Sistem digital dan gelombang

Rezha Ramadhan Pratama 1703015094 Materi Aljabar Boolean Aturan – Aturan Aljabar Boolean Commutative law of addition A+B = B+A The order of ORing does not matter Commutative law of Multiplication AB = BA The order of ANDing does not matter   Associative law addition A + (B + C) = (A + B) + C The group of ORed variables does not matter         5   A (BC) = (AB) C The group of ANDed variables does not matter Distributive Law A(B + C) = AB + AC  (A + B) (C + D) = AC + AD + BC + BD BOOLEAN RULES : 1)      A + 0 = A In math if you add 0 you have changed nothing In Boolean Algebra ORing with 0 changes nothing 2)      A + 1 = 1      ORing with 1 must give a 1 since if any input is 1 an OR gate will give a 1 3)      A  * 0 = 0 In math if 0 is multiplied with anything you get 0. If you AND anything with 0 you get 0 4)      A * 1 = A ANDing anything with 1 wi...

Rezha Ramadhan Pratama 1703015094 Tugas 3. Rangkuman materi Aljabar Boolean Gerbang Logika dan Aljabar Boolean Aljabar Boolean adalah alat yang penting dalam menggambarkan, menganalisa, merancang, dan mengimplementasikan rangkaian digital. Ø    Konstanta Boolean dan Variabel. Aljabar Boolean dibawah ini hanya mempunyai dua nilai : 0 dan 1. Logika 0 dapat dikatakan : false, off, low, no, saklar terbuka. Logika 1 dapat dikatakan: true, on, high, yes, saklar tertutup. Tiga operasi logika dasar: OR, AND, dan NOT. Ø    Tabel Kebenaran Sebuah tabel kebenaran menggambarkan hubungan antara input dan ouput sebuah rangkaian logika. Jumlah The number of entries corresponds to the number of inputs. For example a 2 input table would have 2 2 = 4 entries. A 3 input table would have 2 3 = 8 entries Ø    OR Operation with OR Gates ·         The Boolean expression for the OR operation is X = A + B This is read as “x equals A or B.”  X...

Rezha Ramadhan Pratama 1703015094 Teorema DeMorgans   Teorema DeMorgans Komplemen dua atau lebih variable gerbang AND sama dengan komplemen variable khusus gerbang OR Persamaan Komplemen 2 atau lebih variable gerbang OR sama dengan komplemen variable khusus gerbang AND Persamaan : Kesetaraan gerbang dan hubungan table kebenaran yang digambarkan oleh Teorema DeMorgan. XY = X + Y X + Y = XY Contoh : Contoh : Analisis Boolean rangkaian Logika Jika A = 1, B = 1, C = 1 and D = 1, maka outputnya adalah ??? Tabel kebenaran: Penyederhanaan menggunakan Aljabar Boolean Contoh : draw your possible logic gate? Simplify this expression using Boolean algebra? Exercise : Analiyze the circuit below 1.       Y = ?? 2.       Simplify the Boolean expression found 1 Exercise : Sumber :  onlinelearning.uhamka.ac.id