Statement of the Problem

Design a digital circuit for a water level monitoring system that generates an alert signal $($A$)$ based on the specified conditions: either the water level is too low, or the water level is too high and the pump is not working.

$2.$ Introduction to Related Topic

Digital Circuits are electronic circuits that can manipulate and process digital signals. Boolean logic involves manipulating the truth values $($true$/$false or $\frac{1}{0})$ using logical operations such as AND, OR and NOT.

In real$-$world applications, such as water level monitoring systems, digital circuits can automate the process of generating alerts to ensure timely interventions. This is crucial for preventing issues like water shortages or overflows, thus safeguarding infrastructure and resources. INCOMPLETE

$3.$ Mathematical Formulation of the Problem

Identify Inputs and Outputs:

L : Water level is normal when $L=1.$

H : Water level is too high when $H=1.$

$P$ : $P$ ump is working when $P=1.$

A: Alert signal

Formulate Conditions using Boolean Algebra

Alert signal A should be generated if:

The water level is too low

The water level is too high and the pump is not working

Water level too low: When the water level is not normal, $L=0.$

Condition $1$: $\frac{?}{\text{b}\text{a}\text{r}}(L)$

Water level too high and the pump is not working: This is the case when $H=1$ and $P=0.$

Condition $2$: $H\frac{}{b}ar(P)$

Combining both conditions using OR $($since the alert should be generated if either condition is met$)$:

$A\frac{?}{b}=ar(L)+(H\frac{}{b}ar(P))$

Translate Conditions into Boolean Expressions.

Truth TableTo high and the pump is not working: This is the case when $H=1$ and $P=0.$

$20f2$ ion $2$:$H\frac{}{b}ar(P)$

$3.$ Combining both conditions using OR $($since the alert should be generated if either condition is met$)$:

$A\frac{?}{b}=ar(L)+(H\frac{}{b}ar(P))$

Translate Conditions into Boolean Expressions.

Truth Table

$4.$ Solution of the Resulting Mathematical Problem

Digital Circuit

Explanation of Circuit Operation:

$5.$ Discussion of Related Topics and Findings

Relevance of Boolean Logic:

Analysis of Designed Circuit:

Real$-$World Applications and Reliability:

$6.$ Conclusions Reached