Un article de Wikipedia.
Compteur modulo 16
But
Déterminer les composants logiques d'un compteur modulo 16.
Introduction
La réalisation est centrée sur des bascules JK Master / Slave (voir Bascule JK sur Wikipedia).
Table de vérité d'une bascule JK
La table de vérité d'une bascule JK est :
| J | K | Q+
|
| 0 | 0 | Q
|
| 0 | 1 | 0
|
| 1 | 0 | 1
|
| 1 | 1 | /Q (le complément de Q)
|
Table des transitions d'une bascule JK
Sa table des transitions déduites de sa table de vérité est :
| Q | Q+ | J | K
|
| 0 | 0 | 0 | x
|
| 0 | 1 | 1 | x
|
| 1 | 0 | x | 1
|
| 1 | 1 | x | 0
|
Compteur modulo 16
Un compteur modulo 16 utilise 4 bascules JK.
Etats du compteur
Les états d'un compteur modulo 16 ainsi que les états de bascules JK sont les suivants :
| Etiquette | 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 | 1 | 0 | x | 0 | x | 0 | x | 1 | x
|
| 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | x | 0 | x | 1 | x | x | 1
|
| 2 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 1 | 0 | x | 0 | x | x | 0 | 1 | x
|
| 3 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | x | 1 | x | x | 1 | x | 1
|
| 4 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | x | x | 0 | 0 | x | 1 | x
|
| 5 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | x | x | 0 | 1 | x | x | 1
|
| 6 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | x | x | 0 | x | 0 | 1 | x
|
| 7 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 1 | x | x | 1 | x | 1 | x | 1
|
| 8 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | x | 0 | 0 | x | 0 | x | 1 | x
|
| 9 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | x | 0 | 0 | x | 1 | x | x | 1
|
| 10 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 1 | x | 0 | 0 | x | x | 0 | 1 | x
|
| 11 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 0 | x | 0 | 1 | x | x | 1 | x | 1
|
| 12 | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | x | 0 | x | 0 | 0 | x | 1 | x
|
| 13 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | x | 0 | x | 0 | 1 | x | x | 1
|
| 14 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | x | 0 | x | 0 | x | 0 | 1 | x
|
| 15 | 1 | 1 | 1 | 1 | 0 | 0 | 0 | 0 | x | 1 | x | 1 | 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
| 12 | 13 | 15 | 14
|
| 10
| 8 | 9 | 11 | 10
|
Réduction des fonctions J et K
Résultats
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 1 | x | x | 1
|
| 01
| 1 | x | x | 1
|
| 11
| 1 | x | x | 1
|
| 10
| 1 | x | x | 1
|
|
Ja = 1 | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | 1 | 1 | x
|
| 01
| x | 1 | 1 | x
|
| 11
| x | 1 | 1 | x
|
| 10
| x | 1 | 1 | x
|
|
Ka = 1 = Ja |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 1 | x | x
|
| 01
| 0 | 1 | x | x
|
| 11
| 0 | 1 | x | x
|
| 10
| 0 | 1 | x | x
|
| Jb = Qa | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | x | 1 | 0
|
| 01
| x | x | 1 | 0
|
| 11
| x | x | 1 | 0
|
| 10
| x | x | 1 | 0
|
| Kb = Qa = Jb |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 0 | 1 | 0
|
| 01
| x | x | x | x
|
| 11
| x | x | x | x
|
| 10
| 0 | 0 | 1 | 0
|
| Jc = QaQb | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | x | x | x
|
| 01
| 0 | 0 | 1 | 0
|
| 11
| 0 | 0 | 1 | 0
|
| 10
| x | x | x | x
|
| Kc = QaQb = Jc |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| 0 | 0 | 0 | 0
|
| 01
| 0 | 0 | 1 | 0
|
| 11
| x | x | x | x
|
| 10
| x | x | x | x
|
| Jd = 1 | |
| QdQc\QbQa | 00 | 01 | 11 | 10
|
| 00
| x | 1 | 1 | x
|
| 01
| x | 1 | 1 | x
|
| 11
| x | 1 | 1 | x
|
| 10
| x | 1 | 1 | x
|
| Kd = 1 |
Conclusions
Ressources
