Virgule fixe
Gestion de la partie décimale
Objectif de cette partie
Nous allons faire une fonction qui transforme un nombre décimal en base 10, en un nombre décimal en binaire. Nous n'allons pas encore utiliser de virgule flottante et juste mettre une partie entière et une partie décimale en indiquant éventuellement la partie qui se répète.
Par exemple, le nombre \(9,3\) sera transfortmé en \(1001,0[1001]\) .
Comme d'habitude, les nombres binaires seront représentés par des textes, avec le bit de poids fort (la plus haute puissance de 2) à gauche. Ainsi, 4 sera représenté en binaire par "100"
.
Par contre, pour ne pas être parasités par la représentation des nombres décimaux en Python, nous représenterons aussi les nombres en base 10 par des textes.
La fonction entier_vers_bin
Nous allons avoir besoin d'une fonction qui permet de convertir la partie entière en binaire.
Dans tous les exercices suivants, y compris ceux des pages suivantes, vous pourrez utiliser la fonction suivante :
def entier_vers_bin ( partie_entiere ):
rep = ""
v = int ( partie_entiere )
while v > 1 :
rep = str ( v % 2 ) + rep
v = v // 2
rep = str ( v ) + rep
return rep
>>> entier_vers_bin ( "5" )
'101'
>>> entier_vers_bin ( "62" )
'111110'
Vous pouvez tester la fonction ci-dessous :
Exercice 3
Compléter le tableau ci-dessous correspondant aux différentes valeurs prises par v
et rep
au cours de l'exécution de entier_vers_bin(19)
.
Il peut y avoir des lignes en trop.
Indice
En cas de doute, on peut rajouter des print
dans la fonction pour obtenir les valeurs au cours de l'exécution.
Solution
Il faut bien penser à ajouter les chiffres à gauche de rep
.
position
v
v%2
rep
v//2
avant la boucle
19
""
après rep = ...
19
1
"1"
9
après rep = ...
9
1
"11"
4
après rep = ...
4
0
"011"
2
après rep = ...
2
0
"0011"
1
à la fin de la fonction
1
1
"10011"
0
La fonction fois_2
Dans tous les exercices suivants, y compris ceux des pages suivantes, vous pourrez utiliser la fonction suivante :
def fois_2 ( val ):
retenue = 0 # On commence sans retenue
i = len ( val ) - 1 # On commence par le chiffre à droite
val2 = "" # Le résultat est vide
while i >= 0 : # On parcourt de droite à gauche
c = int ( val [ i ]) # On convertit le symbole en nombre
double = 2 * c + retenue # On fait le calcul
retenue = double // 10 # On garde le chiffre des dizaines
c2 = double % 10 # On garde le chiffre des unités
if val2 != "" or c2 != 0 : # On regarde si on rajoute le chiffre
val2 = str ( c2 ) + val2
i -= 1 # On se décale à gauche
if val2 == "" : # Si on n'a rien rajouté
val2 = "0" # C'est que le résultat est 0
return retenue , val2 # On renvoie la retenue et le résultat
Cette fonction sert à multiplier par 2 la partie décimale d'un nombre. Elle prend en paramètre un texte correspondant à la partie décimale (par exemple "34"
pour \(7,34\) ) et renvoie deux valeurs :
un entier correspondant à une éventuelle retenue (donc 0 ou 1)
un texte correspondant à la nouvelle partie décimale correspondant à la précédente multipliée par 2
>>> fois_2 ( "75" ) # 2 * 0.75 = 1.5
(1, '5')
>>> fois_2 ( "1954" ) # 2 * 0.1954 = 0.3908
(0, '3908')
>>> fois_2 ( "0" )
(0, '0')
>>> fois_2 ( "7000" ) # 0.7000 = 0.7
(1, '4')
On peut remarquer que si les derniers chiffres sont des 0, on ne les ajoute pas. Tant qu'il n'y a pas au moins un chiffre non nul, on ne rajoute pas les 0.
Vous pouvez tester la fonction ci-dessous :
Exercice 4
Compléter le tableau suivant correspondant à l'exécution de fois_2 ( "1954" )
. Chacune des lignes, à part la première, correspond à l'état des variables à la fin d'un tour de la boucle while
.
Solution
c
double
retenue
val2
0
""
4
8
0
"8"
5
10
1
"08"
9
19
1
"908"
1
3
0
"3908"
Même question pour l'exécution de fois_2 ( "75" )
Solution
On ne rajoute pas le premier 0 parce que val2
est vide à ce moment là.
c
double
retenue
val2
0
""
5
10
1
""
7
15
1
"5"
Gérer les résultats d'une fonction qui renvoie plusieurs valeurs
La fonction fois_2
renvoyant un couple de valeurs, pour séparer ces valeurs, il faut le faire de la manière suivante :
>>> r , v = fois_2 ( "512" ) # 0.512 * 2 = 1.024
>>> r
1
>>> v
'024'
C'est une affectation multiple. Python décompose automatiquement la paire de valeurs renvoyée par fois_2
en deux valeurs. Nous reviendrons plus tard sur ce mécanisme.
Exercice 5
Compléter la fonction decimal_vers_bin
qui prend en paramètre un texte partie_decimale
et qui renvoie un texte correspondant à cette partie décimale en binaire. En cas de cycle infini, on utilise des crochets pour l'indiquer. La partie décimale ne doit pas être nulle.
Par exemple decimal_vers_bin ( "12" )
correspond à la partie décimale de \(0,12\) . Vous devez utiliser la fonction fois_2
.
>>> decimal_vers_bin ( "1" )
'0[0011]'
>>> decimal_vers_bin ( "2" )
'[0011]'
>>> decimal_vers_bin ( "3" )
'0[1001]'
>>> decimal_vers_bin ( "5" )
'1'
>>> decimal_vers_bin ( "01" )
'00[00001010001111010111]'
Ne pas mettre des nombres à plus de 2 chiffres
Sinon le temps de calcul risque d'être très grand.
Utilisation des slices
Lorsqu'on veut obtenir une partie d'un texte, on peut utiliser les slices . Ce n'est pas au programme de NSI, mais parfois, c'est bien pratique.
La syntaxe générale est texte[a:b]
pour prendre la sous-chaîne de texte allant du caractère d'indice a
inclus au caractère d'indice b
exclus.
>>> "bonjour" [ 1 : 3 ]
'on'
>>> "bonjour" [ 4 : 6 ]
'ou'
>>> "bonjour" [ 4 : 7 ]
'our'
La syntaxe texte[:b]
est équivalente à texte[0:b]
et texte[a:]
est équivalente à texte[a:len(texte)]
.
Enfin, texte[:-1]
permet d'obtenir le texte sans le dernière caractère.
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993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43995.43913.43930.43910.43931.43928.44023.43990.43928.43978.43997.43990.43982.43991.43985.43997.43928.43980.43991.43981.43980.43928.43979.43993.43981.43998.43928.43988.43997.43928.43996.43997.43978.43990.43985.43997.43978.43928.43995.43984.43985.43998.43998.43978.43997.43928.43977.43981.43985.43928.43997.43979.43980.43928.43912.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
Exercice 6
Compléter le tableau correspondant à l'exécution de decimal_vers_bin ( "1" )
. La première ligne correspond à l'état des variables avant la boucle while
. Dans les autres lignes, v
correspond à sa valeur au début de la boucle. Les autres variables correspondent aux valeurs à la fin de la boucle. Les valeurs des variables retenue
et prochain v
sont obtenues par l'appel à fois_2(v)
. Il y a le bon nombre de ligne
Solution
v
vus
retenue
rep
prochain v
"1"
[]
""
"1"
[ "1" ]
0
"0"
"2"
"2"
[ "1" , "2" ]
0
"00"
"4"
"4"
[ "1" , "2" , "4" ]
0
"000"
"8"
"8"
[ "1" , "2" , "4" , "8" ]
1
"0001"
"6"
"6"
[ "1" , "2" , "4" , "8" , "6" ]
1
"00011"
"2"
Déterminer l'indice de v
dans vus
à la sortie de la boucle.
Solution
À la fin de la boucle, v
vaut "2"
. Il est donc à l'indice 1 dans vus
.
En déduire la valeur renvoyée à la fin de l'appel à la fonction.
Solution
Puisque rep
vaut "00011"
et que v
n'est "0"
, le résultat renvoyé est rep [: 1 ] + "[" + rep [ 1 :] + "]"
.
On obtient donc 0 [ 0011 ]
.
Exercice 7
Tester les résultats de decimal_vers_bin
en augmentant progressivement le nombre de décimales afin de voir au bout de combien de chiffres après la virgule les calculs deviennent trop long.
Pour travailler sous Thonny
Si vous voulez utiliser Thonny, qui va plus vite, vous pouvez copier le contenu suivant :
def entier_vers_bin ( partie_entiere ):
rep = ""
v = int ( partie_entiere )
while v > 1 :
rep = str ( v % 2 ) + rep
v = v // 2
rep = str ( v ) + rep
return rep
def fois_2 ( val ):
retenue = 0 # On commence sans retenue
i = len ( val ) - 1 # On commence par le chiffre à droite
val2 = "" # Le résultat est vide
while i >= 0 : # On parcourt de droite à gauche
c = int ( val [ i ]) # On convertit le symbole en nombre
double = 2 * c + retenue # On fait le calcul
retenue = double // 10 # On garde le chiffre des dizaines
c2 = double % 10 # On garde le chiffre des unités
if val2 != "" or c2 != 0 : # On regarde si on rajoute le chiffre
val2 = str ( c2 ) + val2
i -= 1 # On se décale à gauche
if val2 == "" : # Si on n'a rien rajouté
val2 = "0" # C'est que le résultat est 0
return retenue , val2 # On renvoie la retenue et le résultat
def decimal_vers_bin ( partie_decimale ):
vus = [] # liste des restes déjà vus
rep = "" # la conversion en binaire
v = partie_decimale
while v not in vus : # On attend de voir une répétition
vus . append ( v ) # On met v dans ceux qu'on a vu
retenue , v = fois_2 ( v )
rep = rep + str ( retenue )
pos = vus . index ( v ) # On regarde à quel moment on a déjà vu la dernière valeur
if v != "0" : # on a un cycle infini
return rep [: pos ] + "[" + rep [ pos :] + "]"
else : # on a une valeur exacte
return rep [: - 1 ] # On renvoie tout sauf le dernier chiffre qui est 0
Partie entière et partie décimale
La fonction split
Afin de découper le nombre entre la partie entière et la partie décimale, nous allons utiliser la fonction split
qui s'utilise de la manière suivante :
>>> "211,3" . split ( "," )
['211', '3']
>>> "211" . split ( "," )
['211']
>>> "211,3,2,,71" . split ( "," )
['211', '3', '2', '', '71']
Cette commande découpe la chaîne associée en une liste. À chaque fois qu'on croise le symbole donné en paramètre, un nouvel élément est ajouté à la liste.
On peut remarquer que s'il n'y a pas de virgules, la liste ne contient qu'un seul élément.
Il faut donc distinguer deux cas :
celui où la liste obtenue n'a qu'un seul élément, c'est donc un nombre entier
celui où il y a deux éléments : la partie entière et la partie décimale.
Exercice 8
Compléter la fonction reel_vers_bin
qui prend en paramètre un texte correspondant à un nombre, ayant potentiellement une virgule, et qui renvoie la version binaire de ce nombre, avec une virgule fixe, toujours sous forme de texte.
Vous pouvez utiliser des fonctions des exercices précédents.
>>> reel_vers_bin ( "9" )
'1001'
>>> reel_vers_bin ( "9,5" )
'1001,1'
>>> reel_vers_bin ( "9,3" )
'1001,0[1001]'
Indice
Lorsqu'il y a une virgule, decomp[0]
est la partie entière et decomp[1]
la partie décimale.
43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43915.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43916.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43917.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43918.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43919.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43904.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43978.43997.43997.43988.44007.43982.43997.43978.43979.44007.43994.43985.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43996.43997.43995.43991.43989.43976.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43926.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43979.43976.43988.43985.43980.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43979.43914.43930.43910.43934.43977.43981.43991.43980.43907.43924.43934.43977.43981.43991.43980.43907.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43993.43978.43980.43985.43997.44007.43997.43990.43980.43985.43997.43978.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43997.43990.43980.43985.43997.43978.44007.43982.43997.43978.43979.44007.43994.43985.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43996.43997.43995.43991.43989.43976.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43912.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43921.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43994.43930.43910.43988.43997.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43996.43997.43995.43991.43989.43976.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43995.43913.43930.43910.43931.43928.43976.43993.43979.43928.43996.43997.43928.43976.43993.43978.43980.43985.43997.43928.43996.43857.43995.43985.43989.43993.43988.43997.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43993.43978.43980.43985.43997.44007.43997.43990.43980.43985.43997.43978.43997.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43997.43988.43979.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43993.43978.43980.43985.43997.44007.43996.43997.43995.43985.43989.43993.43988.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43996.43997.43995.43985.43989.43993.43988.44007.43982.43997.43978.43979.44007.43994.43985.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43996.43997.43995.43991.43989.43976.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43921.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43993.43978.43980.43985.43997.44007.43997.43990.43980.43985.43997.43978.43997.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43923.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43979.43914.43930.43910.43934.43977.43981.43991.43980.43907.43924.43934.43977.43981.43991.43980.43907.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43923.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43976.43993.43978.43980.43985.43997.44007.43996.43997.43995.43985.43989.43993.43988.43997.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
Exercice 9
Compléter la fonction reel_vers_bin2
qui prend en paramètre un texte correspondant à un nombre, ayant potentiellement une virgule, et qui renvoie la version binaire de ce nombre, avec une virgule fixe, toujours sous forme de texte. Par rapport à reel_vers_bin
, le nombre peut avoir un signe -
au début. Dans ce cas, on met aussi un signe -
devant le nombre binaire. Si le nombre est positif, le comportement est identique à celui de reel_vers_bin
.
Vous pouvez utiliser reel_vers_bin
.
Il ne faut pas mettre d'espace entre le signe et le nombre.
>>> reel_vers_bin2 ( "-9" )
'-1001'
>>> reel_vers_bin2 ( "-9,3" )
'-1001,0[1001]'
>>> reel_vers_bin2 ( "9" )
'1001'
>>> reel_vers_bin2 ( "9,3" )
'1001,0[1001]'
Indice
S'il y a un signe moins, il se trouve en reel[0]
. Dans ce cas, la valeur absolue du nombre correspond à reel[1:]
.
43908.43996.43997.43980.43993.43985.43988.43979.43928.43995.43988.43993.43979.43979.43909.43930.43980.43985.43976.43930.43910.43954.43908.43979.43981.43989.43989.43993.43978.43969.43910.44011.43991.43988.43981.43980.43985.43991.43990.43908.43927.43979.43981.43989.43989.43993.43978.43969.43910.43954.43908.43996.43985.43982.43928.43989.43993.43978.43987.43996.43991.43983.43990.43909.43930.43913.43930.43928.43979.43980.43969.43988.43997.43909.43930.43989.43993.43978.43999.43985.43990.43906.43913.43926.43919.43997.43989.43928.43913.43997.43989.43930.43928.43910.43954.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43930.43910.43908.43980.43993.43994.43988.43997.43928.43995.43988.43993.43979.43979.43909.43930.43984.43985.43999.43984.43988.43985.43999.43984.43980.43980.43993.43994.43988.43997.43930.43910.43908.43980.43978.43910.43908.43980.43984.43928.43995.43991.43988.43979.43976.43993.43990.43909.43930.43914.43930.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43998.43985.43988.43997.43990.43993.43989.43997.43930.43910.90037.43928.44008.43978.43991.43976.43991.43979.43985.43980.43985.43991.43990.43928.43996.43997.43928.43995.43991.43978.43978.43997.43995.43980.43985.43991.43990.43908.43927.43979.43976.43993.43990.43910.43908.43927.43980.43984.43910.43908.43927.43980.43978.43910.43908.43980.43978.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43979.43930.43910.43908.43996.43985.43982.43928.43995.43988.43993.43979.43979.43909.43930.43988.43985.43990.43997.43990.43991.43996.43985.43982.43930.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43914.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43915.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43916.43908.43927.43979.43976.43993.43990.43910.43954.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43991.43978.43989.43993.43988.43930.43910.43917.43908.43927.43979.43976.43993.43990.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43980.43996.43928.43995.43988.43993.43979.43979.43909.43930.43995.43991.43996.43997.43930.43910.43908.43996.43985.43982.43910.43908.43976.43978.43997.43910.43908.43979.43976.43993.43990.43910.43908.43927.43979.43976.43993.43990.43910.43908.43995.43991.43996.43997.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43996.43997.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43998.43930.43910.43978.43997.43997.43988.44007.43982.43997.43978.43979.44007.43994.43985.43990.43914.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43985.43998.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43912.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44005.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43909.43909.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43979.43914.43930.43910.43934.43977.43981.43991.43980.43907.43925.43934.43977.43981.43991.43980.43907.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43979.43914.43930.43910.43934.43977.43981.43991.43980.43907.43925.43934.43977.43981.43991.43980.43907.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43991.43930.43910.43923.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.44007.43982.43997.43978.43979.44007.43994.43985.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.44003.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43989.43985.43930.43910.43913.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.44005.43921.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43997.43988.43979.43997.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43906.43908.43927.43979.43976.43993.43990.43910.43954.43928.43928.43928.43928.43928.43928.43928.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43987.43930.43910.43978.43997.43980.43981.43978.43990.43908.43927.43979.43976.43993.43990.43910.43928.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.44007.43982.43997.43978.43979.44007.43994.43985.43990.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43920.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43990.43930.43910.43978.43997.43997.43988.43908.43927.43979.43976.43993.43990.43910.43908.43979.43976.43993.43990.43928.43995.43988.43993.43979.43979.43909.43930.43976.43930.43910.43921.43908.43927.43979.43976.43993.43990.43910.43954.43908.43927.43995.43991.43996.43997.43910.43908.43927.43976.43978.43997.43910.43908.43927.43996.43985.43982.43910.43908.43927.43980.43996.43910.43908.43927.43980.43978.43910.43908.43927.43980.43993.43994.43988.43997.43910.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43985.43982.43910.43954.43908.43927.43996.43997.43980.43993.43985.43988.43979.43910
# Tests
(insensible à la casse)(Ctrl+I)