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you will learn the basics in Boolean logic circuits Understand that control systems are made of logic gates and they rely on the logic rules (Boolean Maths) To be able to control a system with electronic devices like a nuclear reactor, you need to predict and conceive all possible events To link the catastrophe of fukushima with unforeseeable cumulative events leading to the melt down. Interpret the results of truth tables Create, modify and interpret simple logic circuit diagrams

4.6 Fundamentals of computer systems 4.6  Logic gates                                https://forms.gle/BFvLroLxGfuP5AA57 4.6  Boolean gate combinations     https://forms.gle/EWYwWDzhwikC1bSVA 4.6  Building_circuits 4.6  Simplifying boolean equations  https://forms.gle/1okaQsUfNR9jsH7C7 4.6  Boolean identities 4.6  De Morgan’s Laws     https://forms.gle/VzVG6UQh2VtmFD8G8 4.6  Gate conversion 4.6  Uses of gates 4.6  Hardware and software This comprehensive guide covers fundamental digital logic concepts including full and half adders, flip-flops, Boolean algebra, and De Morgan’s laws. Full adders perform three-bit addition using Sum = A⊕B⊕Cin and Carry = AB+BCin+ACin equations. Half adders handle two-bit addition with Sum = A⊕B and Carry = A·B. D-type flip-flops store single bits, updating on clock edges. De Morgan’s laws state (A+B)’ = A’·B’ and (A·B)’ = A’+B’, enabling circuit simplification. Boolean algebra simplification reduces complex expressions using absorption, distribution, and complement laws. Logic gates (AND, OR, NAND, NOR, XOR) form the foundation of digital circuits. NAND and NOR are universal gates, capable of implementing any Boolean function. Circuit analysis involves truth tables, Boolean expressions, and gate-level implementation. Understanding these concepts is essential for digital system design, computer architecture, and embedded systems development. Logic Circuit and Flip-Flop Understanding Question 1: Full Adder Circuit 1. Function: To perform addition of three binary digits (A, B, and Cin) 2. 3. Sum output when A=0, B=1, Cin=1: Sum = A ⊕ B ⊕ Cin = 0 ⊕ 1 ⊕ 1 = 0 4. 5. Truth Table for Full Adder (A B Cin → Sum Cout): 6. 1.0 0 0 → 0 0 2.0 0 1 → 1 0 3.0 1 0 → 1 0 4.0 1 1 → 0 1 5.1 0 0 → 1 0 6.1 0 1 → 0 1 7.1 1 0 → 0 1 8.1 1 1 → 1 1 7. Sum Boolean expression: A ⊕ B ⊕ Cin 8. 9. Carry Boolean expression: Cout = A·B + B·Cin + A·Cin 10. Question 2: Half Adder 1. Boolean equations: Sum = A ⊕ B, Carry = A · B 2. 3. Circuit diagram: Option 3 is closest (though none are perfectly drawn for a half adder - should be XOR for sum, AND for carry) 4. D-Type Flip-Flop 1. Purpose: To store a single bit and update its value on the rising edge of a clock pulse 2. 3. Output: Q = D (copied from input at rising edge) 4. De Morgan’s Laws Quiz Key De Morgan’s Laws: First law: (A + B)’ = A’ · B’ Second law: (A · B)’ = A’ + B’ Boolean Algebra Simplification Key simplifications: 1.Y = X(X + YZ) = X 2.Y = B + BC’ = B 3.Y = (X + Y’)(X + Y’) = X + Y’ 4.Y = XYZ + XYZ’ + XY’Z + XY’Z’ = X 5.Y = A’B’C + A’BC + AB’C + ABC = C 6.Y = X’YZ + XY’Z + XYZ = YZ + XZ Logic Gates Quiz Key points: 1.EXOR: High output when only one input is high 2.NAND gate: Inverted AND operation 3.NOR gate: Inverted OR operation 4.Making gates with inverters: NAND from AND: Invert the output NOR from NAND: Invert both inputs AND from OR: Invert both inputs and output