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Simplification des quines

Simplification des quines

par Le Grincheux  


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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.

Catégories: Général, Bêtisier
 15.11.13 11:50,

Aucun commentaire pour le moment


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Formulaire en cours de chargement...


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