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