Lesson Notes By Weeks and Term v4 - SHS 3
ELECTRONIC COMPONENTS AND CIRCUITS
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ELECTRONIC COMPONENTS AND CIRCUITS
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Subject: Applied Technology
Class: SHS 3
Term: 2nd Term
Week: 18
Grade code: 2.5.2.LI.8
Strand code: 4
Sub-strand code: 2
Content standard code: 2.5.2.CS.1
Indicator code: 2.5.2.LI.8
Theme: ELECTRICAL AND ELECTRONIC TECHNOLOGY
Subtheme: ELECTRONIC COMPONENTS AND CIRCUITS
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Welcome, future engineers and technicians! Today, we are diving into the "brain language" of every digital device you use—from your mobile phone to the traffic lights in Accra, to the computer in the school's ICT lab. This language is called Boolean Algebra. Just like we simplify algebraic expressions in mathematics to make them easier to solve, we simplify Boolean expressions to make electronic circuits simpler, cheaper, faster, and more reliable. A complex circuit with 10 logic gates might be simplified to one with only 5 gates, saving cost and energy. Mastering this skill is fundamental to designing and troubleshooting any digital system.
Before we dive into the new theorems, let's quickly recall our basic Boolean operations: AND (Product): Represented by a dot (`.`) or just placing variables together (e.g., `A.B` or `AB`). Output is 1 only if ALL inputs are 1. OR (Sum): Represented by a plus sign (`+`) (e.g., `A + B`). Output is 1 if AT LEAST ONE input is 1. NOT (Inverse/Complement): Represented by a bar over the variable ( `Ā` ) or a prime symbol (`A'`). It inverts the input (0 becomes 1, 1 becomes 0).
Now, let's learn our powerful new tools for simplification. Concept 1: De Morgan's Theorems
Augustus De Morgan, a mathematician, gave us two powerful theorems that help us deal with expressions that are negated (inverted). They provide a way to convert expressions from AND-form to OR-form and vice-versa, which is incredibly useful.
A simple way to remember De Morgan's theorems is the phrase: "Break the bar, change the sign."