Промежуточные таблицы истинности:A∧V:
(A∧V)∧B:
A | V | B | A∧V | (A∧V)∧B |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
¬B:
C∧(¬B):
C | B | ¬B | C∧(¬B) |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
A∧(¬B):
A | B | ¬B | A∧(¬B) |
0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 |
1 | 1 | 0 | 0 |
C∧V:
(C∧V)∧B:
C | V | B | C∧V | (C∧V)∧B |
0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 1 | 1 |
¬((A∧V)∧B):
A | V | B | A∧V | (A∧V)∧B | ¬((A∧V)∧B) |
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 | 1 | 0 | 1 |
1 | 1 | 1 | 1 | 1 | 0 |
(¬((A∧V)∧B))∧V:
A | V | B | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V |
0 | 0 | 0 | 0 | 0 | 1 | 0 |
0 | 0 | 1 | 0 | 0 | 1 | 0 |
0 | 1 | 0 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 1 | 1 |
1 | 0 | 0 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 1 | 0 | 1 | 1 |
1 | 1 | 1 | 1 | 1 | 0 | 0 |
((¬((A∧V)∧B))∧V)∧(C∧(¬B)):
A | V | B | C | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ¬B | C∧(¬B) | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 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 | 0 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
(((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V:
A | V | B | C | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ¬B | C∧(¬B) | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) | (((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)):
A | V | B | C | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ¬B | C∧(¬B) | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) | (((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V | ¬B | A∧(¬B) | ((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
(((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V:
A | V | B | C | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ¬B | C∧(¬B) | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) | (((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V | ¬B | A∧(¬B) | ((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)) | (((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
((((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V)∧((C∧V)∧B):
A | V | B | C | A∧V | (A∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ¬B | C∧(¬B) | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) | (((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V | ¬B | A∧(¬B) | ((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)) | (((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V | C∧V | (C∧V)∧B | ((((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V)∧((C∧V)∧B) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 |
Общая таблица истинности:
A | V | B | C | A∧V | (A∧V)∧B | ¬B | C∧(¬B) | A∧(¬B) | C∧V | (C∧V)∧B | ¬((A∧V)∧B) | (¬((A∧V)∧B))∧V | ((¬((A∧V)∧B))∧V)∧(C∧(¬B)) | (((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V | ((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)) | (((((¬((A∧V)∧B))∧V)∧(C∧(¬B)))∧V)∧(A∧(¬B)))∧V | ¬(A∧V∧B)∧V∧(C∧¬B)∧V∧(A∧¬B)∧V∧(C∧V∧B) |
0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 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 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 |
0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 0 |
1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Логическая схема:
Совершенная дизъюнктивная нормальная форма (СДНФ):
По таблице истинности:
A | V | B | C | 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 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
В таблице истинности нет набора значений переменных при которых функция истинна!
Совершенная конъюнктивная нормальная форма (СКНФ):
По таблице истинности:
A | V | B | C | 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 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
F
скнф = (A∨V∨B∨C) ∧ (A∨V∨B∨¬C) ∧ (A∨V∨¬B∨C) ∧ (A∨V∨¬B∨¬C) ∧ (A∨¬V∨B∨C) ∧ (A∨¬V∨B∨¬C) ∧ (A∨¬V∨¬B∨C) ∧ (A∨¬V∨¬B∨¬C) ∧ (¬A∨V∨B∨C) ∧ (¬A∨V∨B∨¬C) ∧ (¬A∨V∨¬B∨C) ∧ (¬A∨V∨¬B∨¬C) ∧ (¬A∨¬V∨B∨C) ∧ (¬A∨¬V∨B∨¬C) ∧ (¬A∨¬V∨¬B∨C) ∧ (¬A∨¬V∨¬B∨¬C)
Логическая cхема:
Построение полинома Жегалкина:
По таблице истинности функции
A | V | B | C | 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 | 0 |
0 | 1 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 1 | 1 | 1 | 0 |
1 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
1 | 0 | 1 | 0 | 0 |
1 | 0 | 1 | 1 | 0 |
1 | 1 | 0 | 0 | 0 |
1 | 1 | 0 | 1 | 0 |
1 | 1 | 1 | 0 | 0 |
1 | 1 | 1 | 1 | 0 |
Построим полином Жегалкина:
F
ж = C
0000 ⊕ C
1000∧A ⊕ C
0100∧V ⊕ C
0010∧B ⊕ C
0001∧C ⊕ C
1100∧A∧V ⊕ C
1010∧A∧B ⊕ C
1001∧A∧C ⊕ C
0110∧V∧B ⊕ C
0101∧V∧C ⊕ C
0011∧B∧C ⊕ C
1110∧A∧V∧B ⊕ C
1101∧A∧V∧C ⊕ C
1011∧A∧B∧C ⊕ C
0111∧V∧B∧C ⊕ C
1111∧A∧V∧B∧C
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 = 0 => С
1000 = 0 ⊕ 0 = 0
F
ж(0100) = С
0000 ⊕ С
0100 = 0 => С
0100 = 0 ⊕ 0 = 0
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 = 0 => С
1100 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(1010) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
1010 = 0 => С
1010 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(1001) = С
0000 ⊕ С
1000 ⊕ С
0001 ⊕ С
1001 = 0 => С
1001 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(0110) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0110 = 0 => С
0110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(0101) = С
0000 ⊕ С
0100 ⊕ С
0001 ⊕ С
0101 = 0 => С
0101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 = 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 = 0 => С
1110 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(1101) = С
0000 ⊕ С
1000 ⊕ С
0100 ⊕ С
0001 ⊕ С
1100 ⊕ С
1001 ⊕ С
0101 ⊕ С
1101 = 0 => С
1101 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(1011) = С
0000 ⊕ С
1000 ⊕ С
0010 ⊕ С
0001 ⊕ С
1010 ⊕ С
1001 ⊕ С
0011 ⊕ С
1011 = 0 => С
1011 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
F
ж(0111) = С
0000 ⊕ С
0100 ⊕ С
0010 ⊕ С
0001 ⊕ С
0110 ⊕ С
0101 ⊕ С
0011 ⊕ С
0111 = 0 => С
0111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
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 = 0 => С
1111 = 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 ⊕ 0 = 0
Таким образом, полином Жегалкина будет равен:
F
ж = 0