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By F.Lagnier,F.Maraninchi, P.Amblard,J.-C.Fernandez, P.Sicard,Ph.Waille

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1)). Soient M et M deux monˆomes g´en´eraux : M = (m, (v1 , v2 , . . , vt )) et M = (m , (v1 , v2 , . . , vt )). On d´efinit un ordre sur les monˆomes g´en´eraux : M ≤ M ⇔ (m ≤ m ) et (v1 , v2 , . . , vt ) ≤ (v1 , v2 , . . , vt ). De la mˆeme fa¸con que pour une fonction simple, on d´efinit les monˆ omes g´en´eraux premiers. Un monˆome g´en´eral M est dit premier pour une fonction g´en´erale F si l’on a : M ≤ F et s’il n’existe pas M = M tel que M ≤ M et M ≤ F. La m´ethode de minimisation en utilisant des tableaux de Karnaugh consiste `a prendre tous les regroupements de cases maximaux sur plusieurs tableaux `a la fois.

Celle des caract`eres dans le paragraphe 5. La notion de taille de la repr´esentation est pr´esente en permanence. 1. 1 Codage binaire A un instant donn´e N fils ´electriques sont chacun `a 0 ou `a 1. Il est n´ecessaire d’identifier chacun des fils par un num´ero, par exemple entre 0 et N − 1. L’en- 50 Repr´esentation des grandeurs semble des N fils peut se trouver dans une des 2N configurations possibles. Les N fils peuvent repr´esenter 2N informations diff´erentes. On parle aussi des 2N valeurs possibles d’une information.

13 – Les bases compl`etes des fonctions f1 et f2 M4 ab 00 cd M1 01 11 10 M6 00 0 0 0 1 01 1 1 0 0 11 1 1 0 0 10 1 1 0 0 M2 f1 M7 M3 ab 00 cd 01 11 10 00 0 0 0 1 01 1 1 1 1 11 0 0 1 1 10 0 0 0 0 f2 M5 Fig. 14 – La base compl`ete de la fonction g´en´erale F = (f1 , f2 ) v2 , . . , vt + vt )). Enfin, on ne garde que les monˆomes les plus grands. 13 sont repr´esent´ees les deux bases compl`etes des fonctions f1 et f2 . Ces deux bases sont irr´edondantes. 14 est repr´esent´ee la base compl`ete de la fonction g´en´erale F = (f1 , f2 ).

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