The LUMS Math Circle session held on January 23, 2026, was the second part of the series “Boolean Algebra: The Mathematics of Logic Gates.” This session aimed to strengthen students’ understanding of Boolean algebra and its role in modern digital electronics through interactive explanations, worksheet-based activities, and a real-world hardware demonstration.

Session Structure and Content

The session began with a brief recap of Part 1, revisiting the basic logic gates—AND, OR, and NOT—and their corresponding truth tables. The instructors used familiar real-life examples to illustrate how logical operations function in everyday decision-making, such as access control systems and electrical switches.

Students were then introduced to key properties of Boolean algebra, some analogous to elementary algebra and others unique to logical systems. Emphasis was placed on how these properties help simplify logical expressions and reduce the number of gates needed in a digital circuit.

Interactive Activities

To reinforce conceptual understanding, students worked through several guided activities:

1. Verification of De Morgan’s Law:
   Students verified the identity
   (AB)' = A' + B'
   by comparing both sides using logical reasoning and truth tables.

2. Distributive Property:
   The identity
   A(B + C) = AB + AC
   was explored to show how OR and AND operations interact.

3. Circuit Optimization Task:
   Students were asked to design a logical circuit for the expression
   AA + AC + AB + BC.
   Initially, this required a larger number of gates. Using Boolean simplification, the expression was reduced to
   A + BC,
   demonstrating how Boolean algebra minimizes hardware complexity. Students compared truth tables of the original and simplified forms to confirm equivalence.

Real-World Application: 5-Bit Digital Lock

A highlight of the session was the visit to the Electrical Engineering Lab, where students observed a 5-bit digital lock setup. The system consisted of five switches connected to a control box and an LED indicator. By experimenting with different switch combinations, students identified patterns governing when the LED turned ON or OFF.

They discovered that:

• When an odd number of switches were closed, the LED turned ON.

• When an even number of switches were closed, the LED remained OFF.

This activity helped students connect abstract Boolean expressions with tangible electronic behavior, illustrating how logic gates operate inside real digital systems.

By the end of the session, students:

• Understood how Boolean algebra underpins digital circuit design.

• Learned to simplify logical expressions using algebraic laws.

• Experienced the practical implementation of logic gates through a physical electronic system.

• Gained insight into how mathematical reasoning leads to efficiency in engineering design.

Conclusion

The session successfully blended mathematical theory with hands-on experimentation. Through logical reasoning, worksheet activities, and direct interaction with a digital lock system, students developed a deeper appreciation of how Boolean algebra forms the foundation of modern electronics and computing.

Acknowledgments

The LUMS Math Circle team sincerely thanks Dr. Nauman Zafar Butt and Dr. Adeel Pasha from the Electrical Engineering Department for conducting this engaging and insightful session. The team also acknowledges the valuable organizational support of Ms. Noreen Sohail, Ms. Shazia Zafar, Mr. Muhammad Qammar, and Mr. Muhammad Javaid Qayoom in making the event a success.

Certificates

At the conclusion of the session, certificates of participation were distributed among the students in recognition of their engagement and successful completion of the activities. This gesture served to motivate participants and commemorate their learning experience in the Math Circle series.

Here are some highlights from the event: