Compteur modulo 24
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Version du 8 mars 2009 à 10:48
Sommaire |
Compteur modulo 24
But
Déterminer les composants logiques d'un compteur modulo 24.
Introduction
Voir le compteur modulo 16.
Compteur modulo 24
Un compteur modulo 24 utilise aussi 6 bascules JK.
Etats du compteur
En se basant sur les informations du compteur modulo 16, les états deviennent les suivants :
| Etat | Q | Q+ | d | c | b | a | ||||||||||||||||||
| d | c | b | a | d | c | b | a | J | K | J | K | J | K | J | K | |||||||||
| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x |
| 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x | x | 0 |
| 2 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x |
| 3 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | x | 0 | x | 0 | x | 1 | x | x | 1 | x | 1 |
| 4 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | 0 | x | 1 | x |
| 5 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x | x | 1 |
| 6 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | x | 0 | 1 | x |
| 7 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | x | 0 | x | 1 | x | x | 1 | 1 | x | x | 1 |
| 8 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | x | 0 | x | 1 | x | 0 | x | 0 | x | 1 | x |
| 9 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | x | 1 | x | x | 1 | 0 | x | 0 | x | x | 1 |
| 10 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | 0 | x | 1 | x |
| 11 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | x | x | 0 | 0 | x | 0 | x | 1 | x | x | 1 |
| 12 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | x | 0 | 1 | x |
| 13 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | x | x | 0 | 0 | x | 1 | x | x | 1 | x | 1 |
| 14 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | 0 | x | 1 | x |
| 15 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | x | x | 0 | 0 | x | x | 0 | 1 | x | x | 1 |
| 16 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | x | 0 | 1 | x |
| 17 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | x | x | 0 | 1 | x | x | 1 | x | 1 | x | 1 |
| 18 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | x | x | 0 | x | 0 | 0 | x | 0 | x | 1 | x |
| 19 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | x | x | 1 | x | 1 | 0 | x | 0 | x | x | 1 |
| 20 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | x | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x |
| 21 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | x | 0 | 0 | x | 0 | x | 0 | x | 1 | x | x | 1 |
| 22 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | x | 1 | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x |
| 23 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | x | 1 | 0 | x | 0 | x | 0 | x | x | 1 | x | 1 |
Matrice de référence
La matrice de référence des états du compteur :
| QdQc\QbQa | 00 | 01 | 11 | 10 |
|---|---|---|---|---|
| 00 | 0 | 1 | 3 | 2 |
| 01 | 4 | 5 | 7 | 6 |
| 11 | - | - | - | - |
| 10 | 8 | 9 | - | - |
Réduction des fonctions J et K
Par rapport au compteur modulo 16, seul Kd et Jb changent :
|
Ja = 1 |
|
Ka = 1 = Ja | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Jb = Qa/Qd |
| Kb = Qa | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Jc = QaQb |
| Kc = QaQb = Jc | |||||||||||||||||||||||||||||||||||||||||||||||||||
| Jd = QaQbQc |
| Kd = Qa |
