Verifying Distributive Law and DeMorgan’s Law

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Table of Contents

Introduction
Equipment List
Theory
Procedure
Data – Screenshots of your tables would go here
Results/Conclusion
Reference

Introduction

The main goal of this lab investigation was to use practical logic circuits to validate DeMorgan’s law and the Distributive Law and learn about CMOS devices’ characteristics.

Participants employed DeMorgan’s Law in this experimental investigation, which states:

(X+Y)’ = X’Y’
(XY)’ = X’ + Y’

The Distributive Law is also applied, which states:

X + YZ = (X+Y) (X+Z)
X(Y+Z) = XY + XZ (Nabulsi et al., 2021).

Equipment List

The following electrical components were used in the investigations:

Breadboard
Dc power supply
74HC04 hex inverter chip
74HC08 quad AND chip
74HC32 quad OR chip

Theory

To demonstrate that these laws were factual and could be validated with logic circuits. Participants then had to accomplish this investigation by making a truth table, which could be conducted by joining a gate’s inputs to switches and its output to an indicator LED. Logic circuits are the basis of this truth table, a presentation in rows and columns that demonstrates how a logic’s truth or falsity differs from that of its components. The results were to be compared with those derived from pre-labs. Each logic circuit generated several equations, including the following:

*=And
+=OR
‘=NOT (inv)

F1 = X+YZ

F2 = (X+Y) (X+Z)

F3 = X(Y+Z)

F4 = XY + XZ

F5 = (X+Y)’

F6 = X’Y’

F7 = (XY)’

F8 = X’ + Y’

Procedure

Participants had to initially collect all materials indicated in the component section to accomplish this scientific experiment. Then, as stated in the theory section of this lab report, participants had to construct the circuits through the breadboard, effectively apply power and input signals, and monitor the output, which was positioned at the LEDs and represented F1, F2, F3, F4, F5, F6, F7, and F8. Participants then tested the inputs of a gate to the switches and the output to an indicator light after finishing the setting by stating the truth table after the diagram that the participants in the pre-lab of this lab report developed.

Data – Screenshots of your tables would go here

The table below is a derived truth table for F1, F2, F3 and F5:

X	Y	Z	F1	F2	F3	F4
0	0	0	0	0	0	0
0	0	1	0	0	0	0
0	1	0	0	0	0	0
0	1	1	1	1	0	0
1	0	0	1	1	0	0
1	0	1	1	1	1	1
1	1	0	1	1	1	1
1	1	1	1	1	1	1

The table below is a derived truth table for F5, F6, F7 and F8:

X	Y	F5	F6	F7	F8
0	0	1	1	1	1
0	1	0	0	1	1
1	0	0	0	1	1
1	1	0	0	0	0

Results/Conclusion

The purposes of the laboratory experiment, then, were accomplished. The groups successfully established the connections and logic circuits that the participants were tasked with developing in the pre-lab segment of this lab report. Groups could also validate Distributive and DeMorgan’s law utilizing logic devices. Finally, teams had the opportunity to learn about the device’s properties. Devices that use CMOS technology. Consider the F1, F2, F3, and F4 truth table, where it is evident that the Distributive law has been established, and the team has demonstrated that it is aware that everything has to be satisfied. Participants may set up this experiment again if necessary to test each configuration. And make sure the values are in agreement.

Reference

Nabulsi, M., Hamad, N., & Alqatawneh, S. (2021). A new approach for simplification of logical propositions with two propositional variables using truth tables. Recent Advances in Computer Science and Communications (Formerly: Recent Patents on Computer Science), 14(9), 2836-2842.

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