Lesson Notes By Weeks and Term v4 - SHS 2
DIGITAL ELECTRONICS
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DIGITAL ELECTRONICS
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Subject: Physics
Class: SHS 2
Term: 2nd Term
Week: 17
Grade code: 2.3.3.LI.3
Strand code: 3
Sub-strand code: 3
Content standard code: 2.3.3.CS.2
Indicator code: 2.3.3.LI.3
Theme: ELECTRIC FIELD, MAGNETIC FIELD AND ELECTRONICS
Subtheme: DIGITAL ELECTRONICS
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Good morning, class. Look around you at the digital world we live in, right here in Ghana. From the smartphone you use for WhatsApp, to the traffic lights in Accra or Kumasi, to the digital TV in your living room, and even the system that processes your Mobile Money (MoMo) transaction. All these devices, no matter how complex, are built on very simple rules. They speak a language called Boolean Algebra. Today, we will learn a key part of this language: how to take a desired outcome (like "when should an alarm ring?") and turn it into a logical statement that a computer can understand. This skill is the foundation of computer programming, electrical engineering, and robotics.
(30 minutes) Part 1: The Building Blocks - Basic Logic and Gates (Recap)
Before we build a house, we need bricks. In digital electronics, our "bricks" are logic gates. Remember that in the digital world, everything is either OFF (represented by 0 or LOW) or ON (represented by 1 or HIGH). Boolean Notation: This is the special algebra we use to write our digital logic rules. A dot (`⋅`) or no symbol means AND. (e.g., `A ⋅ B` or `AB`) A plus sign (`+`) means OR. (e.g., `A + B`) A bar over a letter (`Ā`) means NOT. (e.g., `Ā`) The Three Basic Gates: NOT Gate (Inverter): Function: It flips the input. If the input is 1, the output is 0. If the input is 0, the output is 1. Boolean Expression: `Y = Ā` (Read as "Y equals NOT A") Truth Table: | A | Y | |---|---| | 0 | 1 | | 1 | 0 | AND Gate: Function: The output is 1 only if all inputs are 1. Think of it as a security door that needs two keys (A AND B) to open. Boolean Expression: `Y = A ⋅ B` (Read as "Y equals A AND B") Truth Table (2-input): | A | B | Y | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 0 | | 1 | 0 | 0 | | 1 | 1 | 1 | OR Gate: Function: The output is 1 if at least one of the inputs is 1. Think of a room with two light switches (A OR B); either one can turn on the light. Boolean Expression: `Y = A + B` (Read as "Y equals A OR B") Truth Table (2-input): | A | B | Y | |---|---|---| | 0 | 0 | 0 | | 0 | 1 | 1 | | 1 | 0 | 1 | | 1 | 1 | 1 | Part 2: The Main Concept - Sum-of-Products (SOP)
Now, let's build something with our bricks. Definition: Sum-of-Products (SOP) is a way of writing a Boolean expression by OR-ing together several AND terms. "Products" refer to the terms created by the AND operation (e.g., `A⋅B`, `Ā⋅B⋅C`). These are also called minterms. "Sum" refers to the final OR operation that combines these product terms (e.g., `(A⋅B) + (Ā⋅C)`). Why is it useful? It provides a direct and straightforward method to create a logical expression for *any* truth table. If you can describe what you want a circuit to do in a truth table, you can use SOP to build the circuit's brain. How to Convert a Truth Table to an SOP Expression (The 4-Step Method)
This is the most important skill for today. Let's use a 3-input truth table as our main example. Imagine a system with three switches (A, B, C) and one light bulb (Y). The truth table below shows when we want the light to be ON (Y=1).