Pour aller plus loin

Conversion de la base 10 en virgule flottante

Faire la conversion dans l'autre sens est un peu plus compliqué. L'algorithme global est le suivant :

• Découper le nombre en partie entière et partie décimale.
• Déterminer le signe.

• Si la partie entière n'est pas nulle, la convertir en binaire, en enlevant le \(1\) de gauche et calculer la puissance de 2 correspondant à ce \(1\).

  Sinon, commencer à calculer la partie décimale en binaire et chercher le premier 1 et la puissance de 2 correspondant.

• Calculer l'exposant en prenant la puissance de 2 trouvée et en ajoutant 127

• Convertir cet exposant en binaire sur 8 bits.
• Calculer la mantisse jusqu'à arriver à 23 bits.
• Si le premier chiffre de la partie décimale restante est 5 ou plus, ajouter 1 à la mantisse.

Exercice 11

Compléter le code de la fonction entier_vers_bin_expo qui prend en paramètre un texte correspondant à un nombre entier strictement positif et qui renvoie l'exposant correspondant à la puissance de 2 associée au 1 le plus à gauche, ainsi que le reste du nombre en binaire.

>>> entier_vers_bin_expo("14") # 14 -> 1110
(3, '110')
>>> entier_vers_bin_expo("5")  # 5 -> 101
(2, '01')
>>> entier_vers_bin_expo("1")  # 1 -> 1
(0, '')

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Exercice 12

Compléter le code de la fonction entier_vers_bin_taille qui prend en paramètres deux entiers entier et taille et renvoie l'écriture binaire sous forme de texte de entier sur taille bits. Si le nombre est trop grand, on ne donne que les taille derniers bits (ceux à droite).

>>> entier_vers_bin_taille(52, 8)
'00110100'
>>> entier_vers_bin_taille(135, 8)
'10000111'
>>> entier_vers_bin_taille(0, 8)
'00000000'

###(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)

Exécuter le code
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(Ctrl+Enter)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : 5/5

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La fonction ajouter_1

Pour l'exercice suivant, vous pouvez utiliser la fonction suivante pour ajouter 1 à la mantisse en cas d'arrondi par excès :

def ajouter_1(nb):
    rep = ""
    retenue = 1
    i = len(nb)
    while i>0:
        i -= 1
        if retenue == 1:
            if nb[i] == "1":
                rep = "0" + rep
            else:
                rep = "1" + rep
                retenue = 0
        else:
            rep = nb[i] + rep
    return rep

Exercice 13

Écrire une fonction reel_vers_flottant qui prend en paramètre un texte correspondant à un nombre décimal en base 10 et qui renvoie le triplet (signe, exposant, mantisse) qui correspond à l'écriture en virgule flottante de ce nombre.

>>> reel_vers_flottant("125")
('0', '10000101', '11110100000000000000000')
>>> reel_vers_flottant("0,3")
('0', '01111101', '00110011001100110011010')
>>> reel_vers_flottant("-51,79")
('1', '10000100', '10011110010100011110110')

Version videVersion avec code à trous

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(Ctrl+S)Valider
(Ctrl+Enter)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : 5/5

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###(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)

Exécuter le code
(Ctrl+S)Valider
(Ctrl+Enter)TéléchargerTéléverserRéinitialiser l'éditeurSauvegarder dans le navigateurÉvaluations restantes : 5/5

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