Boolean Algebra explained | commutative law | Associative Law | distributive law | AND law | OR law

Boolean algebra, a mathematical system dealing with binary values, uses several laws to simplify expressions and solve problems. These laws include commutative, associative, distributive, AND, OR, inversion, De Morgan's, and complement laws. Key Laws of Boolean Algebra: Commutative Law: The order of operands in AND and OR operations doesn't affect the result (e.g., A + B = B + A and A * B = B * A). Associative Law: Grouping of operands in AND and OR operations doesn't affect the result (e.g., (A + B) + C = A + (B + C) and (A * B) * C = A * (B * C)). Distributive Law: Expanding an expression with AND and OR (e.g., A * (B + C) = (A * B) + (A * C)). AND Law: Simplifies AND operations, including the identity law (e.g., A * 0 = 0, A * 1 = A), and the complement law (e.g., A * ~A = 0). OR Law: Simplifies OR operations, including the identity law (e.g., A + 0 = A, A + 1 = 1) and the complement law (e.g., A + ~A = 1). Inversion Law: Double negation of a variable results in the original variable (e.g., (A')' = A). De Morgan's Law: Relates AND and OR operations with negation (e.g., (A + B)' = A' * B'). Complement Law: A variable ANDed with its complement is 0, and a variable ORed with its complement is 1 (e.g., A * ~A = 0, A + ~A = 1). Identity Law: A ANDed with 1 is A, and A ORed with 0 is A (e.g., A * 1 = A, A + 0 = A). Idempotent Law: A ORed or ANDed with itself is A (e.g., A + A = A, A * A = A). Absorption Law: A ORed with (A AND B) is A, and A ANDed with (A OR B) is A (e.g., A + (A * B) = A, A * (A + B) = A). Annulment Law: A variable ANDed with 0 is 0, and a variable ORed with 1 is 1 (e.g., A * 0 = 0, A + 1 = 1). Double Negation Law: Double negation of a variable results in the original variable (e.g., (A')' = A). These laws are crucial for simplifying and manipulating Boolean expressions in various applications, including digital circuits and logic gate design. NAND GATE AS UNIVERSAL GATE:   • NAND GATE AS UNIVERSAL GATE | BASIC GATES ...   NOR GATE AS UNIVERSAL GATE:   • NOR GATE AS UNIVERSAL GATE | BASIC GATES U...   LOGIC GATES EXPLAINED:   • LOGIC GATES  EXPLAINED | UNIVERSAL GATES |...   BINARY ADDITION:   • Binary addition | Number system   BINARY SUBTRACTION:   • Binary subtraction | Number system   BINARY MULTIPLICATION:   • Binary Multiplication | Number system   BINARY DIVISION:   • Binary division | Number system| Digital e...   1's AND 2'S COMPLEMENTS:   • 1's and 2's complement | sign magnitude fo...   CLASSIFICATION OF BINARY CODES:   • Classification of binary codes | numeric |...   GRAY CODE:   • Gray code | binary to gray | gray to binar...   XS-3 CODE:   • XS-3 Code Explained with Solved Examples   ------------------------------------------------------------------------------------------------------------ Time stamps: 0:00-Intro 0:40- Overview of all laws 1:00- All formulas 1:20- Why do we need Boolean algebra 2:30-AND LAW 5:30-OR LAW 8:30-Commutative law 9:00-Associative law 13:30- Commutative law for universal gates 13:50- Associative law for universal gates 14:50-Distributive lae 16:00-Absorption law