Промежуточные таблицы истинности:¬X:
X2∧X3:
X1∧(¬X):
X1 | X | ¬X | X1∧(¬X) |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
X1∨(X2∧X3):
X1 | X2 | X3 | X2∧X3 | X1∨(X2∧X3) |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 1 | 1 |
(X1∨(X2∧X3))∨(X1∧(¬X)):
X1 | X2 | X3 | X | X2∧X3 | X1∨(X2∧X3) | ¬X | X1∧(¬X) | (X1∨(X2∧X3))∨(X1∧(¬X)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 |
Y≡((X1∨(X2∧X3))∨(X1∧(¬X))):
Y | X1 | X2 | X3 | X | X2∧X3 | X1∨(X2∧X3) | ¬X | X1∧(¬X) | (X1∨(X2∧X3))∨(X1∧(¬X)) | Y≡((X1∨(X2∧X3))∨(X1∧(¬X))) |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 |
Общая таблица истинности:
Y | X1 | X2 | X3 | X | ¬X | X2∧X3 | X1∧(¬X) | X1∨(X2∧X3) | (X1∨(X2∧X3))∨(X1∧(¬X)) | Y≡X1∨X2∧X3∨X1∧¬X |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:
Y | X1 | X2 | X3 | X | F |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 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 | 0 |
0 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
F
сднф = ¬Y∧¬X1∧¬X2∧¬X3∧¬X ∨ ¬Y∧¬X1∧¬X2∧¬X3∧X ∨ ¬Y∧¬X1∧¬X2∧X3∧¬X ∨ ¬Y∧¬X1∧¬X2∧X3∧X ∨ ¬Y∧¬X1∧X2∧¬X3∧¬X ∨ ¬Y∧¬X1∧X2∧¬X3∧X ∨ Y∧¬X1∧X2∧X3∧¬X ∨ Y∧¬X1∧X2∧X3∧X ∨ Y∧X1∧¬X2∧¬X3∧¬X ∨ Y∧X1∧¬X2∧¬X3∧X ∨ Y∧X1∧¬X2∧X3∧¬X ∨ Y∧X1∧¬X2∧X3∧X ∨ Y∧X1∧X2∧¬X3∧¬X ∨ Y∧X1∧X2∧¬X3∧X ∨ Y∧X1∧X2∧X3∧¬X ∨ Y∧X1∧X2∧X3∧X
Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:
Y | X1 | X2 | X3 | X | F |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 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 | 0 |
0 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
F
скнф = (Y∨X1∨¬X2∨¬X3∨X) ∧ (Y∨X1∨¬X2∨¬X3∨¬X) ∧ (Y∨¬X1∨X2∨X3∨X) ∧ (Y∨¬X1∨X2∨X3∨¬X) ∧ (Y∨¬X1∨X2∨¬X3∨X) ∧ (Y∨¬X1∨X2∨¬X3∨¬X) ∧ (Y∨¬X1∨¬X2∨X3∨X) ∧ (Y∨¬X1∨¬X2∨X3∨¬X) ∧ (Y∨¬X1∨¬X2∨¬X3∨X) ∧ (Y∨¬X1∨¬X2∨¬X3∨¬X) ∧ (¬Y∨X1∨X2∨X3∨X) ∧ (¬Y∨X1∨X2∨X3∨¬X) ∧ (¬Y∨X1∨X2∨¬X3∨X) ∧ (¬Y∨X1∨X2∨¬X3∨¬X) ∧ (¬Y∨X1∨¬X2∨X3∨X) ∧ (¬Y∨X1∨¬X2∨X3∨¬X)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции
Y | X1 | X2 | X3 | X | Fж |
0 | 0 | 0 | 0 | 0 | 1 |
0 | 0 | 0 | 0 | 1 | 1 |
0 | 0 | 0 | 1 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 |
0 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 1 | 0 | 1 | 1 |
0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 0 |
0 | 1 | 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 | 0 |
0 | 1 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 1 |
1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 |
Построим полином Жегалкина:
F
ж = C
00000 ⊕ C
10000∧Y ⊕ C
01000∧X1 ⊕ C
00100∧X2 ⊕ C
00010∧X3 ⊕ C
00001∧X ⊕ C
11000∧Y∧X1 ⊕ C
10100∧Y∧X2 ⊕ C
10010∧Y∧X3 ⊕ C
10001∧Y∧X ⊕ C
01100∧X1∧X2 ⊕ C
01010∧X1∧X3 ⊕ C
01001∧X1∧X ⊕ C
00110∧X2∧X3 ⊕ C
00101∧X2∧X ⊕ C
00011∧X3∧X ⊕ C
11100∧Y∧X1∧X2 ⊕ C
11010∧Y∧X1∧X3 ⊕ C
11001∧Y∧X1∧X ⊕ C
10110∧Y∧X2∧X3 ⊕ C
10101∧Y∧X2∧X ⊕ C
10011∧Y∧X3∧X ⊕ C
01110∧X1∧X2∧X3 ⊕ C
01101∧X1∧X2∧X ⊕ C
01011∧X1∧X3∧X ⊕ C
00111∧X2∧X3∧X ⊕ C
11110∧Y∧X1∧X2∧X3 ⊕ C
11101∧Y∧X1∧X2∧X ⊕ C
11011∧Y∧X1∧X3∧X ⊕ C
10111∧Y∧X2∧X3∧X ⊕ C
01111∧X1∧X2∧X3∧X ⊕ C
11111∧Y∧X1∧X2∧X3∧X
Так как F
ж(00000) = 1, то С
00000 = 1.
Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы:
F
ж(10000) = С
00000 ⊕ С
10000 = 0 => С
10000 = 1 ⊕ 0 = 1
F
ж(01000) = С
00000 ⊕ С
01000 = 0 => С
01000 = 1 ⊕ 0 = 1
F
ж(00100) = С
00000 ⊕ С
00100 = 1 => С
00100 = 1 ⊕ 1 = 0
F
ж(00010) = С
00000 ⊕ С
00010 = 1 => С
00010 = 1 ⊕ 1 = 0
F
ж(00001) = С
00000 ⊕ С
00001 = 1 => С
00001 = 1 ⊕ 1 = 0
F
ж(11000) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
11000 = 1 => С
11000 = 1 ⊕ 1 ⊕ 1 ⊕ 1 = 0
F
ж(10100) = С
00000 ⊕ С
10000 ⊕ С
00100 ⊕ С
10100 = 0 => С
10100 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(10010) = С
00000 ⊕ С
10000 ⊕ С
00010 ⊕ С
10010 = 0 => С
10010 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(10001) = С
00000 ⊕ С
10000 ⊕ С
00001 ⊕ С
10001 = 0 => С
10001 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(01100) = С
00000 ⊕ С
01000 ⊕ С
00100 ⊕ С
01100 = 0 => С
01100 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(01010) = С
00000 ⊕ С
01000 ⊕ С
00010 ⊕ С
01010 = 0 => С
01010 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(01001) = С
00000 ⊕ С
01000 ⊕ С
00001 ⊕ С
01001 = 0 => С
01001 = 1 ⊕ 1 ⊕ 0 ⊕ 0 = 0
F
ж(00110) = С
00000 ⊕ С
00100 ⊕ С
00010 ⊕ С
00110 = 0 => С
00110 = 1 ⊕ 0 ⊕ 0 ⊕ 0 = 1
F
ж(00101) = С
00000 ⊕ С
00100 ⊕ С
00001 ⊕ С
00101 = 1 => С
00101 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(00011) = С
00000 ⊕ С
00010 ⊕ С
00001 ⊕ С
00011 = 1 => С
00011 = 1 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(11100) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00100 ⊕ С
11000 ⊕ С
10100 ⊕ С
01100 ⊕ С
11100 = 1 => С
11100 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(11010) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00010 ⊕ С
11000 ⊕ С
10010 ⊕ С
01010 ⊕ С
11010 = 1 => С
11010 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(11001) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00001 ⊕ С
11000 ⊕ С
10001 ⊕ С
01001 ⊕ С
11001 = 1 => С
11001 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(10110) = С
00000 ⊕ С
10000 ⊕ С
00100 ⊕ С
00010 ⊕ С
10100 ⊕ С
10010 ⊕ С
00110 ⊕ С
10110 = 1 => С
10110 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
F
ж(10101) = С
00000 ⊕ С
10000 ⊕ С
00100 ⊕ С
00001 ⊕ С
10100 ⊕ С
10001 ⊕ С
00101 ⊕ С
10101 = 0 => С
10101 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(10011) = С
00000 ⊕ С
10000 ⊕ С
00010 ⊕ С
00001 ⊕ С
10010 ⊕ С
10001 ⊕ С
00011 ⊕ С
10011 = 0 => С
10011 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(01110) = С
00000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00010 ⊕ С
01100 ⊕ С
01010 ⊕ С
00110 ⊕ С
01110 = 0 => С
01110 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 = 1
F
ж(01101) = С
00000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00001 ⊕ С
01100 ⊕ С
01001 ⊕ С
00101 ⊕ С
01101 = 0 => С
01101 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(01011) = С
00000 ⊕ С
01000 ⊕ С
00010 ⊕ С
00001 ⊕ С
01010 ⊕ С
01001 ⊕ С
00011 ⊕ С
01011 = 0 => С
01011 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(00111) = С
00000 ⊕ С
00100 ⊕ С
00010 ⊕ С
00001 ⊕ С
00110 ⊕ С
00101 ⊕ С
00011 ⊕ С
00111 = 0 => С
00111 = 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(11110) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00010 ⊕ С
11000 ⊕ С
10100 ⊕ С
10010 ⊕ С
01100 ⊕ С
01010 ⊕ С
00110 ⊕ С
11100 ⊕ С
11010 ⊕ С
10110 ⊕ С
01110 ⊕ С
11110 = 1 => С
11110 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 = 0
F
ж(11101) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00001 ⊕ С
11000 ⊕ С
10100 ⊕ С
10001 ⊕ С
01100 ⊕ С
01001 ⊕ С
00101 ⊕ С
11100 ⊕ С
11001 ⊕ С
10101 ⊕ С
01101 ⊕ С
11101 = 1 => С
11101 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(11011) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00010 ⊕ С
00001 ⊕ С
11000 ⊕ С
10010 ⊕ С
10001 ⊕ С
01010 ⊕ С
01001 ⊕ С
00011 ⊕ С
11010 ⊕ С
11001 ⊕ С
10011 ⊕ С
01011 ⊕ С
11011 = 1 => С
11011 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(10111) = С
00000 ⊕ С
10000 ⊕ С
00100 ⊕ С
00010 ⊕ С
00001 ⊕ С
10100 ⊕ С
10010 ⊕ С
10001 ⊕ С
00110 ⊕ С
00101 ⊕ С
00011 ⊕ С
10110 ⊕ С
10101 ⊕ С
10011 ⊕ С
00111 ⊕ С
10111 = 1 => С
10111 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
F
ж(01111) = С
00000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00010 ⊕ С
00001 ⊕ С
01100 ⊕ С
01010 ⊕ С
01001 ⊕ С
00110 ⊕ С
00101 ⊕ С
00011 ⊕ С
01110 ⊕ С
01101 ⊕ С
01011 ⊕ С
00111 ⊕ С
01111 = 0 => С
01111 = 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(11111) = С
00000 ⊕ С
10000 ⊕ С
01000 ⊕ С
00100 ⊕ С
00010 ⊕ С
00001 ⊕ С
11000 ⊕ С
10100 ⊕ С
10010 ⊕ С
10001 ⊕ С
01100 ⊕ С
01010 ⊕ С
01001 ⊕ С
00110 ⊕ С
00101 ⊕ С
00011 ⊕ С
11100 ⊕ С
11010 ⊕ С
11001 ⊕ С
10110 ⊕ С
10101 ⊕ С
10011 ⊕ С
01110 ⊕ С
01101 ⊕ С
01011 ⊕ С
00111 ⊕ С
11110 ⊕ С
11101 ⊕ С
11011 ⊕ С
10111 ⊕ С
01111 ⊕ С
11111 = 1 => С
11111 = 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 0
Таким образом, полином Жегалкина будет равен:
F
ж = 1 ⊕ Y ⊕ X1 ⊕ X2∧X3 ⊕ X1∧X2∧X3
Логическая схема, соответствующая полиному Жегалкина: