Промежуточные таблицы истинности:X1∨X2:
X3∨X4:
X5∨X6:
(X1∨X2)∧(X3∨X4):
X1 | X2 | X3 | X4 | X1∨X2 | X3∨X4 | (X1∨X2)∧(X3∨X4) |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
((X1∨X2)∧(X3∨X4))∧(X5∨X6):
X1 | X2 | X3 | X4 | X5 | X6 | X1∨X2 | X3∨X4 | (X1∨X2)∧(X3∨X4) | X5∨X6 | ((X1∨X2)∧(X3∨X4))∧(X5∨X6) |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Общая таблица истинности:
X1 | X2 | X3 | X4 | X5 | X6 | X1∨X2 | X3∨X4 | X5∨X6 | (X1∨X2)∧(X3∨X4) | (X1∨X2)∧(X3∨X4)∧(X5∨X6) |
0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:
X1 | X2 | X3 | X4 | X5 | X6 | F |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
F
сднф = ¬X1∧X2∧¬X3∧X4∧¬X5∧X6 ∨ ¬X1∧X2∧¬X3∧X4∧X5∧¬X6 ∨ ¬X1∧X2∧¬X3∧X4∧X5∧X6 ∨ ¬X1∧X2∧X3∧¬X4∧¬X5∧X6 ∨ ¬X1∧X2∧X3∧¬X4∧X5∧¬X6 ∨ ¬X1∧X2∧X3∧¬X4∧X5∧X6 ∨ ¬X1∧X2∧X3∧X4∧¬X5∧X6 ∨ ¬X1∧X2∧X3∧X4∧X5∧¬X6 ∨ ¬X1∧X2∧X3∧X4∧X5∧X6 ∨ X1∧¬X2∧¬X3∧X4∧¬X5∧X6 ∨ X1∧¬X2∧¬X3∧X4∧X5∧¬X6 ∨ X1∧¬X2∧¬X3∧X4∧X5∧X6 ∨ X1∧¬X2∧X3∧¬X4∧¬X5∧X6 ∨ X1∧¬X2∧X3∧¬X4∧X5∧¬X6 ∨ X1∧¬X2∧X3∧¬X4∧X5∧X6 ∨ X1∧¬X2∧X3∧X4∧¬X5∧X6 ∨ X1∧¬X2∧X3∧X4∧X5∧¬X6 ∨ X1∧¬X2∧X3∧X4∧X5∧X6 ∨ X1∧X2∧¬X3∧X4∧¬X5∧X6 ∨ X1∧X2∧¬X3∧X4∧X5∧¬X6 ∨ X1∧X2∧¬X3∧X4∧X5∧X6 ∨ X1∧X2∧X3∧¬X4∧¬X5∧X6 ∨ X1∧X2∧X3∧¬X4∧X5∧¬X6 ∨ X1∧X2∧X3∧¬X4∧X5∧X6 ∨ X1∧X2∧X3∧X4∧¬X5∧X6 ∨ X1∧X2∧X3∧X4∧X5∧¬X6 ∨ X1∧X2∧X3∧X4∧X5∧X6
Логическая cхема:
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:
X1 | X2 | X3 | X4 | X5 | X6 | F |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
F
скнф = (X1∨X2∨X3∨X4∨X5∨X6) ∧ (X1∨X2∨X3∨X4∨X5∨¬X6) ∧ (X1∨X2∨X3∨X4∨¬X5∨X6) ∧ (X1∨X2∨X3∨X4∨¬X5∨¬X6) ∧ (X1∨X2∨X3∨¬X4∨X5∨X6) ∧ (X1∨X2∨X3∨¬X4∨X5∨¬X6) ∧ (X1∨X2∨X3∨¬X4∨¬X5∨X6) ∧ (X1∨X2∨X3∨¬X4∨¬X5∨¬X6) ∧ (X1∨X2∨¬X3∨X4∨X5∨X6) ∧ (X1∨X2∨¬X3∨X4∨X5∨¬X6) ∧ (X1∨X2∨¬X3∨X4∨¬X5∨X6) ∧ (X1∨X2∨¬X3∨X4∨¬X5∨¬X6) ∧ (X1∨X2∨¬X3∨¬X4∨X5∨X6) ∧ (X1∨X2∨¬X3∨¬X4∨X5∨¬X6) ∧ (X1∨X2∨¬X3∨¬X4∨¬X5∨X6) ∧ (X1∨X2∨¬X3∨¬X4∨¬X5∨¬X6) ∧ (X1∨¬X2∨X3∨X4∨X5∨X6) ∧ (X1∨¬X2∨X3∨X4∨X5∨¬X6) ∧ (X1∨¬X2∨X3∨X4∨¬X5∨X6) ∧ (X1∨¬X2∨X3∨X4∨¬X5∨¬X6) ∧ (X1∨¬X2∨X3∨¬X4∨X5∨X6) ∧ (X1∨¬X2∨¬X3∨X4∨X5∨X6) ∧ (X1∨¬X2∨¬X3∨¬X4∨X5∨X6) ∧ (¬X1∨X2∨X3∨X4∨X5∨X6) ∧ (¬X1∨X2∨X3∨X4∨X5∨¬X6) ∧ (¬X1∨X2∨X3∨X4∨¬X5∨X6) ∧ (¬X1∨X2∨X3∨X4∨¬X5∨¬X6) ∧ (¬X1∨X2∨X3∨¬X4∨X5∨X6) ∧ (¬X1∨X2∨¬X3∨X4∨X5∨X6) ∧ (¬X1∨X2∨¬X3∨¬X4∨X5∨X6) ∧ (¬X1∨¬X2∨X3∨X4∨X5∨X6) ∧ (¬X1∨¬X2∨X3∨X4∨X5∨¬X6) ∧ (¬X1∨¬X2∨X3∨X4∨¬X5∨X6) ∧ (¬X1∨¬X2∨X3∨X4∨¬X5∨¬X6) ∧ (¬X1∨¬X2∨X3∨¬X4∨X5∨X6) ∧ (¬X1∨¬X2∨¬X3∨X4∨X5∨X6) ∧ (¬X1∨¬X2∨¬X3∨¬X4∨X5∨X6)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции
X1 | X2 | X3 | X4 | X5 | X6 | Fж |
0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 0 | 1 | 1 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 1 | 0 |
0 | 0 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 1 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 1 | 1 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 1 | 0 |
0 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 1 | 1 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 1 | 1 |
0 | 1 | 0 | 1 | 1 | 0 | 1 |
0 | 1 | 0 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 1 |
0 | 1 | 1 | 0 | 1 | 1 | 1 |
0 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 1 | 1 |
0 | 1 | 1 | 1 | 1 | 0 | 1 |
0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 |
1 | 0 | 0 | 1 | 1 | 0 | 1 |
1 | 0 | 0 | 1 | 1 | 1 | 1 |
1 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 1 | 0 | 1 | 0 | 1 |
1 | 0 | 1 | 0 | 1 | 1 | 1 |
1 | 0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 1 | 1 |
1 | 0 | 1 | 1 | 1 | 0 | 1 |
1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 0 | 1 | 1 | 0 | 1 |
1 | 1 | 0 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 0 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 1 |
1 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 1 | 1 |
Построим полином Жегалкина:
F
ж = C
000000 ⊕ C
100000∧X1 ⊕ C
010000∧X2 ⊕ C
001000∧X3 ⊕ C
000100∧X4 ⊕ C
000010∧X5 ⊕ C
000001∧X6 ⊕ C
110000∧X1∧X2 ⊕ C
101000∧X1∧X3 ⊕ C
100100∧X1∧X4 ⊕ C
100010∧X1∧X5 ⊕ C
100001∧X1∧X6 ⊕ C
011000∧X2∧X3 ⊕ C
010100∧X2∧X4 ⊕ C
010010∧X2∧X5 ⊕ C
010001∧X2∧X6 ⊕ C
001100∧X3∧X4 ⊕ C
001010∧X3∧X5 ⊕ C
001001∧X3∧X6 ⊕ C
000110∧X4∧X5 ⊕ C
000101∧X4∧X6 ⊕ C
000011∧X5∧X6 ⊕ C
111000∧X1∧X2∧X3 ⊕ C
110100∧X1∧X2∧X4 ⊕ C
110010∧X1∧X2∧X5 ⊕ C
110001∧X1∧X2∧X6 ⊕ C
101100∧X1∧X3∧X4 ⊕ C
101010∧X1∧X3∧X5 ⊕ C
101001∧X1∧X3∧X6 ⊕ C
100110∧X1∧X4∧X5 ⊕ C
100101∧X1∧X4∧X6 ⊕ C
100011∧X1∧X5∧X6 ⊕ C
011100∧X2∧X3∧X4 ⊕ C
011010∧X2∧X3∧X5 ⊕ C
011001∧X2∧X3∧X6 ⊕ C
010110∧X2∧X4∧X5 ⊕ C
010101∧X2∧X4∧X6 ⊕ C
010011∧X2∧X5∧X6 ⊕ C
001110∧X3∧X4∧X5 ⊕ C
001101∧X3∧X4∧X6 ⊕ C
001011∧X3∧X5∧X6 ⊕ C
000111∧X4∧X5∧X6 ⊕ C
111100∧X1∧X2∧X3∧X4 ⊕ C
111010∧X1∧X2∧X3∧X5 ⊕ C
111001∧X1∧X2∧X3∧X6 ⊕ C
110110∧X1∧X2∧X4∧X5 ⊕ C
110101∧X1∧X2∧X4∧X6 ⊕ C
110011∧X1∧X2∧X5∧X6 ⊕ C
101110∧X1∧X3∧X4∧X5 ⊕ C
101101∧X1∧X3∧X4∧X6 ⊕ C
101011∧X1∧X3∧X5∧X6 ⊕ C
100111∧X1∧X4∧X5∧X6 ⊕ C
011110∧X2∧X3∧X4∧X5 ⊕ C
011101∧X2∧X3∧X4∧X6 ⊕ C
011011∧X2∧X3∧X5∧X6 ⊕ C
010111∧X2∧X4∧X5∧X6 ⊕ C
001111∧X3∧X4∧X5∧X6 ⊕ C
111110∧X1∧X2∧X3∧X4∧X5 ⊕ C
111101∧X1∧X2∧X3∧X4∧X6 ⊕ C
111011∧X1∧X2∧X3∧X5∧X6 ⊕ C
110111∧X1∧X2∧X4∧X5∧X6 ⊕ C
101111∧X1∧X3∧X4∧X5∧X6 ⊕ C
011111∧X2∧X3∧X4∧X5∧X6 ⊕ C
111111∧X1∧X2∧X3∧X4∧X5∧X6
Так как F
ж(000000) = 0, то С
000000 = 0.
Далее подставляем все остальные наборы в порядке возрастания числа единиц, подставляя вновь полученные значения в следующие формулы:
F
ж(100000) = С
000000 ⊕ С
100000 = 0 => С
100000 = 0 ⊕ 0 = 0
F
ж(010000) = С
000000 ⊕ С
010000 = 0 => С
010000 = 0 ⊕ 0 = 0
F
ж(001000) = С
000000 ⊕ С
001000 = 0 => С
001000 = 0 ⊕ 0 = 0
F
ж(000100) = С
000000 ⊕ С
000100 = 0 => С
000100 = 0 ⊕ 0 = 0
F
ж(000010) = С
000000 ⊕ С
000010 = 0 => С
000010 = 0 ⊕ 0 = 0
F
ж(000001) = С
000000 ⊕ С
000001 = 0 => С
000001 = 0 ⊕ 0 = 0
F
ж(110000) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
110000 = 0 => С
110000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(101000) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
101000 = 0 => С
101000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(100100) = С
000000 ⊕ С
100000 ⊕ С
000100 ⊕ С
100100 = 0 => С
100100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(100010) = С
000000 ⊕ С
100000 ⊕ С
000010 ⊕ С
100010 = 0 => С
100010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(100001) = С
000000 ⊕ С
100000 ⊕ С
000001 ⊕ С
100001 = 0 => С
100001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(011000) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
011000 = 0 => С
011000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(010100) = С
000000 ⊕ С
010000 ⊕ С
000100 ⊕ С
010100 = 0 => С
010100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(010010) = С
000000 ⊕ С
010000 ⊕ С
000010 ⊕ С
010010 = 0 => С
010010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(010001) = С
000000 ⊕ С
010000 ⊕ С
000001 ⊕ С
010001 = 0 => С
010001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001100) = С
000000 ⊕ С
001000 ⊕ С
000100 ⊕ С
001100 = 0 => С
001100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001010) = С
000000 ⊕ С
001000 ⊕ С
000010 ⊕ С
001010 = 0 => С
001010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001001) = С
000000 ⊕ С
001000 ⊕ С
000001 ⊕ С
001001 = 0 => С
001001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(000110) = С
000000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000110 = 0 => С
000110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(000101) = С
000000 ⊕ С
000100 ⊕ С
000001 ⊕ С
000101 = 0 => С
000101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(000011) = С
000000 ⊕ С
000010 ⊕ С
000001 ⊕ С
000011 = 0 => С
000011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(111000) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
110000 ⊕ С
101000 ⊕ С
011000 ⊕ С
111000 = 0 => С
111000 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(110100) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000100 ⊕ С
110000 ⊕ С
100100 ⊕ С
010100 ⊕ С
110100 = 0 => С
110100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(110010) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000010 ⊕ С
110000 ⊕ С
100010 ⊕ С
010010 ⊕ С
110010 = 0 => С
110010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(110001) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000001 ⊕ С
110000 ⊕ С
100001 ⊕ С
010001 ⊕ С
110001 = 0 => С
110001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(101100) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000100 ⊕ С
101000 ⊕ С
100100 ⊕ С
001100 ⊕ С
101100 = 0 => С
101100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(101010) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000010 ⊕ С
101000 ⊕ С
100010 ⊕ С
001010 ⊕ С
101010 = 1 => С
101010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(101001) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000001 ⊕ С
101000 ⊕ С
100001 ⊕ С
001001 ⊕ С
101001 = 1 => С
101001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(100110) = С
000000 ⊕ С
100000 ⊕ С
000100 ⊕ С
000010 ⊕ С
100100 ⊕ С
100010 ⊕ С
000110 ⊕ С
100110 = 1 => С
100110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(100101) = С
000000 ⊕ С
100000 ⊕ С
000100 ⊕ С
000001 ⊕ С
100100 ⊕ С
100001 ⊕ С
000101 ⊕ С
100101 = 1 => С
100101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(100011) = С
000000 ⊕ С
100000 ⊕ С
000010 ⊕ С
000001 ⊕ С
100010 ⊕ С
100001 ⊕ С
000011 ⊕ С
100011 = 0 => С
100011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(011100) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
011000 ⊕ С
010100 ⊕ С
001100 ⊕ С
011100 = 0 => С
011100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(011010) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000010 ⊕ С
011000 ⊕ С
010010 ⊕ С
001010 ⊕ С
011010 = 1 => С
011010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(011001) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000001 ⊕ С
011000 ⊕ С
010001 ⊕ С
001001 ⊕ С
011001 = 1 => С
011001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(010110) = С
000000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000010 ⊕ С
010100 ⊕ С
010010 ⊕ С
000110 ⊕ С
010110 = 1 => С
010110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(010101) = С
000000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000001 ⊕ С
010100 ⊕ С
010001 ⊕ С
000101 ⊕ С
010101 = 1 => С
010101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(010011) = С
000000 ⊕ С
010000 ⊕ С
000010 ⊕ С
000001 ⊕ С
010010 ⊕ С
010001 ⊕ С
000011 ⊕ С
010011 = 0 => С
010011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001110) = С
000000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
001100 ⊕ С
001010 ⊕ С
000110 ⊕ С
001110 = 0 => С
001110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001101) = С
000000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000001 ⊕ С
001100 ⊕ С
001001 ⊕ С
000101 ⊕ С
001101 = 0 => С
001101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(001011) = С
000000 ⊕ С
001000 ⊕ С
000010 ⊕ С
000001 ⊕ С
001010 ⊕ С
001001 ⊕ С
000011 ⊕ С
001011 = 0 => С
001011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(000111) = С
000000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
000111 = 0 => С
000111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(111100) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
110000 ⊕ С
101000 ⊕ С
100100 ⊕ С
011000 ⊕ С
010100 ⊕ С
001100 ⊕ С
111000 ⊕ С
110100 ⊕ С
101100 ⊕ С
011100 ⊕ С
111100 = 0 => С
111100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(111010) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000010 ⊕ С
110000 ⊕ С
101000 ⊕ С
100010 ⊕ С
011000 ⊕ С
010010 ⊕ С
001010 ⊕ С
111000 ⊕ С
110010 ⊕ С
101010 ⊕ С
011010 ⊕ С
111010 = 1 => С
111010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(111001) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000001 ⊕ С
110000 ⊕ С
101000 ⊕ С
100001 ⊕ С
011000 ⊕ С
010001 ⊕ С
001001 ⊕ С
111000 ⊕ С
110001 ⊕ С
101001 ⊕ С
011001 ⊕ С
111001 = 1 => С
111001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(110110) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000010 ⊕ С
110000 ⊕ С
100100 ⊕ С
100010 ⊕ С
010100 ⊕ С
010010 ⊕ С
000110 ⊕ С
110100 ⊕ С
110010 ⊕ С
100110 ⊕ С
010110 ⊕ С
110110 = 1 => С
110110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(110101) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000001 ⊕ С
110000 ⊕ С
100100 ⊕ С
100001 ⊕ С
010100 ⊕ С
010001 ⊕ С
000101 ⊕ С
110100 ⊕ С
110001 ⊕ С
100101 ⊕ С
010101 ⊕ С
110101 = 1 => С
110101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(110011) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000010 ⊕ С
000001 ⊕ С
110000 ⊕ С
100010 ⊕ С
100001 ⊕ С
010010 ⊕ С
010001 ⊕ С
000011 ⊕ С
110010 ⊕ С
110001 ⊕ С
100011 ⊕ С
010011 ⊕ С
110011 = 0 => С
110011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(101110) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
101000 ⊕ С
100100 ⊕ С
100010 ⊕ С
001100 ⊕ С
001010 ⊕ С
000110 ⊕ С
101100 ⊕ С
101010 ⊕ С
100110 ⊕ С
001110 ⊕ С
101110 = 1 => С
101110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(101101) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000001 ⊕ С
101000 ⊕ С
100100 ⊕ С
100001 ⊕ С
001100 ⊕ С
001001 ⊕ С
000101 ⊕ С
101100 ⊕ С
101001 ⊕ С
100101 ⊕ С
001101 ⊕ С
101101 = 1 => С
101101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(101011) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000010 ⊕ С
000001 ⊕ С
101000 ⊕ С
100010 ⊕ С
100001 ⊕ С
001010 ⊕ С
001001 ⊕ С
000011 ⊕ С
101010 ⊕ С
101001 ⊕ С
100011 ⊕ С
001011 ⊕ С
101011 = 1 => С
101011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(100111) = С
000000 ⊕ С
100000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
100100 ⊕ С
100010 ⊕ С
100001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
100110 ⊕ С
100101 ⊕ С
100011 ⊕ С
000111 ⊕ С
100111 = 1 => С
100111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(011110) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
011000 ⊕ С
010100 ⊕ С
010010 ⊕ С
001100 ⊕ С
001010 ⊕ С
000110 ⊕ С
011100 ⊕ С
011010 ⊕ С
010110 ⊕ С
001110 ⊕ С
011110 = 1 => С
011110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(011101) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000001 ⊕ С
011000 ⊕ С
010100 ⊕ С
010001 ⊕ С
001100 ⊕ С
001001 ⊕ С
000101 ⊕ С
011100 ⊕ С
011001 ⊕ С
010101 ⊕ С
001101 ⊕ С
011101 = 1 => С
011101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(011011) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000010 ⊕ С
000001 ⊕ С
011000 ⊕ С
010010 ⊕ С
010001 ⊕ С
001010 ⊕ С
001001 ⊕ С
000011 ⊕ С
011010 ⊕ С
011001 ⊕ С
010011 ⊕ С
001011 ⊕ С
011011 = 1 => С
011011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(010111) = С
000000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
010100 ⊕ С
010010 ⊕ С
010001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
010110 ⊕ С
010101 ⊕ С
010011 ⊕ С
000111 ⊕ С
010111 = 1 => С
010111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 = 1
F
ж(001111) = С
000000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
001100 ⊕ С
001010 ⊕ С
001001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
001110 ⊕ С
001101 ⊕ С
001011 ⊕ С
000111 ⊕ С
001111 = 0 => С
001111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(111110) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
110000 ⊕ С
101000 ⊕ С
100100 ⊕ С
100010 ⊕ С
011000 ⊕ С
010100 ⊕ С
010010 ⊕ С
001100 ⊕ С
001010 ⊕ С
000110 ⊕ С
111000 ⊕ С
110100 ⊕ С
110010 ⊕ С
101100 ⊕ С
101010 ⊕ С
100110 ⊕ С
011100 ⊕ С
011010 ⊕ С
010110 ⊕ С
001110 ⊕ С
111100 ⊕ С
111010 ⊕ С
110110 ⊕ С
101110 ⊕ С
011110 ⊕ С
111110 = 1 => С
111110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(111101) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000001 ⊕ С
110000 ⊕ С
101000 ⊕ С
100100 ⊕ С
100001 ⊕ С
011000 ⊕ С
010100 ⊕ С
010001 ⊕ С
001100 ⊕ С
001001 ⊕ С
000101 ⊕ С
111000 ⊕ С
110100 ⊕ С
110001 ⊕ С
101100 ⊕ С
101001 ⊕ С
100101 ⊕ С
011100 ⊕ С
011001 ⊕ С
010101 ⊕ С
001101 ⊕ С
111100 ⊕ С
111001 ⊕ С
110101 ⊕ С
101101 ⊕ С
011101 ⊕ С
111101 = 1 => С
111101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(111011) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000010 ⊕ С
000001 ⊕ С
110000 ⊕ С
101000 ⊕ С
100010 ⊕ С
100001 ⊕ С
011000 ⊕ С
010010 ⊕ С
010001 ⊕ С
001010 ⊕ С
001001 ⊕ С
000011 ⊕ С
111000 ⊕ С
110010 ⊕ С
110001 ⊕ С
101010 ⊕ С
101001 ⊕ С
100011 ⊕ С
011010 ⊕ С
011001 ⊕ С
010011 ⊕ С
001011 ⊕ С
111010 ⊕ С
111001 ⊕ С
110011 ⊕ С
101011 ⊕ С
011011 ⊕ С
111011 = 1 => С
111011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(110111) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
110000 ⊕ С
100100 ⊕ С
100010 ⊕ С
100001 ⊕ С
010100 ⊕ С
010010 ⊕ С
010001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
110100 ⊕ С
110010 ⊕ С
110001 ⊕ С
100110 ⊕ С
100101 ⊕ С
100011 ⊕ С
010110 ⊕ С
010101 ⊕ С
010011 ⊕ С
000111 ⊕ С
110110 ⊕ С
110101 ⊕ С
110011 ⊕ С
100111 ⊕ С
010111 ⊕ С
110111 = 1 => С
110111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 = 1
F
ж(101111) = С
000000 ⊕ С
100000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
101000 ⊕ С
100100 ⊕ С
100010 ⊕ С
100001 ⊕ С
001100 ⊕ С
001010 ⊕ С
001001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
101100 ⊕ С
101010 ⊕ С
101001 ⊕ С
100110 ⊕ С
100101 ⊕ С
100011 ⊕ С
001110 ⊕ С
001101 ⊕ С
001011 ⊕ С
000111 ⊕ С
101110 ⊕ С
101101 ⊕ С
101011 ⊕ С
100111 ⊕ С
001111 ⊕ С
101111 = 1 => С
101111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(011111) = С
000000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
011000 ⊕ С
010100 ⊕ С
010010 ⊕ С
010001 ⊕ С
001100 ⊕ С
001010 ⊕ С
001001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
011100 ⊕ С
011010 ⊕ С
011001 ⊕ С
010110 ⊕ С
010101 ⊕ С
010011 ⊕ С
001110 ⊕ С
001101 ⊕ С
001011 ⊕ С
000111 ⊕ С
011110 ⊕ С
011101 ⊕ С
011011 ⊕ С
010111 ⊕ С
001111 ⊕ С
011111 = 1 => С
011111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 = 1
F
ж(111111) = С
000000 ⊕ С
100000 ⊕ С
010000 ⊕ С
001000 ⊕ С
000100 ⊕ С
000010 ⊕ С
000001 ⊕ С
110000 ⊕ С
101000 ⊕ С
100100 ⊕ С
100010 ⊕ С
100001 ⊕ С
011000 ⊕ С
010100 ⊕ С
010010 ⊕ С
010001 ⊕ С
001100 ⊕ С
001010 ⊕ С
001001 ⊕ С
000110 ⊕ С
000101 ⊕ С
000011 ⊕ С
111000 ⊕ С
110100 ⊕ С
110010 ⊕ С
110001 ⊕ С
101100 ⊕ С
101010 ⊕ С
101001 ⊕ С
100110 ⊕ С
100101 ⊕ С
100011 ⊕ С
011100 ⊕ С
011010 ⊕ С
011001 ⊕ С
010110 ⊕ С
010101 ⊕ С
010011 ⊕ С
001110 ⊕ С
001101 ⊕ С
001011 ⊕ С
000111 ⊕ С
111100 ⊕ С
111010 ⊕ С
111001 ⊕ С
110110 ⊕ С
110101 ⊕ С
110011 ⊕ С
101110 ⊕ С
101101 ⊕ С
101011 ⊕ С
100111 ⊕ С
011110 ⊕ С
011101 ⊕ С
011011 ⊕ С
010111 ⊕ С
001111 ⊕ С
111110 ⊕ С
111101 ⊕ С
111011 ⊕ С
110111 ⊕ С
101111 ⊕ С
011111 ⊕ С
111111 = 1 => С
111111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 0 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 ⊕ 1 = 1
Таким образом, полином Жегалкина будет равен:
F
ж = X1∧X3∧X5 ⊕ X1∧X3∧X6 ⊕ X1∧X4∧X5 ⊕ X1∧X4∧X6 ⊕ X2∧X3∧X5 ⊕ X2∧X3∧X6 ⊕ X2∧X4∧X5 ⊕ X2∧X4∧X6 ⊕ X1∧X2∧X3∧X5 ⊕ X1∧X2∧X3∧X6 ⊕ X1∧X2∧X4∧X5 ⊕ X1∧X2∧X4∧X6 ⊕ X1∧X3∧X4∧X5 ⊕ X1∧X3∧X4∧X6 ⊕ X1∧X3∧X5∧X6 ⊕ X1∧X4∧X5∧X6 ⊕ X2∧X3∧X4∧X5 ⊕ X2∧X3∧X4∧X6 ⊕ X2∧X3∧X5∧X6 ⊕ X2∧X4∧X5∧X6 ⊕ X1∧X2∧X3∧X4∧X5 ⊕ X1∧X2∧X3∧X4∧X6 ⊕ X1∧X2∧X3∧X5∧X6 ⊕ X1∧X2∧X4∧X5∧X6 ⊕ X1∧X3∧X4∧X5∧X6 ⊕ X2∧X3∧X4∧X5∧X6 ⊕ X1∧X2∧X3∧X4∧X5∧X6
Логическая схема, соответствующая полиному Жегалкина: