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Таблица истинности ONLINE
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Таблица истинности для функции (X∨Y∨Z)∧(X∨Y∨¬Z)∧(¬X∨Y∨¬Z)∧(¬X∨¬Y∨¬Z):
Промежуточные таблицы истинности:X∨Y: (X∨Y)∨Z: X | Y | Z | X∨Y | (X∨Y)∨Z | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
¬Z: (X∨Y)∨(¬Z): X | Y | Z | X∨Y | ¬Z | (X∨Y)∨(¬Z) | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
¬X: (¬X)∨Y: X | Y | ¬X | (¬X)∨Y | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
((¬X)∨Y)∨(¬Z): X | Y | Z | ¬X | (¬X)∨Y | ¬Z | ((¬X)∨Y)∨(¬Z) | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
¬Y: (¬X)∨(¬Y): X | Y | ¬X | ¬Y | (¬X)∨(¬Y) | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
((¬X)∨(¬Y))∨(¬Z): X | Y | Z | ¬X | ¬Y | (¬X)∨(¬Y) | ¬Z | ((¬X)∨(¬Y))∨(¬Z) | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
((X∨Y)∨Z)∧((X∨Y)∨(¬Z)): X | Y | Z | X∨Y | (X∨Y)∨Z | X∨Y | ¬Z | (X∨Y)∨(¬Z) | ((X∨Y)∨Z)∧((X∨Y)∨(¬Z)) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
(((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)): X | Y | Z | X∨Y | (X∨Y)∨Z | X∨Y | ¬Z | (X∨Y)∨(¬Z) | ((X∨Y)∨Z)∧((X∨Y)∨(¬Z)) | ¬X | (¬X)∨Y | ¬Z | ((¬X)∨Y)∨(¬Z) | (((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 |
((((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)))∧(((¬X)∨(¬Y))∨(¬Z)): X | Y | Z | X∨Y | (X∨Y)∨Z | X∨Y | ¬Z | (X∨Y)∨(¬Z) | ((X∨Y)∨Z)∧((X∨Y)∨(¬Z)) | ¬X | (¬X)∨Y | ¬Z | ((¬X)∨Y)∨(¬Z) | (((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)) | ¬X | ¬Y | (¬X)∨(¬Y) | ¬Z | ((¬X)∨(¬Y))∨(¬Z) | ((((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)))∧(((¬X)∨(¬Y))∨(¬Z)) | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
Общая таблица истинности:X | Y | Z | X∨Y | (X∨Y)∨Z | ¬Z | (X∨Y)∨(¬Z) | ¬X | (¬X)∨Y | ((¬X)∨Y)∨(¬Z) | ¬Y | (¬X)∨(¬Y) | ((¬X)∨(¬Y))∨(¬Z) | ((X∨Y)∨Z)∧((X∨Y)∨(¬Z)) | (((X∨Y)∨Z)∧((X∨Y)∨(¬Z)))∧(((¬X)∨Y)∨(¬Z)) | (X∨Y∨Z)∧(X∨Y∨¬Z)∧(¬X∨Y∨¬Z)∧(¬X∨¬Y∨¬Z) | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: X | Y | Z | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
F сднф = ¬X∧Y∧¬Z ∨ ¬X∧Y∧Z ∨ X∧¬Y∧¬Z ∨ X∧Y∧¬Z Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: X | Y | Z | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
F скнф = (X∨Y∨Z) ∧ (X∨Y∨¬Z) ∧ (¬X∨Y∨¬Z) ∧ (¬X∨¬Y∨¬Z) Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции X | Y | Z | Fж | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 |
Построим полином Жегалкина: F ж = C 000 ⊕ C 100∧X ⊕ C 010∧Y ⊕ C 001∧Z ⊕ C 110∧X∧Y ⊕ C 101∧X∧Z ⊕ C 011∧Y∧Z ⊕ C 111∧X∧Y∧Z 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 = 1 => С 010 = 0 ⊕ 1 = 1 F ж(001) = С 000 ⊕ С 001 = 0 => С 001 = 0 ⊕ 0 = 0 F ж(110) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 110 = 1 => С 110 = 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1 F ж(101) = С 000 ⊕ С 100 ⊕ С 001 ⊕ С 101 = 0 => С 101 = 0 ⊕ 1 ⊕ 0 ⊕ 0 = 1 F ж(011) = С 000 ⊕ С 010 ⊕ С 001 ⊕ С 011 = 1 => С 011 = 0 ⊕ 1 ⊕ 0 ⊕ 1 = 0 F ж(111) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 001 ⊕ С 110 ⊕ С 101 ⊕ С 011 ⊕ С 111 = 0 => С 111 = 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0 Таким образом, полином Жегалкина будет равен: F ж = X ⊕ Y ⊕ X∧Y ⊕ X∧Z Логическая схема, соответствующая полиному Жегалкина:
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