Lesson Notes By Weeks and Term v4 - SHS 2
Digital and Analogue System Design
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Digital and Analogue System Design
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Subject: Robotics
Class: SHS 2
Term: 2nd Term
Week: 8
Grade code: 2.2.1.LI.2
Strand code: 2
Sub-strand code: 1
Content standard code: 2.2.1.CS.1
Indicator code: 2.2.1.LI.2
Theme: Robot Design Methodologies
Subtheme: Digital and Analogue System Design
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In our last lessons, we learned about logic gates and how to represent digital logic using Boolean expressions and truth tables. However, the initial Boolean expressions we get from a truth table are often long and complicated. Imagine building a robot's brain or a traffic light controller with many unnecessary logic gates. It would be expensive, slow, and consume too much power! Today, we will learn a powerful graphical technique called the Karnaugh Map (K-Map). The K-Map is a visual tool that helps us simplify complex Boolean expressions into their simplest, most efficient form.
2.1 Why Do We Need to Optimise Digital Circuits?
Imagine you are building an automatic irrigation system for a farm in the Afram Plains. You could build it with 20 logic gates, or you could build the *exact same system* with only 5 gates. Which one would you choose?
Optimising (or simplifying) a digital circuit means reducing the number of logic gates and inputs required to perform the same function. The benefits are significant: Lower Cost: Fewer gates mean fewer integrated circuits (ICs) to buy. Increased Speed: Signals travel through fewer gates, reducing the overall propagation delay. The circuit becomes faster. Lower Power Consumption: Each gate consumes a small amount of electricity. Fewer gates mean less power is needed, which is important for battery-powered robots or in areas with an unstable power supply (dumsor). Increased Reliability: Simpler circuits have fewer components and connections that can fail.
The Karnaugh Map is our primary tool for achieving this optimisation. 2.2 What is a Karnaugh Map (K-Map)?