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Таблица истинности для функции ¬(K∨¬M∨N)∧¬(¬K∨M∨N)∧¬(K∨M∨¬N)∧¬(¬K∨¬M∨¬N)∧¬(K∨M∨N):
Промежуточные таблицы истинности:¬M: K∨(¬M): K | M | ¬M | K∨(¬M) | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 |
(K∨(¬M))∨N: K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
¬K: (¬K)∨M: K | M | ¬K | (¬K)∨M | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 |
((¬K)∨M)∨N: K | M | N | ¬K | (¬K)∨M | ((¬K)∨M)∨N | 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 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
¬N: K∨M: (K∨M)∨(¬N): K | M | N | K∨M | ¬N | (K∨M)∨(¬N) | 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 |
(¬K)∨(¬M): K | M | ¬K | ¬M | (¬K)∨(¬M) | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
((¬K)∨(¬M))∨(¬N): K | M | N | ¬K | ¬M | (¬K)∨(¬M) | ¬N | ((¬K)∨(¬M))∨(¬N) | 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 |
(K∨M)∨N: K | M | N | K∨M | (K∨M)∨N | 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 |
¬((K∨(¬M))∨N): K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬((K∨(¬M))∨N) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
¬(((¬K)∨M)∨N): K | M | N | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬(((¬K)∨M)∨N) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 |
¬((K∨M)∨(¬N)): K | M | N | K∨M | ¬N | (K∨M)∨(¬N) | ¬((K∨M)∨(¬N)) | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 |
¬(((¬K)∨(¬M))∨(¬N)): K | M | N | ¬K | ¬M | (¬K)∨(¬M) | ¬N | ((¬K)∨(¬M))∨(¬N) | ¬(((¬K)∨(¬M))∨(¬N)) | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
¬((K∨M)∨N): K | M | N | K∨M | (K∨M)∨N | ¬((K∨M)∨N) | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 |
(¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)): K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬((K∨(¬M))∨N) | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬(((¬K)∨M)∨N) | (¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))): K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬((K∨(¬M))∨N) | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬(((¬K)∨M)∨N) | (¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)) | K∨M | ¬N | (K∨M)∨(¬N) | ¬((K∨M)∨(¬N)) | ((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
нажмите на таблицу для просмотра*(((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))): K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬((K∨(¬M))∨N) | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬(((¬K)∨M)∨N) | (¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)) | K∨M | ¬N | (K∨M)∨(¬N) | ¬((K∨M)∨(¬N)) | ((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))) | ¬K | ¬M | (¬K)∨(¬M) | ¬N | ((¬K)∨(¬M))∨(¬N) | ¬(((¬K)∨(¬M))∨(¬N)) | (((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 |
нажмите на таблицу для просмотра*((((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))))∧(¬((K∨M)∨N)): K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬((K∨(¬M))∨N) | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬(((¬K)∨M)∨N) | (¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)) | K∨M | ¬N | (K∨M)∨(¬N) | ¬((K∨M)∨(¬N)) | ((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))) | ¬K | ¬M | (¬K)∨(¬M) | ¬N | ((¬K)∨(¬M))∨(¬N) | ¬(((¬K)∨(¬M))∨(¬N)) | (((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))) | K∨M | (K∨M)∨N | ¬((K∨M)∨N) | ((((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))))∧(¬((K∨M)∨N)) | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
нажмите на таблицу для просмотра*Общая таблица истинности:K | M | N | ¬M | K∨(¬M) | (K∨(¬M))∨N | ¬K | (¬K)∨M | ((¬K)∨M)∨N | ¬N | K∨M | (K∨M)∨(¬N) | (¬K)∨(¬M) | ((¬K)∨(¬M))∨(¬N) | (K∨M)∨N | ¬((K∨(¬M))∨N) | ¬(((¬K)∨M)∨N) | ¬((K∨M)∨(¬N)) | ¬(((¬K)∨(¬M))∨(¬N)) | ¬((K∨M)∨N) | (¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)) | ((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))) | (((¬((K∨(¬M))∨N))∧(¬(((¬K)∨M)∨N)))∧(¬((K∨M)∨(¬N))))∧(¬(((¬K)∨(¬M))∨(¬N))) | ¬(K∨¬M∨N)∧¬(¬K∨M∨N)∧¬(K∨M∨¬N)∧¬(¬K∨¬M∨¬N)∧¬(K∨M∨N) | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
нажмите на таблицу для просмотра* Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности: K | M | N | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
В таблице истинности нет набора значений переменных при которых функция истинна!
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности: K | M | N | F | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
F скнф = (K∨M∨N) ∧ (K∨M∨¬N) ∧ (K∨¬M∨N) ∧ (K∨¬M∨¬N) ∧ (¬K∨M∨N) ∧ (¬K∨M∨¬N) ∧ (¬K∨¬M∨N) ∧ (¬K∨¬M∨¬N) Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции K | M | N | Fж | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 |
Построим полином Жегалкина: F ж = C 000 ⊕ C 100∧K ⊕ C 010∧M ⊕ C 001∧N ⊕ C 110∧K∧M ⊕ C 101∧K∧N ⊕ C 011∧M∧N ⊕ C 111∧K∧M∧N 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 = 0 => С 100 = 0 ⊕ 0 = 0 F ж(010) = С 000 ⊕ С 010 = 0 => С 010 = 0 ⊕ 0 = 0 F ж(001) = С 000 ⊕ С 001 = 0 => С 001 = 0 ⊕ 0 = 0 F ж(110) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 110 = 0 => С 110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0 F ж(101) = С 000 ⊕ С 100 ⊕ С 001 ⊕ С 101 = 0 => С 101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0 F ж(011) = С 000 ⊕ С 010 ⊕ С 001 ⊕ С 011 = 0 => С 011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0 F ж(111) = С 000 ⊕ С 100 ⊕ С 010 ⊕ С 001 ⊕ С 110 ⊕ С 101 ⊕ С 011 ⊕ С 111 = 0 => С 111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0 Таким образом, полином Жегалкина будет равен: F ж = 0
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