Boolean Algebra 1 a Boolean addition OR AB
Boolean Algebra 1 a. Boolean addition (OR): A+B = B+A 1 b. Boolean multiplication (AND): A • B = B • A 2 a. Boolean addition (OR): (A+B)+C = A+(B+C) = A+B+C 2 b. Boolean Multiplication (AND): (A • B) • C = A • (B • C) = A • B • C = ABC 3 a. A • (B+C) = A • B+A • C 3 b. A+(B • C) = (A+B) • (A+C) 3 c. A + AB = A 4 a. A • 1 = A 5 a. A • 0 = 0 6 a. A • A = A A + A΄B = A + B 4 b. A+0 = A 5 b. A+1 = 1 6 b. A+A = A (A + B)(A + C) = A + BC A + A΄ = 1 De Morgan’s Theorem AA΄ = 0 Law 1. A΄ + B΄ = (A • B)΄ Inverting the inputs to an OR gate 8 a. A • (A+B) = A changes its function to NAND. 8 b. A+(A • B) = A Law 2. 8 c. A+(A+B) = (A+B) A΄ • B΄ = (A +B )΄ Inverting the inputs to an AND gate 8 d. A • (A • B) = (A • B) changes its function to NOR Π. Δ. Μ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ & ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ. 3
K-Maps solving Ανεβατόρι S 1 0 1 1 0 0 0 1 1 0 S 1 S 2 B 1 B 2 M 00 01 11 10 S 2 0 0 0 1 1 1 0 B 1 1 1 0 0 0 1 0 000 C 1 B 2 0 0 1 1 0 0 0 001 M 0 0 0 0 1 1 011 C 1 0 1 1 1 0 0 010 C 2 0 0 0 1 1 110 C 1 M 0 0 0 1 1 111 100 C 1 C 1= S 1 S 2 B 1’ B 2’ M’ + S 1 S 2’B 2’M’ + S 2’ B 1’ B 2’ M’= S 2’ B 2’ M’(B 1’+S 1) Π. Δ. Μ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ & ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ. 6
K-Maps solving Ανεβατόρι S 1 0 1 1 0 0 0 1 1 0 S 1 S 2 B 1 B 2 M 00 01 11 10 S 2 0 0 0 1 1 1 0 B 1 1 1 0 0 0 1 0 000 C 2 B 2 0 0 1 1 0 0 0 001 M 0 0 0 0 1 1 011 C 1 0 1 1 1 0 0 0 1 0 0 C 2 0 0 0 1 1 1 0 0 1 1 010 110 C 2 C 2 M 0 0 0 1 1 111 100 C 2= Π. Δ. Μ ΤΜΗΜΑ ΗΛΕΚΤΡΟΛΟΓΩΝ ΜΗΧΑΝΙΚΩΝ & ΜΗΧΑΝΙΚΩΝ ΥΠΟΛΟΓΙΣΤΩΝ. . 7
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