Ajout précisions plage de nombres sur processeurs 16 bits

This commit is contained in:
Guyot 2021-11-01 19:38:24 +01:00
parent 4e0fa7a25b
commit f46b93c59f
10 changed files with 79650 additions and 76577 deletions

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@ -15,7 +15,6 @@
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@ -9,31 +9,31 @@
\BOOKMARK [3][]{Outline0.1.7.40}{S\351curit\351}{Outline0.1}% 9 \BOOKMARK [3][]{Outline0.1.7.40}{S\351curit\351}{Outline0.1}% 9
\BOOKMARK [2][]{Outline0.2}{DF Informations et donn\351es}{}% 10 \BOOKMARK [2][]{Outline0.2}{DF Informations et donn\351es}{}% 10
\BOOKMARK [3][]{Outline0.2.1.46}{Stockage : binaire}{Outline0.2}% 11 \BOOKMARK [3][]{Outline0.2.1.46}{Stockage : binaire}{Outline0.2}% 11
\BOOKMARK [3][]{Outline0.2.2.82}{Texte, codage, encodage}{Outline0.2}% 12 \BOOKMARK [3][]{Outline0.2.2.85}{Texte, codage, encodage}{Outline0.2}% 12
\BOOKMARK [3][]{Outline0.2.3.86}{Formats de fichier}{Outline0.2}% 13 \BOOKMARK [3][]{Outline0.2.3.89}{Formats de fichier}{Outline0.2}% 13
\BOOKMARK [3][]{Outline0.2.4.89}{Bases de donn\351es}{Outline0.2}% 14 \BOOKMARK [3][]{Outline0.2.4.92}{Bases de donn\351es}{Outline0.2}% 14
\BOOKMARK [2][]{Outline0.3}{DF Algo. et programmation}{}% 15 \BOOKMARK [2][]{Outline0.3}{DF Algo. et programmation}{}% 15
\BOOKMARK [3][]{Outline0.3.1.94}{Introduction}{Outline0.3}% 16 \BOOKMARK [3][]{Outline0.3.1.97}{Introduction}{Outline0.3}% 16
\BOOKMARK [3][]{Outline0.3.2.96}{Langages}{Outline0.3}% 17 \BOOKMARK [3][]{Outline0.3.2.99}{Langages}{Outline0.3}% 17
\BOOKMARK [3][]{Outline0.3.3.97}{Programmation}{Outline0.3}% 18 \BOOKMARK [3][]{Outline0.3.3.100}{Programmation}{Outline0.3}% 18
\BOOKMARK [2][]{Outline0.4}{DF Informatique et soci\351t\351}{}% 19 \BOOKMARK [2][]{Outline0.4}{DF Informatique et soci\351t\351}{}% 19
\BOOKMARK [2][]{Outline0.5}{OC Notions compl\351mentaires}{}% 20 \BOOKMARK [2][]{Outline0.5}{OC Notions compl\351mentaires}{}% 20
\BOOKMARK [3][]{Outline0.5.1.106}{Introduction}{Outline0.5}% 21 \BOOKMARK [3][]{Outline0.5.1.109}{Introduction}{Outline0.5}% 21
\BOOKMARK [3][]{Outline0.5.2.107}{Le texte}{Outline0.5}% 22 \BOOKMARK [3][]{Outline0.5.2.110}{Le texte}{Outline0.5}% 22
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\beamer@slide {rvbtsv}{203} \beamer@slide {rvbtsv}{206}
\beamer@slide {notes}{294} \beamer@slide {notes}{297}

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@ -37,6 +37,13 @@
\usepackage{fancybox} \usepackage{fancybox}
\usepackage{multirow} \usepackage{multirow}
\usepackage{amsmath} \usepackage{amsmath}
\usepackage{siunitx}
\sisetup{
per-mode = symbol-or-fraction,
exponent-product = \cdot,
output-decimal-marker = {,},
binary-units
}
\usepackage{amsfonts} \usepackage{amsfonts}
\usepackage{amssymb} \usepackage{amssymb}
\usepackage{array} \usepackage{array}
@ -932,6 +939,86 @@ L'ordre de grandeur correspond à la notation décimale :
\end{enumerate} \end{enumerate}
\end{frame} \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} \begin{frame}{Exercices}
\small \small
\only<1-2>{Sur un processeur 16 bits, combien de nombres entiers non signés peut on représenter ?\\ \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<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 ?\\ \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)} (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<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.} \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} \end{frame}

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\babel@toc {french}{} \babel@toc {french}{}
\beamer@subsectionintoc {0}{1}{Introduction}{3}{0}{0} \beamer@subsectionintoc {0}{1}{Introduction}{3}{0}{0}
\beamer@sectionintoc {1}{DF Systèmes numériques}{4}{0}{1} \beamer@sectionintoc {1}{DF Syst\IeC {\`e}mes num\IeC {\'e}riques}{4}{0}{1}
\beamer@subsectionintoc {1}{1}{Problématique}{5}{0}{1} \beamer@subsectionintoc {1}{1}{Probl\IeC {\'e}matique}{5}{0}{1}
\beamer@subsectionintoc {1}{2}{Matériel}{12}{0}{1} \beamer@subsectionintoc {1}{2}{Mat\IeC {\'e}riel}{12}{0}{1}
\beamer@subsectionintoc {1}{3}{Systèmes d'exploitation}{24}{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}{4}{Licences}{26}{0}{1}
\beamer@subsectionintoc {1}{5}{Applications}{32}{0}{1} \beamer@subsectionintoc {1}{5}{Applications}{32}{0}{1}
\beamer@subsectionintoc {1}{6}{Réseau}{34}{0}{1} \beamer@subsectionintoc {1}{6}{R\IeC {\'e}seau}{34}{0}{1}
\beamer@subsectionintoc {1}{7}{Sécurité}{40}{0}{1} \beamer@subsectionintoc {1}{7}{S\IeC {\'e}curit\IeC {\'e}}{40}{0}{1}
\beamer@sectionintoc {2}{DF Informations et données}{45}{0}{2} \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}{1}{Stockage : binaire}{46}{0}{2}
\beamer@subsectionintoc {2}{2}{Texte, codage, encodage}{82}{0}{2} \beamer@subsectionintoc {2}{2}{Texte, codage, encodage}{85}{0}{2}
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\beamer@subsectionintoc {2}{4}{Bases de données}{89}{0}{2} \beamer@subsectionintoc {2}{4}{Bases de donn\IeC {\'e}es}{92}{0}{2}
\beamer@sectionintoc {3}{DF Algo. et programmation}{93}{0}{3} \beamer@sectionintoc {3}{DF Algo. et programmation}{96}{0}{3}
\beamer@subsectionintoc {3}{1}{Introduction}{94}{0}{3} \beamer@subsectionintoc {3}{1}{Introduction}{97}{0}{3}
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\beamer@subsectionintoc {5}{1}{Introduction}{106}{0}{5} \beamer@subsectionintoc {5}{1}{Introduction}{109}{0}{5}
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\beamer@subsectionintoc {5}{5}{Programmation}{236}{0}{5} \beamer@subsectionintoc {5}{5}{Programmation}{239}{0}{5}
\beamer@sectionintoc {6}{Annexes}{236}{0}{6} \beamer@sectionintoc {6}{Annexes}{239}{0}{6}
\beamer@subsectionintoc {6}{1}{Motorisation télescope}{237}{0}{6} \beamer@subsectionintoc {6}{1}{Motorisation t\IeC {\'e}lescope}{240}{0}{6}
\beamer@subsectionintoc {6}{2}{LibreOffice}{241}{0}{6} \beamer@subsectionintoc {6}{2}{LibreOffice}{244}{0}{6}
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\beamer@subsectionintoc {7}{1}{Constituants des pages}{261}{0}{7} \beamer@subsectionintoc {7}{1}{Constituants des pages}{264}{0}{7}
\beamer@subsectionintoc {7}{2}{Les CMS : Systèmes de Management de Contenu}{272}{0}{7} \beamer@subsectionintoc {7}{2}{Les CMS : Syst\IeC {\`e}mes de Management de Contenu}{275}{0}{7}
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