0	1	1
1	0	1
1	1	0

Exercises

1. Exclusive-OR (XOR) Gate

· Logical Symbol: (Draw standard 2-input XOR gate: OR gate with an additional curved line before the inputs)

· Logical Expression: Q = A ⊕ B

· Truth Table:

A	B	Q
0	0
0	1
1	0
1	1

2. Exclusive-NOR (XNOR) Gate

· Logical Symbol: (Draw standard 2-input XNOR gate: XOR gate symbol with small circle at output)

· Logical Expression: Q = ¬(A ⊕ B) or Q = A ⊙ B

· Truth Table:

A	B	Q
0	0
0	1
1	0
1	1

Result / Conclusion

This practical successfully demonstrated the unique operational characteristics and verified the truth tables of Exclusive-OR (XOR) and Exclusive-NOR (XNOR) gates. These special-purpose gates are essential for functions such as data comparison and error detection in digital systems.