Lesson Notes By Weeks and Term v4 - SHS 2

Lesson Video

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Performance objectives

• Explain Karnaugh Maps for optimising digital systems.
• Create a truth table from functional requirements.
• Derive a simplified Boolean expression using a K-Map.
• Design a schematic of an optimized digital circuit.

Lesson summary

This lesson introduces a powerful visual tool used by engineers and computer scientists called the Karnaugh Map (K-Map). In Ghana, as we use more and more digital devices like smartphones, traffic lights, and automated systems in our homes and industries, making them efficient is very important. Inefficient circuits use more electricity (increasing ECG bills!), are slower, and cost more to build because they use more components. K-Maps provide a simple, graphical method to simplify complex Boolean logic expressions.

Lesson notes

2.1. From Boolean Algebra to K-Maps: The "Why"

In our previous lessons, we learned how to represent logic using Boolean Algebra. For example, `F = A'BC + ABC + AB'C`. We can try to simplify this using algebraic rules:

`F = AC(B' + B) + A'BC` `F = AC(1) + A'BC` `F = AC + A'BC`

This is simpler, but how do we know it's the *simplest* possible form? For complex expressions, it becomes very difficult to be sure.

Evaluation guide

• Apply Karnaugh Maps to optimise digital systems.
• Initiating Talk for Learning:
• Discuss Karnaugh Maps and their application for digital
• circuit optimisation using working examples.