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zhO6(byx1%o!2d7qw(8!}v(0W9O=cO>?)^K-yied`n1{pel8-CdWiN16FZ8a`e|AvL z<B;8pX?ja-UNpu<FxLxz^OTSKutlCNL9Q)9!Y#r6Lu%J&&8~h&F1|xMzI;@#o5uNa z^_%$9C2x;w+sRIn+y293sfV+julB0<-!k1UUa+>44J%oAce!$x-u=&+VHf{a&VQC5 zYbIhlKQ($5*Angn`#b)8$gF#5vcF_k$i>a#ju*TA5C6aJ`otBpkSZ=oEGnreN=@T3 Rv@|g{Fy>NKb@g}S0sws|@DKn1 literal 0 HcmV?d00001 diff --git a/20191212/hp-20191212.tex b/20191212/hp-20191212.tex new file mode 100644 index 0000000..b1c85d5 --- /dev/null +++ b/20191212/hp-20191212.tex @@ -0,0 +1,712 @@ +% hp-20191212.pdf - Lecture Slides on Low-Level Programming +% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019 Peter Gerwinski +% +% This document is free software: you can redistribute it and/or +% modify it either under the terms of the Creative Commons +% Attribution-ShareAlike 3.0 License, or under the terms of the +% GNU General Public License as published by the Free Software +% Foundation, either version 3 of the License, or (at your option) +% any later version. +% +% This document is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this document. If not, see <http://www.gnu.org/licenses/>. +% +% You should have received a copy of the Creative Commons +% Attribution-ShareAlike 3.0 Unported License along with this +% document. If not, see <http://creativecommons.org/licenses/>. + +% README: make, Byte-Reihenfolge - Endianness, Binärdarstellung negativer Zahlen, Speicherausrichtung - Alignment + +\documentclass[10pt,t]{beamer} + +\usepackage{pgslides} +\usepackage{pdftricks} +\usepackage{tikz} + +\begin{psinputs} + \usepackage[utf8]{inputenc} + \usepackage[german]{babel} + \usepackage[T1]{fontenc} + \usepackage{helvet} + \renewcommand*\familydefault{\sfdefault} + \usepackage{pstricks,pst-grad} +\end{psinputs} + +\title{Hardwarenahe Programmierung} +\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski} +\date{12.\ Dezember 2019} + +\begin{document} + +\maketitleframe + +\nosectionnonumber{\inserttitle} + +\begin{frame} + + \shownosectionnonumber + + \begin{itemize} + \item[\textbf{1}] \textbf{EinfĂ¼hrung} + \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}} + \item[\textbf{2}] \textbf{EinfĂ¼hrung in C} + \item[\textbf{3}] \textbf{Bibliotheken} + \begin{itemize} + \item[3.1] Der Präprozessor + \item[3.2] Bibliotheken einbinden + \item[3.3] Bibliotheken verwenden + \color{red} + \item[3.4] Projekt organisieren: make + \end{itemize} + \vspace*{-\smallskipamount} + \item[\textbf{4}] \textbf{Hardwarenahe Programmierung} + \begin{itemize} + \vspace*{-0.1cm} + \item[\dots] +% \item[4.3] Interrupts + \color{orange} + \item[4.4] volatile-Variable + \color{red} + \item[4.6] Byte-Reihenfolge -- Endianness + \item[4.7] Binärdarstellung negativer Zahlen + \item[4.8] Speicherausrichtung -- Alignment + \end{itemize} + \item[\textbf{5}] \textbf{Algorithmen} + \begin{itemize} + \color{medgreen} + \item[5.1] Differentialgleichungen + \color{black} + \vspace*{-0.1cm} + \item[\dots] + \end{itemize} + \vspace*{-\smallskipamount} + \item[\textbf{\dots}] + \end{itemize} + +\end{frame} + +\setcounter{section}{3} +\section{Algorithmen} +\subsection{Differentialgleichungen} + +\begin{frame}[fragile] + + \showsection + \showsubsection + + \textbf{Beispiel 1: GleichmĂ¤ĂŸig beschleunigte Bewegung} -- Schräger Wurf + + \strut\hfill + \begin{minipage}{2.5cm} + \vspace*{0.6cm} + \begin{align*} + x'(t) &= v_x(t) \\[0.65cm] + y'(t) &= v_y(t) \\[0.75cm] + v_x'(t) &= 0 \\[0.65cm] + v_y'(t) &= -g + \end{align*} + \vspace*{0.0cm} + \end{minipage}% +% \only<1>{\hspace*{9.49cm}}\strut + \only<1->{\hfill$\Rightarrow$\hfill}% + \begin{onlyenv}<1> + \begin{minipage}{8.3cm} + \begin{align*} + x(t) &= \int v_x(t)\,dt + \visible<1>{= \int v_{0x}\,dt} + \visible<1>{= x_0 + v_{0x}\cdot t}\\[\medskipamount] + y(t) &= \int v_y(t)\,dt + \visible<1>{= \int v_{0y} - g\cdot t\,dt} + \visible<1>{= y_0 + v_{0y}\cdot t + - {\textstyle\frac12}gt^2}\\[\bigskipamount] + v_x(t) &= \int 0\,dt + \visible<1>{= v_{0x}} \\[\medskipamount] + v_y(t) &= \int -g\,dt + \visible<1>{= v_{0y} - g\cdot t} + \end{align*} + \end{minipage}% + \end{onlyenv}% + \begin{onlyenv}<2> + \begin{minipage}{3.5cm} + \vspace*{0.5cm} + \begin{lstlisting}[gobble=8,xleftmargin=0.5em] + ¡x += vx * dt;¿ + \end{lstlisting} + \vspace{0.75cm} + \begin{lstlisting}[gobble=8,xleftmargin=0.5em] + ¡y += vy * dt;¿ + \end{lstlisting} + \vspace{0.90cm} + \begin{lstlisting}[gobble=8,xleftmargin=0.5em] + ¡vx += 0 * dt;¿ + \end{lstlisting} + \vspace{0.75cm} + \begin{lstlisting}[gobble=8,xleftmargin=0.5em] + ¡vy += -g * dt;¿ + \end{lstlisting} + \end{minipage}% + \begin{minipage}{5.13cm} + Siehe: \file{gtk-16.c} + \end{minipage} + \end{onlyenv}% + \hfill\strut + +\end{frame} + +\begin{frame}[fragile] + \showsection + \showsubsection + + \textbf{Beispiel 1: GleichmĂ¤ĂŸig beschleunigte Bewegung} + + \medskip + + \textbf{Beispiel 2: Mathematisches Pendel} + + \vspace*{-2\bigskipamount} + + \begin{picture}(0,0) + \put(8,-6.5){\includegraphics{pendulum.pdf}} + \end{picture} + + \begin{eqnarray*} + \varphi'(t) &=& \omega(t) \\[\smallskipamount] + \omega'(t) &=& -\frac{g}{l}\cdot\sin\varphi(t)\hspace*{7.1cm} + \end{eqnarray*} + \vspace*{-1.5\medskipamount} + \begin{itemize} + \item + Von Hand (analytisch):\\ + Lösung raten (Ansatz), Parameter berechnen + \item + Mit Computer (numerisch):\\ + Eulersches Polygonzugverfahren + \end{itemize} + \smallskip + \begin{lstlisting}[gobble=0] + phi += dt * omega; + omega += - dt * g / l * sin (phi); + \end{lstlisting} + +% \pause + \bigskip + + \textbf{Beispiel 3:} Praktikumsaufgabe + +\end{frame} + +\setcounter{section}{2} +\section{Bibliotheken} +\setcounter{subsection}{3} +\subsection{Projekt organisieren: make} + +\begin{frame}[fragile] + + \showsubsection + \begin{itemize} + \item + \only<4->{explizite und implizite} Regeln + \begin{onlyenv}<2> + \smallskip + \begin{lstlisting}[language=make,gobble=10] + hello-6: hello-6.o pruzzel.o + gcc hello-6.o pruzzel.o -o hello-6 + + pruzzel.o: pruzzel.c pruzzel.h + gcc -Wall -O pruzzel.c -c + + hello-6.o: hello-6.c pruzzel.h + gcc -Wall -O hello-6.c -c + \end{lstlisting} + \end{onlyenv} + \begin{onlyenv}<4> + \smallskip + \begin{lstlisting}[language=make,gobble=10] + TARGET = hello-6 + OBJECTS = hello-6.o pruzzel.o + HEADERS = pruzzel.h + CFLAGS = -Wall -O + + $(TARGET): $(OBJECTS) + gcc $(OBJECTS) -o $(TARGET) + + %.o: %.c $(HEADERS) + gcc $(CFLAGS) $< -c + + clean: + rm -f $(OBJECTS) $(TARGET) + \end{lstlisting} + \end{onlyenv} + \item + Makros + \begin{onlyenv}<3> + \smallskip + \begin{lstlisting}[language=make,gobble=10] + TARGET = hello-6 + OBJECTS = hello-6.o pruzzel.o + HEADERS = pruzzel.h + CFLAGS = -Wall -O + + $(TARGET): $(OBJECTS) + gcc $(OBJECTS) -o $(TARGET) + + pruzzel.o: pruzzel.c $(HEADERS) + gcc $(CFLAGS) pruzzel.c -c + + hello-6.o: hello-6.c $(HEADERS) + gcc $(CFLAGS) hello-6.c -c + + clean: + rm -f $(OBJECTS) $(TARGET) + \end{lstlisting} + \vspace*{-1cm} + \end{onlyenv} + \begin{onlyenv}<5-> + \smallskip + \arrowitem + 3 Sprachen: C, Präprozessor, make + \end{onlyenv} + \end{itemize} + +\end{frame} + +\setcounter{section}{3} +\section{Hardwarenahe Programmierung} +\setcounter{subsection}{3} +\subsection{volatile-Variable} + +\begin{frame}[fragile] + + \showsubsection + + Externes Gerät ruft (per Stromsignal) Unterprogramm auf + + Zeiger hinterlegen: "`Interrupt-Vektor"' + + Beispiel: Taster + + \vspace*{-2.5pt} + + \begin{minipage}[t]{5cm} + \begin{onlyenv}<1> + \begin{lstlisting}[gobble=8] + ¡#include <avr/interrupt.h> + ... + + uint8_t key_pressed = 0; + + ISR (INT0_vect) + { + key_pressed = 1; + }¿ + \end{lstlisting} + \end{onlyenv} + \begin{onlyenv}<2> + \begin{lstlisting}[gobble=8] + ¡#include <avr/interrupt.h> + ... + + volatile uint8_t key_pressed = 0; + + ISR (INT0_vect) + { + key_pressed = 1; + }¿ + \end{lstlisting} + \end{onlyenv} + \end{minipage}\hfill + \begin{minipage}[t]{6cm} + \begin{lstlisting}[gobble=6] + ¡int main (void) + { + ... + + while (1) + { + while (!key_pressed) + ; /* just wait */ + PORTD ^= 0x40; + key_pressed = 0; + } + return 0; + }¿ + \end{lstlisting} + \end{minipage} + + \pause + \begin{picture}(0,0) + \color{red} + \put(10.3,4.0){\makebox(0,0)[b]{\begin{minipage}{6cm} + \begin{center} + \textbf{volatile}:\\ + Speicherzugriff\\ + nicht wegoptimieren + \end{center} + \end{minipage}}} + \put(10.3,3.95){\makebox(0,0)[tr]{\tikz{\draw[-latex](0,0)--(-0.5,-0.9);}}} + \end{picture} + +\end{frame} + +\begin{frame}[fragile] + + \showsubsection + + Was ist eigentlich \lstinline{PORTD}? + + \bigskip + \pause + + \lstinline[style=cmd]{avr-gcc -Wall -Os -mmcu=atmega328p blink-3.c -E} + + \bigskip + \pause + \lstinline{PORTD = 0x01;}\\ + \textarrow\quad + \lstinline[style=terminal]{(*(volatile uint8_t *)((0x0B) + 0x20)) = 0x01;}\\ + \pause + \begin{picture}(0,2)(0,-1.7) + \color{red} + \put(5.75,0.3){$\underbrace{\rule{2.95cm}{0pt}}_{\mbox{Zahl: \lstinline|0x2B|}}$} + \pause + \put(1.55,0.3){$\underbrace{\rule{4.0cm}{0pt}}_{\mbox{\shortstack[t]{Umwandlung in Zeiger\\ + auf \lstinline|volatile uint8_t|}}}$} + \pause + \put(1.32,-1){\makebox(0,0)[b]{\tikz{\draw[-latex](0,0)--(0,1.3)}}} + \put(1.12,-1.1){\makebox(0,0)[tl]{Dereferenzierung des Zeigers}} + \end{picture} + + \pause + \textarrow\quad + \lstinline|volatile uint8_t|-Variable an Speicheradresse \lstinline|0x2B| + + \pause + \bigskip + \bigskip + + \textarrow\quad + \lstinline|PORTA = PORTB = PORTC = PORTD = 0| ist eine schlechte Idee. + +\end{frame} + +\subsection{Byte-Reihenfolge -- Endianness} +\subsubsection{Konzept} + +\begin{frame}[fragile] + + \showsubsection + \showsubsubsection + + Eine Zahl geht Ă¼ber mehrere Speicherzellen.\\ + Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen + + \smallskip + + Welche Bits liegen wo? + + \pause + \bigskip + + $1027 = 1024 + 2 + 1 = 0000\,0100\,0000\,0011_2 = 0403_{16}$ + + \pause + \bigskip + Speicherzellen: + + \medskip + \begin{tabular}{|c|c|l}\cline{1-2} + \raisebox{-0.25ex}{04} & \raisebox{-0.25ex}{03} & \strut Big-Endian "`groĂŸes Ende zuerst"' \\\cline{1-2} + \multicolumn{2}{c}{} & \pause fĂ¼r Menschen leichter lesbar \pause \\ + \multicolumn{3}{c}{} \\[-5pt]\cline{1-2} + \raisebox{-0.25ex}{03} & \raisebox{-0.25ex}{04} & \strut Little-Endian "`kleines Ende zuerst"' \\\cline{1-2} + \multicolumn{2}{c}{} & \pause bei Additionen effizienter + \end{tabular} + + \pause + \medskip + \textarrow\ Geschmackssache + \pause\\ + \quad\textbf{\dots\ auĂŸer bei Datenaustausch!} + +% \pause +% \bigskip +% +% Aber: nicht verwechseln! \qquad $0304_{16} = 772$ + +\end{frame} + +\begin{frame} + + \showsubsection + \showsubsubsection + + Eine Zahl geht Ă¼ber mehrere Speicherzellen.\\ + Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen + + \smallskip + + Welche Bits liegen wo? + + \medskip + + \textarrow\ Geschmackssache\\ + \textbf{\dots\ auĂŸer bei Datenaustausch!} + + \begin{itemize} + \item + Dateiformate + \item + DatenĂ¼bertragung + \end{itemize} + +\end{frame} + +\subsubsection{Dateiformate} + +\begin{frame} + + \showsubsection + \showsubsubsection + + Audio-Formate: Reihenfolge der Bytes in 16- und 32-Bit-Zahlen + \begin{itemize} + \item + RIFF-WAVE-Dateien (\file{.wav}): Little-Endian + \item + Au-Dateien (\file{.au}): Big-Endian + \pause + \item + ältere AIFF-Dateien (\file{.aiff}): Big-Endian + \item + neuere AIFF-Dateien (\file{.aiff}): Little-Endian + \end{itemize} + + \pause + \bigskip + + Grafik-Formate: Reihenfolge der Bits in den Bytes + \begin{itemize} + \item + PBM-Dateien: Big-Endian\only<4->{, MSB first} + \item + XBM-Dateien: Little-Endian\only<4->{, LSB first} + \end{itemize} + \only<4->{MSB/LSB = most/least significant bit} + +\end{frame} + +\subsubsection{DatenĂ¼bertragung} + +\begin{frame} + + \showsubsection + \showsubsubsection + + \begin{itemize} + \item + RS-232 (serielle Schnittstelle): LSB first + \item + I$^2$C: MSB first + \item + USB: beides + \pause + \medskip + \item + Ethernet: LSB first + \item + TCP/IP (Internet): Big-Endian + \end{itemize} + +\end{frame} + +\subsection{Binärdarstellung negativer Zahlen} + +\begin{frame}[fragile] + + \showsubsection + + Speicher ist begrenzt!\\ + \textarrow\ feste Anzahl von Bits + + \medskip + + 8-Bit-Zahlen ohne Vorzeichen: \lstinline{uint8_t}\\ + \textarrow\ Zahlenwerte von \lstinline{0x00} bis \lstinline{0xff} = 0 bis 255\\ + \pause + \textarrow\ 255 + 1 = 0 + + \pause + \medskip + + 8-Bit-Zahlen mit Vorzeichen: \lstinline{int8_t}\\ + \lstinline{0xff} = 255 ist die "`natĂ¼rliche"' Schreibweise fĂ¼r $-1$.\\ + \pause + \textarrow\ Zweierkomplement + + \pause + \medskip + + Oberstes Bit = 1: negativ\\ + Oberstes Bit = 0: positiv\\ + \textarrow\ 127 + 1 = $-128$ + +\end{frame} + +\begin{frame}[fragile] + + \showsubsection + + Speicher ist begrenzt!\\ + \textarrow\ feste Anzahl von Bits + + \medskip + + 16-Bit-Zahlen ohne Vorzeichen: + \lstinline{uint16_t}\hfill\lstinline{uint8_t}\\ + \textarrow\ Zahlenwerte von \lstinline{0x0000} bis \lstinline{0xffff} + = 0 bis 65535\hfill 0 bis 255\\ + \textarrow\ 65535 + 1 = 0\hfill 255 + 1 = 0 + + \medskip + + 16-Bit-Zahlen mit Vorzeichen: + \lstinline{int16_t}\hfill\lstinline{int8_t}\\ + \lstinline{0xffff} = 66535 ist die "`natĂ¼rliche"' Schreibweise fĂ¼r $-1$.\hfill + \lstinline{0xff} = 255 = $-1$\\ + \textarrow\ Zweierkomplement + + \medskip + + Oberstes Bit = 1: negativ\\ + Oberstes Bit = 0: positiv\\ + \textarrow\ 32767 + 1 = $-32768$ + + \bigskip + Literatur: \url{http://xkcd.com/571/} + +\end{frame} + +\begin{frame}[fragile] + + \showsubsection + + Frage: \emph{FĂ¼r welche Zahl steht der Speicherinhalt\, + \raisebox{2pt}{% + \tabcolsep0.25em + \begin{tabular}{|c|c|}\hline + \rule{0pt}{11pt}a3 & 90 \\\hline + \end{tabular}} + (hexadezimal)?} + + \pause + \smallskip + Antwort: \emph{Das kommt darauf an.} ;--) + + \pause + \medskip + Little-Endian: + + \smallskip + + \begin{tabular}{lrl} + als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\ + als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\ + als \lstinline,int16_t,: & $-28509$\\ + als \lstinline,uint16_t,: & $37027$\\ + \lstinline,int32_t, oder grĂ¶ĂŸer: & $37027$ + & (zusätzliche Bytes mit Nullen aufgefĂ¼llt) + \end{tabular} + + \pause + \medskip + Big-Endian: + + \smallskip + + \begin{tabular}{lrl} + als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\ + als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\ + als \lstinline,int16_t,: & $-23664$\\ + als \lstinline,uint16_t,: & $41872$\\ + als \lstinline,int32_t,: & $-1550843904$ & (zusätzliche Bytes\\ + als \lstinline,uint32_t,: & $2744123392$ & mit Nullen aufgefĂ¼llt)\\ + als \lstinline,int64_t,: & $-6660823848880963584$\\ + als \lstinline,uint64_t,: & $11785920224828588032$\\ + \end{tabular} + + \vspace*{-1cm} + +\end{frame} + +\subsection{Speicherausrichtung -- Alignment} + +\begin{frame}[fragile] + + \showsubsection + + \begin{lstlisting} + #include <stdint.h> + + uint8_t a; + uint16_t b; + uint8_t c; + \end{lstlisting} + + \pause + \bigskip + + Speicheradresse durch 2 teilbar -- "`16-Bit-Alignment"' + \begin{itemize} + \item + 2-Byte-Operation: effizienter + \pause + \item + \dots\ oder sogar nur dann erlaubt + \pause + \arrowitem + Compiler optimiert Speicherausrichtung + \end{itemize} + + \medskip + + \pause + \begin{minipage}{3cm} + \begin{lstlisting}[gobble=6] + ¡uint8_t a; + uint8_t dummy; + uint16_t b; + uint8_t c;¿ + \end{lstlisting} + \end{minipage} + \pause + \begin{minipage}{3cm} + \begin{lstlisting}[gobble=6] + ¡uint8_t a; + uint8_t c; + uint16_t b;¿ + \end{lstlisting} + \end{minipage} + + \pause + \vspace{-1.75cm} + \strut\hfill + \begin{minipage}{6.5cm} + Fazit: + \begin{itemize} + \item + \textbf{Adressen von Variablen\\ + sind systemabhängig} + \item + Bei Definition von Datenformaten\\ + Alignment beachten \textarrow\ effizienter + \end{itemize} + \end{minipage} + +\end{frame} + +\end{document} diff --git a/20191212/pendulum.pdf b/20191212/pendulum.pdf new file mode 120000 index 0000000..7d1d873 --- /dev/null +++ b/20191212/pendulum.pdf @@ -0,0 +1 @@ +../common/pendulum.pdf \ No newline at end of file diff --git a/README.md b/README.md index d82dab8..319f985 100644 --- a/README.md +++ b/README.md @@ -26,6 +26,7 @@ Vortragsfolien und Beispiele: * [21.11.2019: Interrupts, volatile-Variable, Bibliotheken: EinfĂ¼hrung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191121/hp-20191121.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20191121/) * [28.11.2019: Präprozessor, Bibliotheken](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191128/hp-20191128.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20191128/) * [05.12.2019: Bibliotheken, Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191205/hp-20191205.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20191205/) + * [12.12.2019: make, Byte-Reihenfolge - Endianness, Binärdarstellung negativer Zahlen, Speicherausrichtung - Alignment](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191212/hp-20191212.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/20191212/) * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/hp-slides-2019ws.pdf) Ăœbungsaufgaben: @@ -62,6 +63,7 @@ Praktikumsunterlagen: --------------------- * [Versuch 1, 17. und 31.10.2019: RSA-VerschlĂ¼sselung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191010/hp-2019ws-p1.pdf) * [Versuch 2, 14. und 21.11.2019: Druckknopfampel](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191107/hp-2019ws-p2.pdf) + * [Versuch 3, 12. und 19.12.2019: Weltraum-Simulation](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191212/hp-2019ws-p3.pdf) Alte Klausuren: --------------- diff --git a/hp-slides-2019ws.pdf b/hp-slides-2019ws.pdf index 22b56fe4981b07e15d49d4c585d8857fc98a2961..b77c320868c3c86b2f19a89b61c8fcd0b0570a54 100644 GIT binary patch delta 177122 zcmaF2zF^PK8UfV+7dKr)JyR~#3s;Wb;4+<Fc#m0l^4l|k6HC;mFPtLnIQavU0Hf*j zi^l}Dm`p7;OEOMlWHg(8a1*b?<PS`Oj26=`{1Q%NGPB(N?<~huZAP={AI}K{Fqs=n zS5z0VVlp?}K2eu(Q4y25(e#CP_(i7Y%kl7R_FdGgHT~ivc92Dt(;fW<9H!fs3&O3j zFx>q3Y$q$D#dOC*?82KHE*Hr#T7tC8Zx;H%%s1U|6R+^}2``ufCs+Q{m_D&jIFQkD 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\pdfbookmark[1]{12.12.2019: make, Byte-Reihenfolge - Endianness, Binärdarstellung negativer Zahlen, Speicherausrichtung - Alignment}{20191212} + \includepdf[pages=-]{20191212/hp-20191212.pdf} \end{document} -- GitLab