Combinational Logic Lab Report

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Abstract

This lab report presents the findings and analysis of experiments conducted to explore combinational logic circuits and their applications. The experiments involved the use of logic gates, Boolean algebra, De Morgan's theorem, and the design of a digital security system. The report provides a comprehensive overview of the theory, methodology, results, and discussion related to the experiments.

Introduction

In this laboratory experiment, the primary objective was to utilize combinational logic to construct various digital control circuits. Logic gates, including AND, OR, NOT, NAND, and NOR gates, were employed as fundamental building blocks for creating these circuits.

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Combinational logic systems were explored to understand their behavior in response to different input combinations. Additionally, De Morgan's theorem was employed to simplify complex digital circuits. The first task involved designing a digital security system that could only be activated with a specific key code.

Theory

Logic Gates

Logic gates are fundamental components of digital circuits, each with specific logic operations based on Boolean algebra.

These gates include:

Gate

Symbol

Truth Table

AND

A	B	Y
0	0	0
0	1	0
1	0	0
1	1	1

A	B	Y
0	0	0
0	1	1
1	0	1
1	1	1

NOT

A	Y
0	1
1	0

NAND

A	B	Y
0	0	1
0	1	1
1	0	1
1	1	0

NOR

A	B	Y
0	0	1
0	1	0
1	0	0
1	1	0

Boolean Algebra

Boolean Algebra, invented by George Boole in 1854, is used to analyze and simplify digital circuits, relying on binary numbers (0 and 1) for operations.

De Morgan's Law

De Morgan's theorem states that an OR gate with all inputs inverted behaves like a NAND gate, and an AND gate with all inputs inverted behaves like a NOR gate.

Task 1 - Security Application

The first task in this lab involved creating a digital security system that would only function when a valid key code was entered.

The code was restricted to 2-bit or 3-bit combinations due to limited inputs in the logic box. The system was designed using NOT and NAND gates.

Solution

To accomplish this task, we utilized De Morgan's theorem to expand our design capabilities beyond the NOT and NAND gates. The logic box featured a four-bit binary counter, cycling from 0000 to 1111, driven by a clock with a frequency of approximately 2 Hz or a push-button.

The code we devised activated a light only when all three bits were in a specific state, ensuring security by requiring the correct combination.

Results and Discussion

Throughout the experiment, we successfully implemented various logic gates and combinational logic circuits using the provided gates. The logic gates behaved as expected, producing the correct output based on their truth tables.

De Morgan's theorem allowed us to simplify complex digital circuits, providing a more efficient way to design and analyze digital systems.

In Task 1, we designed a digital security system that met the specified requirements. The system effectively allowed access only when the correct code was entered, demonstrating the practical application of combinational logic in real-world scenarios.

Conclusion

This laboratory experiment provided valuable insights into the principles of combinational logic, logic gates, Boolean algebra, and De Morgan's theorem. We gained a deeper understanding of how these concepts can be applied to create digital control circuits and systems with practical applications, such as digital security.

References

[1] WhatIs.com. 2020. What Is Logic Gate (AND, OR, XOR, NOT, NAND, NOR And XNOR)? A Definition From Whatis.Com. [online] Available at: [Accessed 10 April 2020].