Practical No. 3

Title: To Verify the Truth Table of Basic Logic Gates

Aim

To understand the fundamental operation of basic logic gates and verify their corresponding truth tables.

Introduction

Digital computers operate using binary logic, where information is represented by two states: ‘0’ and ‘1’. Logic gates are the fundamental building blocks of digital circuits that perform logical operations on these binary inputs to produce a binary output. There are three basic logic gates: AND, OR, and NOT. Each gate has a unique function that can be precisely described by its truth table. A truth table systematically lists all possible combinations of inputs to a logic gate and shows the resulting output for each combination, serving as a complete definition of the gate’s behavior. Understanding and verifying these truth tables is crucial for comprehending how digital circuits process information. This practical focuses on the concepts covered in Chapter 2.2 Basic Logic Gates from your course material.

Procedure / Example

This practical involves examining the behavior of AND, OR, and NOT gates by applying all possible input combinations and observing their respective outputs. For each gate, you will draw its logical symbol and complete a truth table based on the observed or calculated output for every input scenario.

Example: Verifying the Truth Table of an AND Gate

1.     Identify Inputs and Output: For a 2-input AND gate, there are two inputs (A, B) and one output (Q).

2.     Determine Possible Input Combinations: With 2 inputs, there are $2^2 = 4$ possible combinations:.

3.     Apply Inputs and Record Output: For each combination:

o    Input A = 0, Input B = 0: The logical AND operation states that if any input is 0, the output is 0. So, Q = 0.

o    Input A = 0, Input B = 1: The output is still 0.

o    Input A = 1, Input B = 0: The output is still 0.

o    Input A = 1, Input B = 1: Only when both inputs are 1, the output is 1. So, Q = 1.

4.     Complete the Truth Table: Fill in the observed/calculated outputs into the truth table.

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

Exercises:

For each of the following basic logic gates, perform the verification by filling in the details below:

1. AND Gate

·         Logical Symbol: (Draw the standard logical symbol for a 2-input AND gate here)

·         Logical Expression: $Q = A \cdot B$

·         Truth Table:

A	B	Q
0	0
0	1
1	0
1	1

2. OR Gate

·         Logical Symbol: (Draw the standard logical symbol for a 2-input OR gate here)

·         Logical Expression: $Q = A + B$

·         Truth Table:

A	B	Q
0	0
0	1
1	0
1	1

3. NOT Gate

·         Logical Symbol: (Draw the standard logical symbol for a NOT gate/inverter here)

·         Logical Expression: $Q = \overline{A}$

·         Truth Table:

A	Q
0
1

Result / Conclusion

This practical successfully demonstrated the fundamental operations of AND, OR, and NOT logic gates. By systematically applying all input combinations and recording the outputs, the truth tables for each basic gate were verified. This exercise solidifies the understanding of how these elementary components form the basis of all digital information processing.