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Таблица истинности ONLINE
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Таблица истинности для функции ¬(A∧B∧C)∧¬(A∨¬(B∧C))∨¬(A∧B)∧¬(A∨C):
Промежуточные таблицы истинности:A∧B: (A∧B)∧C: A | B | C | A∧B | (A∧B)∧C | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
B∧C: ¬(B∧C): B | C | B∧C | ¬(B∧C) | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
A∨(¬(B∧C)): A | B | C | B∧C | ¬(B∧C) | A∨(¬(B∧C)) | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
A∨C: ¬((A∧B)∧C): A | B | C | A∧B | (A∧B)∧C | ¬((A∧B)∧C) | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
¬(A∨(¬(B∧C))): A | B | C | B∧C | ¬(B∧C) | A∨(¬(B∧C)) | ¬(A∨(¬(B∧C))) | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
¬(A∧B): A | B | A∧B | ¬(A∧B) | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
¬(A∨C): A | C | A∨C | ¬(A∨C) | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
(¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))): A | B | C | A∧B | (A∧B)∧C | ¬((A∧B)∧C) | B∧C | ¬(B∧C) | A∨(¬(B∧C)) | ¬(A∨(¬(B∧C))) | (¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))) | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
(¬(A∧B))∧(¬(A∨C)): A | B | C | A∧B | ¬(A∧B) | A∨C | ¬(A∨C) | (¬(A∧B))∧(¬(A∨C)) | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
((¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))))∨((¬(A∧B))∧(¬(A∨C))): A | B | C | A∧B | (A∧B)∧C | ¬((A∧B)∧C) | B∧C | ¬(B∧C) | A∨(¬(B∧C)) | ¬(A∨(¬(B∧C))) | (¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))) | A∧B | ¬(A∧B) | A∨C | ¬(A∨C) | (¬(A∧B))∧(¬(A∨C)) | ((¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))))∨((¬(A∧B))∧(¬(A∨C))) | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
Общая таблица истинности:A | B | C | A∧B | (A∧B)∧C | B∧C | ¬(B∧C) | A∨(¬(B∧C)) | A∨C | ¬((A∧B)∧C) | ¬(A∨(¬(B∧C))) | ¬(A∧B) | ¬(A∨C) | (¬((A∧B)∧C))∧(¬(A∨(¬(B∧C)))) | (¬(A∧B))∧(¬(A∨C)) | ¬(A∧B∧C)∧¬(A∨¬(B∧C))∨¬(A∧B)∧¬(A∨C) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: A | B | C | F | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
F сднф = ¬A∧¬B∧¬C ∨ ¬A∧B∧¬C ∨ ¬A∧B∧C Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: A | B | C | F | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
F скнф = (A∨B∨¬C) ∧ (¬A∨B∨C) ∧ (¬A∨B∨¬C) ∧ (¬A∨¬B∨C) ∧ (¬A∨¬B∨¬C) Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции A | B | C | Fж | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
Построим полином Жегалкина: F ж = C 000 ⊕ C 100∧A ⊕ C 010∧B ⊕ C 001∧C ⊕ C 110∧A∧B ⊕ C 101∧A∧C ⊕ C 011∧B∧C ⊕ C 111∧A∧B∧C Так как F ж(000) = 1, то С 000 = 1. Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы: F ж(100) = С 000 ⊕ С 100 = 0 => С 100 = 1 ⊕ 0 = 1 F ж(010) = С 000 ⊕ С 010 = 1 => С 010 = 1 ⊕ 1 = 0 F ж(001) = С 000 ⊕ С 001 = 0 => С 001 = 1 ⊕ 0 = 1 F ж(110) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 110 = 0 => С 110 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0 F ж(101) = С 000 ⊕ С 100 ⊕ С 001 ⊕ С 101 = 0 => С 101 = 1 ⊕ 1 ⊕ 1 ⊕ 0 = 1 F ж(011) = С 000 ⊕ С 010 ⊕ С 001 ⊕ С 011 = 1 => С 011 = 1 ⊕ 0 ⊕ 1 ⊕ 1 = 1 F ж(111) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 001 ⊕ С 110 ⊕ С 101 ⊕ С 011 ⊕ С 111 = 0 => С 111 = 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 = 1 Таким образом, полином Жегалкина будет равен: F ж = 1 ⊕ A ⊕ C ⊕ A∧C ⊕ B∧C ⊕ A∧B∧C Логическая схема, соответствующая полиному Жегалкина:
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