Catégorie: "Général"
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Random photo
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Ajout à l'automate d'une surveillance de la haute tension
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Lors de la phase d'allumage, l'automate ne surveillait pas l'absence de haute tension (états 1 et 2). Ce nouvel automate vérifie ce point et indique une erreur en cas de présence de haute tension.
Fig. 1 : dernière version de l'automate (la même chose en grand)
La nouvelle table de transition est la suivante :
| Entrées |
États futurs et |
|||||||||||||||||||
| Q3 | Q2 | Q1 | Q0 | I | PBT | PHT | C15 | C255 | Q3 | Q2 | Q1 | Q0 | J3 | K3 | J2 | K2 | J1 | K1 | J0 | K0 |
| 0 | 0 | 0 | 0 | X | X | 0 | 0 | 0 | 0 | X | X | X | X | |||||||
| 0 | 0 | 0 | 0 | 1 | X | X | X | X | 0 | 0 | 0 | 1 | X | X | X | 1 | X | |||
| 0 | 0 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | ||||
| 0 | 0 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | ||||
| 0 | 0 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | |||
| 0 | 0 | 0 | 1 | 1 | X | X | 0 | 0 | 0 | 1 | X | X | X | X | ||||||
| 0 | 0 | 0 | 1 | 1 | X | 1 | X | 0 | 1 | 1 | 1 | X | 1 | X | 1 | X | X | |||
| 0 | 0 | 0 | 1 | 1 | X | 1 | X | X | 0 | 1 | 1 | 1 | X | 1 | X | 1 | X | X | ||
| 0 | 0 | 0 | 1 | X | X | X | X | 1 | 0 | 0 | 1 | 1 | X | X | X | X | ||||
| 0 | 0 | 0 | 1 | 1 | 1 | 1 | X | 0 | 0 | 1 | 0 | X | X | 1 | X | X | 1 | |||
| 0 | 0 | 1 | 0 | X | X | X | X | 1 | 0 | 0 | 1 | 1 | X | X | X | 1 | 1 | X | ||
| 0 | 0 | 1 | 0 | 1 | 1 | X | 0 | 0 | 1 | 0 | X | X | X | X | ||||||
| 0 | 0 | 1 | 0 | 1 | X | 1 | X | X | 0 | 1 | 1 | 1 | X | 1 | X | X | 1 | X | ||
| 0 | 0 | 1 | 0 | 1 | X | X | X | 0 | 1 | 1 | 1 | X | 1 | X | X | 1 | X | |||
| 0 | 0 | 1 | 0 | 1 | 1 | X | 1 | 0 | 0 | 1 | 1 | X | X | X | 1 | X | ||||
| 0 | 0 | 1 | 1 | X | 1 | X | X | 0 | 0 | 1 | 1 | X | X | X | X | |||||
| 0 | 0 | 1 | 1 | X | 1 | 1 | 1 | X | 0 | 1 | 0 | 0 | X | 1 | X | X | 1 | X | 1 | |
| 0 | 0 | 1 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | 1 | X | X | X | ||||
| 0 | 0 | 1 | 1 | X | 1 | 1 | X | 0 | 1 | 1 | 1 | X | 1 | X | X | X | ||||
| 0 | 1 | 0 | 0 | 1 | 1 | 1 | X | X | 0 | 1 | 0 | 0 | X | X | X | X | ||||
| 0 | 1 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | |||
| 0 | 1 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | |||
| 0 | 1 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | ||||
| 0 | 1 | 0 | 0 | X | X | X | X | 1 | 1 | 0 | 1 | 1 | X | X | X | 1 | X | |||
| 1 | 1 | 0 | 1 | X | 1 | X | X | 1 | 1 | 0 | 1 | X | X | X | X | |||||
| 1 | 1 | 0 | 1 | X | 1 | X | 1 | X | 0 | 1 | 0 | 1 | X | 1 | X | X | X | |||
| 1 | 1 | 0 | 1 | X | X | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | 1 | ||
| 0 | 1 | 0 | 1 | 1 | X | X | X | X | 0 | 1 | 0 | 0 | X | X | X | X | 1 | |||
| 0 | 1 | 0 | 1 | 1 | X | 0 | 1 | 0 | 1 | X | X | X | X | |||||||
| 0 | 1 | 0 | 1 | X | X | X | 0 | 1 | 1 | 0 | X | X | 1 | X | X | 1 | ||||
| 0 | 1 | 0 | 1 | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | X | 1 | X | X | 1 | |||
| 0 | 1 | 0 | 1 | 1 | X | 1 | 1 | 0 | 0 | 1 | 1 | X | X | 1 | X | X | ||||
| 1 | 0 | 0 | 1 | X | X | X | X | X | 1 | 0 | 0 | 0 | X | X | X | X | 1 | |||
| 1 | 0 | 0 | 0 | X | X | X | 1 | 0 | 0 | 0 | X | X | X | X | ||||||
| 1 | 0 | 0 | 0 | X | 1 | 1 | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | ||
| 1 | 0 | 0 | 0 | X | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | |
| 1 | 0 | 0 | 0 | X | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | ||
| 1 | 0 | 0 | 0 | X | 1 | X | 0 | 0 | 0 | 0 | X | 1 | X | X | X | |||||
| 0 | 1 | 1 | 0 | X | X | X | X | 0 | 1 | 1 | 0 | X | X | X | X | |||||
| 0 | 1 | 1 | 0 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | X | X | 1 | X | |||
| 0 | 1 | 1 | 1 | X | X | X | X | 0 | 0 | 0 | 0 | X | X | 1 | X | 1 | X | 1 | ||
| 0 | 1 | 1 | 1 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | X | X | X | ||||
Tab. 2 : transitions de l'automate
Automate, suite
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Comme il faut toujours remettre son ouvrage sur le travail, voici la dernière version de l'automate à états finis gérant l'alimentation.
Fig. 1 : dernière version de l'automate (la même chose en grand)
J'espère cette fois-ci n'avoir rien oublié. Ce nouvel automate comporte onze états, donc nécessite quatre bascules au lieu de trois. Il faut donc réétudier les sorties du circuit à l'aide de nouveaux tableaux de Karnaugh.
| B | Q1Q0 | |||
| Q3Q2 | 00 | 01 | 11 | 10 |
| 00 | 1 | 1 | 1 | |
| 01 | 1 | 1 | ||
| 11 | X | 1 | X | X |
| 10 | X | X | ||
Tab. 1 : allumage de la basse tension
B=Q1'Q2+Q0Q2'Q3'+Q1Q2'
| H | Q1Q0 | |||
| Q3Q2 | 00 | 01 | 11 | 10 |
| 00 | 1 | |||
| 01 | 1 | |||
| 11 | X | X | X | |
| 10 | X | X | ||
Tab. 2 : allumage de la haute tension
H=Q2Q1'Q0'+Q2'Q1Q0
| R | Q1Q0 | |||
| Q3Q2 | 00 | 01 | 11 | 10 |
| 00 | 1 | |||
| 01 | 1 | 1 | 1 | |
| 11 | X | X | X | |
| 10 | 1 | X | X | |
Tab. 3 : blocage du compteur à zéro
R=Q3'Q1'Q0'+Q3Q2'Q0+Q2Q1
| E | Q1Q0 | |||
| Q3Q2 | 00 | 01 | 11 | 10 |
| 00 | ||||
| 01 | 1 | 1 | ||
| 11 | X | X | X | |
| 10 | X | X | ||
Tab. 4 : indicateur d'erreur
E=Q2Q1
Le schéma des quatre sorties devient alors :
Fig. 1 : câblage des sorties (la même chose en grand)
Reste à écrire la table des transitions et à simplifier les quines.
| Entrées |
États futurs et |
|||||||||||||||||||
| Q3 | Q2 | Q1 | Q0 | I | PBT | PHT | C15 | C255 | Q3 | Q2 | Q1 | Q0 | J3 | K3 | J2 | K2 | J1 | K1 | J0 | K0 |
| 0 | 0 | 0 | 0 | X | X | 0 | 0 | 0 | 0 | X | X | X | X | |||||||
| 0 | 0 | 0 | 0 | 1 | X | X | X | X | 0 | 0 | 0 | 1 | X | X | X | 1 | X | |||
| 0 | 0 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | ||||
| 0 | 0 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | ||||
| 0 | 0 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | |||
| 0 | 0 | 0 | 1 | 1 | X | X | X | 0 | 0 | 0 | 1 | X | X | X | X | |||||
| 0 | 0 | 0 | 1 | 1 | X | 1 | X | 0 | 1 | 1 | 1 | X | 1 | X | 1 | X | X | |||
| 0 | 0 | 0 | 1 | X | X | X | X | 1 | 0 | 0 | 1 | 1 | X | X | X | X | ||||
| 0 | 0 | 0 | 1 | 1 | 1 | X | 1 | X | 0 | 0 | 1 | 0 | X | X | 1 | X | X | 1 | ||
| 0 | 0 | 1 | 0 | X | X | X | X | 1 | 0 | 0 | 1 | 1 | X | X | X | 1 | 1 | X | ||
| 0 | 0 | 1 | 0 | 1 | 1 | X | X | 0 | 0 | 1 | 0 | X | X | X | X | |||||
| 0 | 0 | 1 | 0 | 1 | X | X | X | 0 | 1 | 1 | 1 | X | 1 | X | X | 1 | X | |||
| 0 | 0 | 1 | 0 | 1 | 1 | X | X | 1 | 0 | 0 | 1 | 1 | X | X | X | 1 | X | |||
| 0 | 0 | 1 | 1 | X | 1 | X | X | 0 | 0 | 1 | 1 | X | X | X | X | |||||
| 0 | 0 | 1 | 1 | X | 1 | 1 | 1 | X | 0 | 1 | 0 | 0 | X | 1 | X | X | 1 | X | 1 | |
| 0 | 0 | 1 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | 1 | X | X | X | ||||
| 0 | 0 | 1 | 1 | X | 1 | 1 | X | 0 | 1 | 1 | 1 | X | 1 | X | X | X | ||||
| 0 | 1 | 0 | 0 | 1 | 1 | 1 | X | X | 0 | 1 | 0 | 0 | X | X | X | X | ||||
| 0 | 1 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | |||
| 0 | 1 | 0 | 0 | 1 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | |||
| 0 | 1 | 0 | 0 | 1 | X | X | 0 | 1 | 1 | 1 | X | X | 1 | X | 1 | X | ||||
| 0 | 1 | 0 | 0 | X | X | X | X | 1 | 1 | 0 | 1 | 1 | X | X | X | 1 | X | |||
| 1 | 1 | 0 | 1 | X | 1 | X | X | 1 | 1 | 0 | 1 | X | X | X | X | |||||
| 1 | 1 | 0 | 1 | X | 1 | X | 1 | X | 0 | 1 | 0 | 1 | X | 1 | X | X | X | |||
| 1 | 1 | 0 | 1 | X | X | X | X | 0 | 1 | 1 | 0 | X | 1 | X | 1 | X | X | 1 | ||
| 0 | 1 | 0 | 1 | 1 | X | X | X | X | 0 | 1 | 0 | 0 | X | X | X | X | 1 | |||
| 0 | 1 | 0 | 1 | 1 | X | 0 | 1 | 0 | 1 | X | X | X | X | |||||||
| 0 | 1 | 0 | 1 | X | X | X | 0 | 1 | 1 | 0 | X | X | 1 | X | X | 1 | ||||
| 0 | 1 | 0 | 1 | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | X | 1 | X | X | 1 | |||
| 0 | 1 | 0 | 1 | 1 | X | 1 | 1 | 0 | 0 | 1 | 1 | X | X | 1 | X | X | ||||
| 1 | 0 | 0 | 1 | X | X | X | X | X | 1 | 0 | 0 | 0 | X | X | X | X | 1 | |||
| 1 | 0 | 0 | 0 | X | X | X | 1 | 0 | 0 | 0 | X | X | X | X | ||||||
| 1 | 0 | 0 | 0 | X | 1 | 1 | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | ||
| 1 | 0 | 0 | 0 | X | 1 | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | |
| 1 | 0 | 0 | 0 | X | 1 | X | X | 0 | 1 | 1 | 0 | X | 1 | 1 | X | 1 | X | X | ||
| 1 | 0 | 0 | 0 | X | 1 | X | 0 | 0 | 0 | 0 | X | 1 | X | X | X | |||||
| 0 | 1 | 1 | 0 | X | X | X | X | 0 | 1 | 1 | 0 | X | X | X | X | |||||
| 0 | 1 | 1 | 0 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | X | X | 1 | X | |||
| 0 | 1 | 1 | 1 | X | X | X | X | 0 | 0 | 0 | 0 | X | X | 1 | X | 1 | X | 1 | ||
| 0 | 1 | 1 | 1 | 1 | X | X | X | X | 0 | 1 | 1 | 1 | X | X | X | X | ||||
Tab. 2 : transitions de l'automate
Simplification des quines
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N'ayant pas encore d'hypercube à ma disposition pour écrire des tableaux de Karnaugh à plus de six variables, il convient d'utiliser les techniques de réduction de Mc Cluskey. Je vous fais grâce des calculs. Pour des raisons de simplicité d'écriture, les apostrophes notent une condition inversée. En voici les résultats :
J2=Q1'Q0'I'PHT+Q1'Q0'I'PBT+Q0IPBT'C15+Q1IPBT'+Q1Q0PBT'+Q1Q0C15
K2=Q0I'PBTPHT'C255+Q1Q0I'
J1=Q2'Q0'I'PHT+Q2'Q0'I'PBT+Q2'Q0IC15+Q2Q0'IPBT'+Q2Q0'IPHT'
+Q2Q0I'PBT'+Q2Q0I'PHT
K1=Q2'Q0'I'+Q2'Q0PBTPHTC15+Q2Q0I'
J0=Q2'Q1'I+IPBT'+Q2Q1'I'+Q2Q1I+Q1'IPHT'+Q2'IC255
K0=Q2'Q1'I'+Q2'PBTPHTC15+Q2Q1'I+Q2Q1I'+Q1'I'PBT'+Q1'I'C255
+Q1'I'PHT+Q2'Q1'PBTC15
Comme la vitesse n'est pas critique, il est possible de factoriser quelque peu certaines expressions.
J2=Q1'Q0'I'(PHT+PBT)+PBT'I(Q0C15+Q1)+Q1Q0(PBT'+C15)
K2=Q0I'(PBTPHT'C255+Q1)
J1=Q2'Q0'I'(PBT+PHT)+Q2Q0'I(PBT'+PHT')+Q2Q0I'(PHT+PBT')+Q2'Q0IC15
J0=Q1'(Q2'I+Q2I')+(IPBT')+Q2Q1I+Q1'IPHT'+Q2'IC255
K0=Q2'Q1'(I'+PBTC15)+Q2'PBTPHTC15+Q1'I'(PBT'+C255+PHT)+Q2(Q1'I+Q1I')
J'ai refait deux fois tous les calculs, je pense ne pas m'être trompé. Or une simulation du circuit ne fonctionne pas comme attendue. S'il commande aux différentes tensions jusqu'à l'allumage complet, basse et haute tensions, il indique une erreur lors de l'extinction. J'ai eu un peu de mal à comprendre mon erreur puisqu'elle ne résidait pas dans la réduction des quines mais dans une hypothèse hasardeuse. Bêtement, j'avais considéré que les basse et haute tensions avaient un temps de descente nul !
Il est donc nécessaire de rajouter une temporisation lors de l'extinction des différentes tensions avant de tester les absences de ces tensions.
Derniers raffinements de l'automate
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Il manque à l'automate un dernier raffinement consistant en une transition allant de l'état 000 (repos) vers l'état 110 (défaut appareil éteint). En effet, si une tension de chauffage ou une haute tension apparaît dans le circuit commandé, l'alimentation est en panne et il convient de le signaler. Le nouveau diagramme des états devient alors :
Fig. 1 : nouveau diagramme d'états (le même en grand)
Cette nouvelle transition ne change rien aux équations des sorties décrites plus tôt. En revanche, la table des transitions devient :
| Entrées | Sorties | |||||||||||||||
| Q2 | Q1 | Q0 | I | PBT | PHT | C15 | C255 | Q'2 | Q'1 | Q'0 | J2 | K2 | J1 | K1 | J0 | K0 |
| X | X | X | X | X | ||||||||||||
| 1 | X | X | 1 | 1 | 1 | X | 1 | X | X | |||||||
| 1 | X | X | 1 | 1 | 1 | X | 1 | X | X | |||||||
| 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | X | ||||||
| 1 | X | X | X | X | 1 | X | X | 1 | X | |||||||
| 1 | X | X | X | X | X | X | X | 1 | ||||||||
| 1 | 1 | X | X | X | 1 | X | X | X | ||||||||
| 1 | 1 | X | 1 | X | 1 | 1 | 1 | 1 | X | 1 | X | X | ||||
| 1 | 1 | 1 | X | 1 | X | 1 | X | 1 | X | X | 1 | |||||
| 1 | X | X | X | X | X | X | 1 | X | ||||||||
| 1 | 1 | X | X | X | 1 | 1 | 1 | 1 | X | X | 1 | X | ||||
| 1 | 1 | 1 | X | X | 1 | X | X | X | ||||||||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | X | 1 | X | |||||
| 1 | 1 | X | X | X | X | 1 | 1 | 1 | 1 | X | X | X | ||||
| 1 | 1 | X | 1 | 1 | X | 1 | 1 | 1 | 1 | X | X | X | ||||
| 1 | 1 | X | 1 | X | X | 1 | 1 | X | X | X | ||||||
| 1 | 1 | X | 1 | 1 | 1 | X | 1 | 1 | X | X | 1 | X | 1 | |||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | ||||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | ||||
| 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | |||||
| 1 | 1 | 1 | 1 | X | X | 1 | X | X | X | |||||||
| 1 | X | X | X | X | 1 | 1 | X | X | 1 | X | ||||||
| 1 | 1 | 1 | X | X | X | X | 1 | X | X | X | 1 | |||||
| 1 | 1 | 1 | X | 1 | X | 1 | X | X | 1 | |||||||
| 1 | 1 | 1 | X | 1 | 1 | X | X | X | ||||||||
| 1 | 1 | X | X | X | 1 | 1 | X | 1 | X | X | 1 | |||||
| 1 | 1 | 1 | 1 | X | X | 1 | 1 | X | 1 | X | X | 1 | ||||
| 1 | 1 | X | X | X | X | 1 | 1 | X | X | X | ||||||
| 1 | 1 | 1 | X | X | X | X | 1 | 1 | 1 | X | X | 1 | X | |||
| 1 | 1 | 1 | 1 | X | X | X | X | 1 | 1 | 1 | X | X | X | |||
| 1 | 1 | 1 | X | X | X | X | X | 1 | X | 1 | X | 1 | ||||
Tab. 1 : nouvelle table des transitions
Nouvelles transitions
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En gardant les mêmes notations qu'à l'article transitions, la nouvelle table de vérité est la suivante :
| Entrées | Sorties | |||||||||||||||
| Q2 | Q1 | Q0 | I | PBT | PHT | C15 | C255 | Q'2 | Q'1 | Q'0 | J2 | K2 | J1 | K1 | J0 | K0 |
| X | X | X | X | X | X | X | ||||||||||
| 1 | X | X | X | X | 1 | X | X | 1 | X | |||||||
| 1 | X | X | X | X | 0 | X | X | X | 1 | |||||||
| 1 | 1 | X | X | X | 1 | X | X | X | ||||||||
| 1 | 1 | X | 1 | X | 1 | 1 | 1 | 1 | X | 1 | X | X | ||||
| 1 | 1 | 1 | X | 1 | X | 1 | X | 1 | X | X | 1 | |||||
| 1 | X | X | X | X | 0 | X | X | 1 | X | |||||||
| 1 | 1 | X | X | X | 1 | 1 | 1 | 1 | X | X | 1 | X | ||||
| 1 | 1 | 1 | X | X | 1 | X | X | X | ||||||||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | X | 1 | X | |||||
| 1 | 1 | X | X | X | X | 1 | 1 | 1 | 1 | X | X | X | ||||
| 1 | 1 | X | 1 | 1 | X | 1 | 1 | 1 | 1 | X | X | X | ||||
| 1 | 1 | X | 1 | X | X | 1 | 1 | X | X | X | ||||||
| 1 | 1 | X | 1 | 1 | 1 | X | 1 | 1 | X | X | 1 | X | 1 | |||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | ||||
| 1 | 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | ||||
| 1 | 1 | X | X | 1 | 1 | 1 | X | 1 | X | 1 | X | |||||
| 1 | 1 | 1 | 1 | X | X | 1 | X | X | X | |||||||
| 1 | X | X | X | X | 1 | 1 | X | X | 1 | X | ||||||
| 1 | 1 | 1 | X | X | X | X | 1 | X | X | X | 1 | |||||
| 1 | 1 | 1 | X | 1 | X | 1 | X | X | 1 | |||||||
| 1 | 1 | 1 | X | 1 | 1 | X | X | X | ||||||||
| 1 | 1 | X | X | X | 1 | 1 | X | 1 | X | X | 1 | |||||
| 1 | 1 | 1 | 1 | X | X | 1 | 1 | X | 1 | X | X | 1 | ||||
| 1 | 1 | X | X | X | X | 1 | 1 | X | X | X | ||||||
| 1 | 1 | 1 | X | X | X | X | 1 | 1 | 1 | X | X | 1 | X | |||
| 1 | 1 | 1 | 1 | X | X | X | X | 1 | 1 | 1 | X | X | X | |||
| 1 | 1 | 1 | X | X | X | X | X | 1 | X | 1 | X | 1 | ||||
Tab. 1 : table de vérité du nouvel automate
Contrairement à la première table de vérité, les entrées J et K des bascules utilisent maintenant des états indifférents notés « X » qui devraient simplifier d'autant la synthèse du circuit logique.
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