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Boolean Algebra Laws — TechAmbitionX Boolean Algebra Laws — TechAmbitionX Cheat-sheet: fundamentals + derived laws. Boolean algebra is the math of 0s and 1s . These rules let you simplify expressions and design efficient circuits. Fundamental Laws Identity: A + 0 = A , A · 1 = A Null / Domination: A + 1 = 1 , A · 0 = 0 Idempotent: A + A = A , A · A = A Complement: A + A' = 1 , A · A' = 0 Involution (Double negation): (A')' = A Algebraic Laws Commutative: A + B = B + A , A · B = B · A Associative: (A + B) + C = A + (B + C) , (A · B) · C = A · (B · C) Distributive: A · (B + C) = A · B + A · C , A + (B · C) = (A + B) · (A + C) Important Simplification Laws Absorption: A + (A · B) = A , A · (A + B) = A Complement / Complementarity: A + A' = 1 , A · A' = 0 De Morgan's Theorems: (A · B)' = A...

Binary Coded Decimal (BCD) — TechAmbitionX 🔹 1. What is BCD? BCD (Binary Coded Decimal) is a way of representing decimal numbers (0–9) in binary form using 4 bits for each digit . Example: Decimal 59 → BCD = 0101 1001 Pure Binary 59 → 111011 Notice how in BCD, each digit is separate (5 = 0101, 9 = 1001). This makes it easier for circuits to display numbers. 🔹 2. Why use BCD? Normal binary is compact, but BCD is better when numbers need to be shown to humans (digit by digit). 💡 Devices like digital clocks, calculators, counters , and 7-segment displays often use BCD internally. 🔹 3. Rules of BCD Each digit = 4 bits (nibble). Valid range = 0000 (0) to 1001 (9). 1010–1111 are invalid in standard BCD. 🔹 4. BCD Truth Table (0–9) Decimal BCD (8421) 0 0...

Logic Gates - Digital Electronics Basics (AND, OR, NOT, etc.) | TechAmbitionX | Notes By Mr. BILRED Logic Gates Definition: Logic gates are the basic building blocks of digital electronics. They take one or more binary inputs (0 = LOW / FALSE, 1 = HIGH / TRUE) and give a single output, based on simple logic rules. Key Idea: They work using Boolean Algebra , where: AND → Multiplication (·) OR → Addition (+) NOT → Complement (′) Types of Basic Logic Gates 1. AND Gate Definition: Output is 1 only when all inputs are 1. Formula: Y = A · B Example IC: 7408 (Quad 2-input AND gate) A B Output (A·B) 0 0 0 0 1 0 1 0 0 1 1 1 2. OR Gate Definition: Output is 1 if any input is 1. Formula: Y = A + B Example IC: 7432 (Quad 2-input OR gate) A B Output (A + B) 0 0 0 0 1 1 1 0 1 1 1 1 3. NOT Gate (Inverter) Definition: ...