Ajout précisions plage de nombres sur processeurs 16 bits
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OCInfoPres.aux
706
OCInfoPres.aux
@ -15,7 +15,6 @@
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\BOOKMARK [3][]{Outline0.1.7.40}{S\351curit\351}{Outline0.1}% 9
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\BOOKMARK [2][]{Outline0.2}{DF Informations et donn\351es}{}% 10
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\BOOKMARK [3][]{Outline0.2.1.46}{Stockage : binaire}{Outline0.2}% 11
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\BOOKMARK [3][]{Outline0.2.2.82}{Texte, codage, encodage}{Outline0.2}% 12
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||||
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||||
\BOOKMARK [2][]{Outline0.3}{DF Algo. et programmation}{}% 15
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||||
\BOOKMARK [3][]{Outline0.3.1.94}{Introduction}{Outline0.3}% 16
|
||||
\BOOKMARK [3][]{Outline0.3.2.96}{Langages}{Outline0.3}% 17
|
||||
\BOOKMARK [3][]{Outline0.3.3.97}{Programmation}{Outline0.3}% 18
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||||
\BOOKMARK [3][]{Outline0.3.1.97}{Introduction}{Outline0.3}% 16
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||||
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||||
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||||
\BOOKMARK [2][]{Outline0.4}{DF Informatique et soci\351t\351}{}% 19
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||||
\BOOKMARK [2][]{Outline0.5}{OC Notions compl\351mentaires}{}% 20
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||||
\BOOKMARK [3][]{Outline0.5.1.106}{Introduction}{Outline0.5}% 21
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||||
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\BOOKMARK [1][]{Outline1}{Annexe}{}% 37
|
||||
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|
||||
\BOOKMARK [2][]{Outline1.9}{Cr\351dits photographiques}{Outline1}% 39
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BIN
OCInfoPres.pdf
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OCInfoPres.pdf
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OCInfoPres.ps
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OCInfoPres.ps
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@ -1,2 +1,2 @@
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|
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@ -37,6 +37,13 @@
|
||||
\usepackage{fancybox}
|
||||
\usepackage{multirow}
|
||||
\usepackage{amsmath}
|
||||
\usepackage{siunitx}
|
||||
\sisetup{
|
||||
per-mode = symbol-or-fraction,
|
||||
exponent-product = \cdot,
|
||||
output-decimal-marker = {,},
|
||||
binary-units
|
||||
}
|
||||
\usepackage{amsfonts}
|
||||
\usepackage{amssymb}
|
||||
\usepackage{array}
|
||||
@ -932,6 +939,86 @@ L'ordre de grandeur correspond à la notation décimale :
|
||||
\end{enumerate}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
Un processeur peut être comparé à une machine à calculer dont l'affichage comporte un nombre limité de chiffres.
|
||||
|
||||
\begin{block}{En décimal}
|
||||
Pour prendre un exemple simple, supposons que notre calculette ne peut calculer qu'avec trois chiffres.
|
||||
|
||||
\smallskip
|
||||
Le nombre de nombres entiers positifs différents qu'elle peut afficher est de \num{e3}. En effet, on comprend bien que ceux-ci varient de 000 à 999. Ils sont donc au nombre de 1000. Le plus petit est 000 et le plus grand 999.
|
||||
|
||||
\smallskip
|
||||
Si une place est réservée au signe, alors le nombre de nombres possible est de \num{e2} nombres positifs (de +00 à +99) et de \num{e2}-1 nombres négatifs (de -01 à -99), soit au total 100 + 99 = 199.
|
||||
\end{block}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
Un processeur peut être comparé à une machine à calculer dont l'affichage comporte un nombre limité de chiffres.
|
||||
|
||||
\begin{block}{En binaire}
|
||||
\begin{center}
|
||||
Entiers positifs sur trois bits~: \_ \_ \_
|
||||
\end{center}
|
||||
\begin{columns}
|
||||
\begin{column}{0.2\textwidth}
|
||||
000 -> 0
|
||||
001 -> 1
|
||||
010 -> 2
|
||||
011 -> 3
|
||||
100 -> 4
|
||||
101 -> 5
|
||||
110 -> 6
|
||||
111 -> 7
|
||||
\end{column}
|
||||
\begin{column}{0.6\textwidth}
|
||||
Au total \(2^3\)=8 chiffres
|
||||
|
||||
Mininum~: 000 -> 0
|
||||
|
||||
Maximum~: 111 ->
|
||||
|
||||
\(1\cdot 2^2+1\cdot 2^1+1\cdot 2^0=4+2+1=7\)
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{block}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}
|
||||
Un processeur peut être comparé à une machine à calculer dont l'affichage comporte un nombre limité de chiffres.
|
||||
|
||||
\begin{block}{En binaire}
|
||||
\begin{center}
|
||||
Entiers signé sur trois bits~: \_ \_ \_
|
||||
\end{center}
|
||||
\begin{columns}
|
||||
\begin{column}{0.2\textwidth}
|
||||
000 -> 0
|
||||
001 -> 1
|
||||
010 -> 2
|
||||
011 -> 3
|
||||
100 -> -0
|
||||
101 -> -1
|
||||
110 -> -2
|
||||
111 -> -3
|
||||
\end{column}
|
||||
\begin{column}{0.6\textwidth}
|
||||
Premier bit~: signe
|
||||
|
||||
\((-1)^0=+1=+\;\) ; \(\;(-1)^1=-1=-\)
|
||||
|
||||
Au total \(2^3\)=8 chiffres
|
||||
|
||||
4 chiffres positifs, 3 chiffres négatifs
|
||||
|
||||
Mininum~: 111 -> -3
|
||||
|
||||
Maximum~: 011 -> 3
|
||||
\end{column}
|
||||
\end{columns}
|
||||
\end{block}
|
||||
\end{frame}
|
||||
|
||||
\begin{frame}{Exercices}
|
||||
\small
|
||||
\only<1-2>{Sur un processeur 16 bits, combien de nombres entiers non signés peut on représenter ?\\
|
||||
@ -939,7 +1026,11 @@ L'ordre de grandeur correspond à la notation décimale :
|
||||
\only<2>{\\\smallskip On a \(2^{16}=65'536\) possibilités, soit autant de nombres.}
|
||||
\only<3-4>{Sur le même processeur, quels sont les plus petits et plus grands nombres entiers signés qui puissent être représentés ?\\
|
||||
(c'est à dire avec la possibilité de faire des nombres positifs et négatifs)}
|
||||
\only<4>{\\\smallskip On a un bit de signe (0 ou 1) et 15 bits pour le nombre, soit \(2^{15}=32'768\) possibilités. On peut donc représenter des nombres de -32'768 à 32'767 (à cause du zéro).}
|
||||
\only<4>{\\\smallskip On a un bit de signe (0 ou 1) et 15 bits pour le nombre, soit \(2^{15}=32'768\) possibilités. On peut donc représenter des nombres de -32'768 à 32'767 (à cause du zéro).
|
||||
|
||||
En effet, le nombre le plus élevé est 0111111111111111, soit \(2^{15}+2^{14}+...+2^1+2^0=32'767\) et le plus faible 1111111111111111, soit \(-32'767\).
|
||||
|
||||
Mais le nombre 1000000000000000 pourrait être utilisé pour -32'768 à la place de -0.}
|
||||
\only<5-6>{Sur un processeur 32 bits, si on met dans un fichier un fois tous les nombres entiers non signés, quel sera en Go la taille du fichier ?}
|
||||
\only<6>{\\\smallskip Avec un tel processeur on a \(2^{32}=4'294'967'296\) nombres possibles (avec le zéro). Chaque nombre est codé sur 32 bits, soit au total \(4'294'967'296\cdot 32=1,37\cdot 10^{11}\) bits. Cela représente \(1,71\cdot 10^{10}\) octets ou \(16'777'216\) ko, ou encore \(16'384\) Mo, c'est-à-dire 16 Go.}
|
||||
\end{frame}
|
||||
|
||||
@ -1,37 +1,37 @@
|
||||
\babel@toc {french}{}
|
||||
\beamer@subsectionintoc {0}{1}{Introduction}{3}{0}{0}
|
||||
\beamer@sectionintoc {1}{DF Systèmes numériques}{4}{0}{1}
|
||||
\beamer@subsectionintoc {1}{1}{Problématique}{5}{0}{1}
|
||||
\beamer@subsectionintoc {1}{2}{Matériel}{12}{0}{1}
|
||||
\beamer@subsectionintoc {1}{3}{Systèmes d'exploitation}{24}{0}{1}
|
||||
\beamer@sectionintoc {1}{DF Syst\IeC {\`e}mes num\IeC {\'e}riques}{4}{0}{1}
|
||||
\beamer@subsectionintoc {1}{1}{Probl\IeC {\'e}matique}{5}{0}{1}
|
||||
\beamer@subsectionintoc {1}{2}{Mat\IeC {\'e}riel}{12}{0}{1}
|
||||
\beamer@subsectionintoc {1}{3}{Syst\IeC {\`e}mes d'exploitation}{24}{0}{1}
|
||||
\beamer@subsectionintoc {1}{4}{Licences}{26}{0}{1}
|
||||
\beamer@subsectionintoc {1}{5}{Applications}{32}{0}{1}
|
||||
\beamer@subsectionintoc {1}{6}{Réseau}{34}{0}{1}
|
||||
\beamer@subsectionintoc {1}{7}{Sécurité}{40}{0}{1}
|
||||
\beamer@sectionintoc {2}{DF Informations et données}{45}{0}{2}
|
||||
\beamer@subsectionintoc {1}{6}{R\IeC {\'e}seau}{34}{0}{1}
|
||||
\beamer@subsectionintoc {1}{7}{S\IeC {\'e}curit\IeC {\'e}}{40}{0}{1}
|
||||
\beamer@sectionintoc {2}{DF Informations et donn\IeC {\'e}es}{45}{0}{2}
|
||||
\beamer@subsectionintoc {2}{1}{Stockage : binaire}{46}{0}{2}
|
||||
\beamer@subsectionintoc {2}{2}{Texte, codage, encodage}{82}{0}{2}
|
||||
\beamer@subsectionintoc {2}{3}{Formats de fichier}{86}{0}{2}
|
||||
\beamer@subsectionintoc {2}{4}{Bases de données}{89}{0}{2}
|
||||
\beamer@sectionintoc {3}{DF Algo. et programmation}{93}{0}{3}
|
||||
\beamer@subsectionintoc {3}{1}{Introduction}{94}{0}{3}
|
||||
\beamer@subsectionintoc {3}{2}{Langages}{96}{0}{3}
|
||||
\beamer@subsectionintoc {3}{3}{Programmation}{97}{0}{3}
|
||||
\beamer@sectionintoc {4}{DF Informatique et société}{100}{0}{4}
|
||||
\beamer@sectionintoc {5}{OC Notions complémentaires}{105}{0}{5}
|
||||
\beamer@subsectionintoc {5}{1}{Introduction}{106}{0}{5}
|
||||
\beamer@subsectionintoc {5}{2}{Le texte}{107}{0}{5}
|
||||
\beamer@subsectionintoc {5}{3}{L'image}{137}{0}{5}
|
||||
\beamer@subsectionintoc {5}{4}{Le son}{227}{0}{5}
|
||||
\beamer@subsectionintoc {5}{5}{Programmation}{236}{0}{5}
|
||||
\beamer@sectionintoc {6}{Annexes}{236}{0}{6}
|
||||
\beamer@subsectionintoc {6}{1}{Motorisation télescope}{237}{0}{6}
|
||||
\beamer@subsectionintoc {6}{2}{LibreOffice}{241}{0}{6}
|
||||
\beamer@subsectionintoc {6}{3}{Évaluations}{254}{0}{6}
|
||||
\beamer@subsectionintoc {6}{4}{Évaluations}{255}{0}{6}
|
||||
\beamer@subsectionintoc {6}{5}{\LaTeX }{256}{0}{6}
|
||||
\beamer@sectionintoc {7}{Internet}{260}{0}{7}
|
||||
\beamer@subsectionintoc {7}{1}{Constituants des pages}{261}{0}{7}
|
||||
\beamer@subsectionintoc {7}{2}{Les CMS : Systèmes de Management de Contenu}{272}{0}{7}
|
||||
\beamer@subsectionintoc {7}{3}{HTML}{277}{0}{7}
|
||||
\beamer@subsectionintoc {7}{4}{Animation javascript}{289}{0}{7}
|
||||
\beamer@subsectionintoc {2}{2}{Texte, codage, encodage}{85}{0}{2}
|
||||
\beamer@subsectionintoc {2}{3}{Formats de fichier}{89}{0}{2}
|
||||
\beamer@subsectionintoc {2}{4}{Bases de donn\IeC {\'e}es}{92}{0}{2}
|
||||
\beamer@sectionintoc {3}{DF Algo. et programmation}{96}{0}{3}
|
||||
\beamer@subsectionintoc {3}{1}{Introduction}{97}{0}{3}
|
||||
\beamer@subsectionintoc {3}{2}{Langages}{99}{0}{3}
|
||||
\beamer@subsectionintoc {3}{3}{Programmation}{100}{0}{3}
|
||||
\beamer@sectionintoc {4}{DF Informatique et soci\IeC {\'e}t\IeC {\'e}}{103}{0}{4}
|
||||
\beamer@sectionintoc {5}{OC Notions compl\IeC {\'e}mentaires}{108}{0}{5}
|
||||
\beamer@subsectionintoc {5}{1}{Introduction}{109}{0}{5}
|
||||
\beamer@subsectionintoc {5}{2}{Le texte}{110}{0}{5}
|
||||
\beamer@subsectionintoc {5}{3}{L'image}{140}{0}{5}
|
||||
\beamer@subsectionintoc {5}{4}{Le son}{230}{0}{5}
|
||||
\beamer@subsectionintoc {5}{5}{Programmation}{239}{0}{5}
|
||||
\beamer@sectionintoc {6}{Annexes}{239}{0}{6}
|
||||
\beamer@subsectionintoc {6}{1}{Motorisation t\IeC {\'e}lescope}{240}{0}{6}
|
||||
\beamer@subsectionintoc {6}{2}{LibreOffice}{244}{0}{6}
|
||||
\beamer@subsectionintoc {6}{3}{\IeC {\'E}valuations}{257}{0}{6}
|
||||
\beamer@subsectionintoc {6}{4}{\IeC {\'E}valuations}{258}{0}{6}
|
||||
\beamer@subsectionintoc {6}{5}{\LaTeX }{259}{0}{6}
|
||||
\beamer@sectionintoc {7}{Internet}{263}{0}{7}
|
||||
\beamer@subsectionintoc {7}{1}{Constituants des pages}{264}{0}{7}
|
||||
\beamer@subsectionintoc {7}{2}{Les CMS : Syst\IeC {\`e}mes de Management de Contenu}{275}{0}{7}
|
||||
\beamer@subsectionintoc {7}{3}{HTML}{280}{0}{7}
|
||||
\beamer@subsectionintoc {7}{4}{Animation javascript}{292}{0}{7}
|
||||
|
||||
Loading…
Reference in New Issue
Block a user