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

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Extra resources for Architectures Logicielles et Materielles

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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.

4). 34 Alg`ebre de Boole et fonctions bool´eennes c (0,0,1) (1,0,1) (0,1,1) (1,1,1) (0,1,0) b (0,0,0) (1,0,0) a 00 01 0 * O 1 O 11 10 O (1,1,0) (b) (a) Fig. 4 – a) Repr´esentation sur un hypercube `a 3 dimensions d’une fonction `a trois variables a, b et c. b) Pr´esentation du tableau de Karnaugh associ´e ; les cases marqu´ees d’un O sont adjacentes `a la case marqu´ee d’une ´etoile. d Fig. 2 Obtention d’une somme de monˆ omes ` a partir d’un tableau de Karnaugh En dimension 2, les colonnes et lignes d’un tableau de Karnaugh sont agenc´ees de telle fa¸con qu’un monˆome de la fonction corresponde `a un rectangle de 2n cases adjacentes portant la valeur 1.

2 Obtention d’une forme polynˆ omiale De nombreuses technologies de r´ealisation des circuits n´ecessitent une forme polynˆomiale. Le crit`ere d’optimisation est alors le nombre de monˆomes apparaissant dans la forme polynˆomiale puis le nombre de variables dans ces monˆomes. Un certain nombre de techniques de simplification respectant ce crit`ere ont ´et´e mises au point et int´egr´ees dans les outils modernes de CAO. Nous montrons ici comment obtenir une forme polynˆomiale r´eduite `a partir d’un tableau de Karnaugh.

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