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'
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7.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
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')
# Tests
(insensible à la casse)(Ctrl+I)