Aller au contenu

Virgule flottante⚓︎

De la virgule flottante vers la base 10

Dans cette partie, nous allons essayer de passer de la virgule flottante à la base 10. Les nombres en virgule flottante seront représentés par un triplet (signe, exposant, mantisse). On considérera des nombres flottants en 32 bits.

Pour convertir le nombre, il faut commencer par calculer la valeur de l'exposant et soustraire \(127\). On obtient alors le nombre \(e\). Si on note \(m_1\), \(m_2\)... les chiffres de la mantisse, on obtient alors la valeur du réel en faisant \(2^e + m_1 \times 2^{e-1} + m_2 \times 2^{e-2} + \ldots + m_{23} \times 2^{e-23}\).

Pour rappel, enlever 1 à l'exposant revient à diviser par 2 le coefficient précédent.

Il ne reste plus qu'à appliquer le signe pour obtenir le résultat.

La fonction bin_vers_entier

On considère la fonction suivante qui permet de transformer un entier donné en binaire en entier en base 10.

def bin_vers_entier(binaire):
    rep = 0
    for b in binaire:
        rep = rep * 2
        if b == "1":
            rep = rep + 1
    return rep

Vous pourrez utiliser cette fonction dans la suite.

Exercice 10

Compléter la fonction flottant_vers_reel qui prend en paramètre un triplet correspondant à un nombre en virgule flottante et qui renvoie le nombre décimal correspondant exprimé en base 10. Les 3 parties du triplet sont des nombres binaires donnés sous forme de texte. Le signe est composé d'un bit, l'exposant de 8 et la mantisse de 23.

>>> flottant_vers_reel(('0', '10000110', '10100110100110000000000'))
211.296875
>>> flottant_vers_reel(('1', '01111101', '10000000000000000000000'))
-0.375

Vous pouvez tester d'autres valeurs sur ce site.

###(Dés-)Active le code après la ligne # Tests (insensible à la casse)
(Ctrl+I)
Tronquer ou non le feedback dans les terminaux (sortie standard & stacktrace / relancer le code pour appliquer)
Évaluations restantes : 5/5

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