# Logique de base/Exercices/Tableau de Karnaugh 1
## Exercice 1
### Tableau 1

| N | N | a b | a b | a b | a b |
| N | N | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 1 | 1 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
| N | N | a b | a b | a b | a b |
| N | N | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 1 | 1 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
| N | N | a b | a b | a b | a b |
| N | N | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 1 | 1 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
* Rassemblement vert : b
* Rassemblement bleu : ${\bar {c}}$
$N=b+{\bar {c}}$

### Tableau 2

| P | P | a b | a b | a b | a b |
| P | P | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 0 | 1 | 1 | 0 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 1 | 0 | 0 | 1 |
| P | P | a b | a b | a b | a b |
| P | P | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 0 | 1 | 1 | 0 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 1 | 0 | 0 | 1 |
| P | P | a b | a b | a b | a b |
| P | P | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 0 | 1 | 1 | 0 |
| c d | 1 1 | 0 | 1 | 1 | 0 |
| c d | 1 0 | 1 | 0 | 0 | 1 |
* Rassemblement bleu : ${\bar {b}}.{\bar {d}}$
* Rassemblement vert : $b.d$
$P={\bar {b}}.{\bar {d}}+b.d$

### Tableau 3

| Q | Q | a b | a b | a b | a b |
| Q | Q | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 0 | 0 |
| c d | 1 0 | 0 | 0 | 0 | 0 |
| Q | Q | a b | a b | a b | a b |
| Q | Q | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 0 | 0 |
| c d | 1 0 | 0 | 0 | 0 | 0 |
| Q | Q | a b | a b | a b | a b |
| Q | Q | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 0 | 0 |
| c d | 1 0 | 0 | 0 | 0 | 0 |
| Q | Q | a b | a b | a b | a b |
| Q | Q | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 1 | 0 | 0 | 1 |
| c d | 0 1 | 1 | 1 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 0 | 0 |
| c d | 1 0 | 0 | 0 | 0 | 0 |
* Rassemblement bleu : ${\bar {c}}.d$
* Rassemblement vert : ${\bar {a}}.d$
* Rassemblement rouge : ${\bar {b}}.{\bar {c}}$
Q=$d.{\bar {c}}+{\bar {a}}.d+{\bar {b}}.{\bar {c}}$

### Tableau 4

| R | R | a b | a b | a b | a b |
| R | R | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 0 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 1 | 1 |
| c d | 1 0 | 0 | 0 | 1 | 0 |
| R | R | a b | a b | a b | a b |
| R | R | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 0 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 1 | 1 |
| c d | 1 0 | 0 | 0 | 1 | 0 |
| R | R | a b | a b | a b | a b |
| R | R | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 0 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 1 | 1 |
| c d | 1 0 | 0 | 0 | 1 | 0 |
| R | R | a b | a b | a b | a b |
| R | R | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 0 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 1 | 1 | 1 | 1 |
| c d | 1 0 | 0 | 0 | 1 | 0 |
* Rassemblement vert : $a.b$
* Rassemblement bleu : $c.d$
* Rassemblement orange : ${\bar {b}}.d$
R = $a.b+c.d+{\bar {b}}.d$

### Tableau 5

| S | S | a b | a b | a b | a b |
| S | S | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 0 | 1 |
| c d | 1 1 | 1 | 0 | 0 | 1 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
| S | S | a b | a b | a b | a b |
| S | S | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 0 | 1 |
| c d | 1 1 | 1 | 0 | 0 | 1 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
| S | S | a b | a b | a b | a b |
| S | S | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 1 | 0 |
| c d | 0 1 | 1 | 0 | 0 | 1 |
| c d | 1 1 | 1 | 0 | 0 | 1 |
| c d | 1 0 | 0 | 1 | 1 | 0 |
* Rassemblement rouge : $b.{\bar {d}}$
* Rassemblement vert : ${\bar {b}}.d$
S=$b.{\bar {d}}+{\bar {b}}.d$

### Tableau 6

| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
| T | T | a b | a b | a b | a b |
| T | T | 0 0 | 0 1 | 1 1 | 1 0 |
| c d | 0 0 | 0 | 1 | 0 | 1 |
| c d | 0 1 | 1 | 0 | 1 | 1 |
| c d | 1 1 | 0 | 1 | 0 | 1 |
| c d | 1 0 | 1 | 1 | 1 | 1 |
* Rassemblement bleu : $a.{\bar {b}}$
* Rassemblement vert : $c.{\bar {d}}$
* Rassemblement rouge : ${\bar {a}}.b.c$
* Rassemblement orange : $a.{\bar {c}}.d$
* Rassemblement jaune : ${\bar {a}}.b.{\bar {d}}$
* Rassemblement mauve : ${\bar {b}}.{\bar {c}}.d$
T=$a.{\bar {b}}+c.{\bar {d}}+{\bar {a}}.b.c+a.{\bar {c}}.d+{\bar {a}}.b.{\bar {d}}+{\bar {b}}.{\bar {c}}.d$
| Algèbre de Boole | Tableau de Karnaugh 2 |