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Таблица истинности ONLINE
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Таблица истинности для функции (¬D→C)∧(P∧¬B→D):
Промежуточные таблицы истинности:¬D: (¬D)→C: | D | C | ¬D | (¬D)→C | | 0 | 0 | 1 | 0 | | 0 | 1 | 1 | 1 | | 1 | 0 | 0 | 1 | | 1 | 1 | 0 | 1 |
¬B: P∧(¬B): | P | B | ¬B | P∧(¬B) | | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 |
(P∧(¬B))→D: | P | B | D | ¬B | P∧(¬B) | (P∧(¬B))→D | | 0 | 0 | 0 | 1 | 0 | 1 | | 0 | 0 | 1 | 1 | 0 | 1 | | 0 | 1 | 0 | 0 | 0 | 1 | | 0 | 1 | 1 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | 0 | | 1 | 0 | 1 | 1 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 |
((¬D)→C)∧((P∧(¬B))→D): | D | C | P | B | ¬D | (¬D)→C | ¬B | P∧(¬B) | (P∧(¬B))→D | ((¬D)→C)∧((P∧(¬B))→D) | | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
Общая таблица истинности:| D | C | P | B | ¬D | (¬D)→C | ¬B | P∧(¬B) | (P∧(¬B))→D | (¬D→C)∧(P∧¬B→D) | | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: | D | C | P | B | F | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 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 |
F сднф = ¬D∧C∧¬P∧¬B ∨ ¬D∧C∧¬P∧B ∨ ¬D∧C∧P∧B ∨ D∧¬C∧¬P∧¬B ∨ D∧¬C∧¬P∧B ∨ D∧¬C∧P∧¬B ∨ D∧¬C∧P∧B ∨ D∧C∧¬P∧¬B ∨ D∧C∧¬P∧B ∨ D∧C∧P∧¬B ∨ D∧C∧P∧B Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: | D | C | P | B | F | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 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 |
F скнф = (D∨C∨P∨B) ∧ (D∨C∨P∨¬B) ∧ (D∨C∨¬P∨B) ∧ (D∨C∨¬P∨¬B) ∧ (D∨¬C∨¬P∨B) Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции | D | C | P | B | Fж | | 0 | 0 | 0 | 0 | 0 | | 0 | 0 | 0 | 1 | 0 | | 0 | 0 | 1 | 0 | 0 | | 0 | 0 | 1 | 1 | 0 | | 0 | 1 | 0 | 0 | 1 | | 0 | 1 | 0 | 1 | 1 | | 0 | 1 | 1 | 0 | 0 | | 0 | 1 | 1 | 1 | 1 | | 1 | 0 | 0 | 0 | 1 | | 1 | 0 | 0 | 1 | 1 | | 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 |
Построим полином Жегалкина: F ж = C 0000 ⊕ C 1000∧D ⊕ C 0100∧C ⊕ C 0010∧P ⊕ C 0001∧B ⊕ C 1100∧D∧C ⊕ C 1010∧D∧P ⊕ C 1001∧D∧B ⊕ C 0110∧C∧P ⊕ C 0101∧C∧B ⊕ C 0011∧P∧B ⊕ C 1110∧D∧C∧P ⊕ C 1101∧D∧C∧B ⊕ C 1011∧D∧P∧B ⊕ C 0111∧C∧P∧B ⊕ C 1111∧D∧C∧P∧B Так как F ж(0000) = 0, то С 0000 = 0. Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы: F ж(1000) = С 0000 ⊕ С 1000 = 1 => С 1000 = 0 ⊕ 1 = 1 F ж(0100) = С 0000 ⊕ С 0100 = 1 => С 0100 = 0 ⊕ 1 = 1 F ж(0010) = С 0000 ⊕ С 0010 = 0 => С 0010 = 0 ⊕ 0 = 0 F ж(0001) = С 0000 ⊕ С 0001 = 0 => С 0001 = 0 ⊕ 0 = 0 F ж(1100) = С 0000 ⊕ С 1000 ⊕ С 0100 ⊕ С 1100 = 1 => С 1100 = 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1 F ж(1010) = С 0000 ⊕ С 1000 ⊕ С 0010 ⊕ С 1010 = 1 => С 1010 = 0 ⊕ 1 ⊕ 0 ⊕ 1 = 0 F ж(1001) = С 0000 ⊕ С 1000 ⊕ С 0001 ⊕ С 1001 = 1 => С 1001 = 0 ⊕ 1 ⊕ 0 ⊕ 1 = 0 F ж(0110) = С 0000 ⊕ С 0100 ⊕ С 0010 ⊕ С 0110 = 0 => С 0110 = 0 ⊕ 1 ⊕ 0 ⊕ 0 = 1 F ж(0101) = С 0000 ⊕ С 0100 ⊕ С 0001 ⊕ С 0101 = 1 => С 0101 = 0 ⊕ 1 ⊕ 0 ⊕ 1 = 0 F ж(0011) = С 0000 ⊕ С 0010 ⊕ С 0001 ⊕ С 0011 = 0 => С 0011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0 F ж(1110) = С 0000 ⊕ С 1000 ⊕ С 0100 ⊕ С 0010 ⊕ С 1100 ⊕ С 1010 ⊕ С 0110 ⊕ С 1110 = 1 => С 1110 = 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 = 1 F ж(1101) = С 0000 ⊕ С 1000 ⊕ С 0100 ⊕ С 0001 ⊕ С 1100 ⊕ С 1001 ⊕ С 0101 ⊕ С 1101 = 1 => С 1101 = 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0 F ж(1011) = С 0000 ⊕ С 1000 ⊕ С 0010 ⊕ С 0001 ⊕ С 1010 ⊕ С 1001 ⊕ С 0011 ⊕ С 1011 = 1 => С 1011 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0 F ж(0111) = С 0000 ⊕ С 0100 ⊕ С 0010 ⊕ С 0001 ⊕ С 0110 ⊕ С 0101 ⊕ С 0011 ⊕ С 0111 = 1 => С 0111 = 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1 F ж(1111) = С 0000 ⊕ С 1000 ⊕ С 0100 ⊕ С 0010 ⊕ С 0001 ⊕ С 1100 ⊕ С 1010 ⊕ С 1001 ⊕ С 0110 ⊕ С 0101 ⊕ С 0011 ⊕ С 1110 ⊕ С 1101 ⊕ С 1011 ⊕ С 0111 ⊕ С 1111 = 1 => С 1111 = 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 1 Таким образом, полином Жегалкина будет равен: F ж = D ⊕ C ⊕ D∧C ⊕ C∧P ⊕ D∧C∧P ⊕ C∧P∧B ⊕ D∧C∧P∧B Логическая схема, соответствующая полиному Жегалкина:
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