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

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Additional info for Architectures Logicielles et Materielles

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Selon la technologie de circuit cible, certaines repr´esentations sont plus ad´equates pour arriver `a une impl´ementation optimis´ee. Une repr´esentation peut bien convenir `a certains types de fonctions et devenir tr`es complexe, voire impossible `a utiliser pour d’autres. Enfin, selon l’outil de CAO (Conception assist´ee par ordinateur) utilis´e, certaines formes sont accept´ees (car bien adapt´ees `a une repr´esentation sur machine) ou non. Le paragraphe 1. pr´esente les principales d´efinitions concernant cette alg`ebre et les fonctions bool´eennes.

8 – La d´ecomposition de Shannon repr´esent´ee par un arbre binaire zaine d’ann´ees. Ils permettent de repr´esenter et de manipuler des fonctions bool´eennes de grande taille. Nous allons d´efinir tout d’abord les arbres de Shannon, un BDD ´etant un graphe acyclique orient´e ayant les mˆemes chemins que l’arbre de Shannon associ´e mais dans lequel il n’y a pas de redondances. Tout l’int´erˆet des BDD est que l’on sait les construire, `a coˆ ut algorithmique int´eressant, `a partir d’une autre repr´esentation (par exemple, une forme alg´ebrique) sans avoir `a construire l’arbre de Shannon (Cf.

X¯2 est associatif. 13 : Th´ eor` eme de Shannon D´emontrer la premi`ere forme du th´eor`eme de Shannon. x¯2 `a partir de la deuxi`eme forme du th´eor`eme de Shannon. 15 : Poids d’un vecteur bool´ een On appelle poids d’un vecteur bool´een le nombre de 1 de ce vecteur. le vecteur (0, 1, 1, 0) a un poids de 2. Donner des expressions bool´eennes des fonctions simples p2 , p1 et p0 qui correspondent au codage en base 2 du poids d’un vecteur de 4 variables bool´eennes x1 , x2 , x3 , x4 . 5. Exercices 47 a f g e b c d Fig.

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Architectures Logicielles et Materielles by P.Amblard, J.-C.Fernandez, F.Lagnier, F.Maraninchi, P.Sicard, Ph.Waille

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