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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 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x
|
| 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | x | 0 | x | 0 | x | 0 | x | 1 | x | x | 0
|
| 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | x | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x
|
| 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | x | 0 | x | 0 | x | 1 | x | x | 1 | x | 1
|
| 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | 0 | x | 1 | x
|
| 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | x | 0 | x | 0 | x | x | 0 | 1 | x | x | 1
|
| 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 1 | 0 | x | 0 | x | 0 | x | x | 0 | x | 0 | 1 | x
|
| 0 | 0 | 0 | 1 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | x | 0 | x | 1 | x | x | 1 | 1 | x | x | 1
|
| 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | x | 0 | x | 1 | x | 0 | x | 0 | x | 1 | x
|
| 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | x | 1 | x | x | 1 | 0 | x | 0 | x | x | 1
|
| 0 | 1 | | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | 0 | x | 1 | x
|
| 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | x | x | 0 | 0 | x | 0 | x | 1 | x | x | 1
|
| 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | x | x | 0 | 0 | x | 0 | x | x | 0 | 1 | x
|
| 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | x | x | 0 | 0 | x | 1 | x | x | 1 | x | 1
|
| 0 | | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | 0 | x | 1 | x
|
| 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | x | x | 0 | 0 | x | x | 0 | 1 | x | x | 1
|
| 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 0 | x | x | 0 | 0 | x | x | 0 | x | 0 | 1 | x
|
| 0 | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | x | x | 0 | 1 | x | x | 1 | x | 1 | x | 1
|
| 0 | 1 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | x | x | 0 | x | 0 | 0 | x | 0 | x | 1 | x
|
| 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | x | x | 1 | x | 1 | 0 | x | 0 | x | x | 1
|
100000 100001 x0 0x 0x 0x 0x 1x
100001 100010 x0 0x 0x 0x 1x x1
100010 100011 x1 0x 0x 0x x0 1x
100011 000000 x1 0x 0x 0x x1 x1
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 :
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 1 | x | x | 1
|
| 01
| 1 | x | x | 1
|
| 11
| - | - | - | -
|
| 10
| 1 | x | - | -
|
|
Ja = 1 | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | 1 | 1 | x
|
| 01
| x | 1 | 1 | x
|
| 11
| - | - | - | -
|
| 10
| x | 1 | - | -
|
|
Ka = 1 = Ja |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 1 | x | x
|
| 01
| 0 | 1 | x | x
|
| 11
| - | - | - | -
|
| 10
| 0 | 0 | - | -
|
| Jb = Qa/Qd | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | x | 1 | 0
|
| 01
| x | x | 1 | 0
|
| 11
| - | - | - | -
|
| 10
| x | x | - | -
|
| Kb = Qa |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 0 | 1 | 0
|
| 01
| x | x | x | x
|
| 11
| - | - | - | -
|
| 10
| 0 | 0 | - | -
|
| Jc = QaQb | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | x | x | x
|
| 01
| 0 | 0 | 1 | 0
|
| 11
| - | - | - | -
|
| 10
| x | x | - | -
|
| Kc = QaQb = Jc |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 0 | 0 | 0
|
| 01
| 0 | 0 | 1 | 0
|
| 11
| - | - | - | -
|
| 10
| x | x | - | -
|
| Jd = QaQbQc | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | x | x | x
|
| 01
| x | x | x | x
|
| 11
| - | - | - | -
|
| 10
| 0 | 1 | - | -
|
| Kd = Qa |
Résultats
Conclusions
Ressources
