From 16f3b0196057e8ee809df074e05dd8c61a8ab90e Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 14 Jan 2021 13:52:02 +0100
Subject: [PATCH] Vorbereitung 14.1.2021

---
 .../InstallationUndVerwendungGTKWin10.pdf     |  Bin 438314 -> 0 bytes
 20210107/hanoi.xcf.gz                         |  Bin 0 -> 6239 bytes
 20210114/400_points_breadboard.jpg            |  Bin 0 -> 131886 bytes
 20210114/Tower_of_Hanoi.jpeg                  |    1 +
 20210114/aufgabe-2.c                          |   15 +
 20210114/aufgabe-3.c                          |   33 +
 20210114/hp-2020ws-p3.pdf                     |  Bin 0 -> 235449 bytes
 20210114/hp-2020ws-p3.tex                     |  195 +++
 20210114/hp-20210114.pdf                      |  Bin 0 -> 395932 bytes
 20210114/hp-20210114.tex                      | 1223 +++++++++++++++++
 20210114/hp-musterloesung-20210114.pdf        |  Bin 0 -> 101457 bytes
 20210114/hp-musterloesung-20210114.tex        |  357 +++++
 20210114/hp-uebung-20210114.pdf               |  Bin 0 -> 110933 bytes
 20210114/hp-uebung-20210114.tex               |  271 ++++
 20210114/io-ports-and-interrupts.pdf          |    1 +
 20210114/landau-symbols-2.pdf                 |    1 +
 20210114/landau-symbols-3.pdf                 |    1 +
 20210114/landau-symbols.pdf                   |    1 +
 20210114/leds.jpg                             |    1 +
 .../logo-hochschule-bochum-cvh-text-v2.pdf    |    1 +
 20210114/logo-hochschule-bochum.pdf           |    1 +
 20210114/pendulum.pdf                         |    1 +
 20210114/pgscript.sty                         |    1 +
 20210114/pgslides.sty                         |    1 +
 README.md                                     |    7 +
 hp-slides-2020ws.pdf                          |  Bin 1388849 -> 2219771 bytes
 hp-slides-2020ws.tex                          |    8 +-
 update                                        |   40 +-
 28 files changed, 2138 insertions(+), 22 deletions(-)
 delete mode 100644 20210107/InstallationUndVerwendungGTKWin10.pdf
 create mode 100644 20210107/hanoi.xcf.gz
 create mode 100644 20210114/400_points_breadboard.jpg
 create mode 120000 20210114/Tower_of_Hanoi.jpeg
 create mode 100644 20210114/aufgabe-2.c
 create mode 100644 20210114/aufgabe-3.c
 create mode 100644 20210114/hp-2020ws-p3.pdf
 create mode 100644 20210114/hp-2020ws-p3.tex
 create mode 100644 20210114/hp-20210114.pdf
 create mode 100644 20210114/hp-20210114.tex
 create mode 100644 20210114/hp-musterloesung-20210114.pdf
 create mode 100644 20210114/hp-musterloesung-20210114.tex
 create mode 100644 20210114/hp-uebung-20210114.pdf
 create mode 100644 20210114/hp-uebung-20210114.tex
 create mode 120000 20210114/io-ports-and-interrupts.pdf
 create mode 120000 20210114/landau-symbols-2.pdf
 create mode 120000 20210114/landau-symbols-3.pdf
 create mode 120000 20210114/landau-symbols.pdf
 create mode 120000 20210114/leds.jpg
 create mode 120000 20210114/logo-hochschule-bochum-cvh-text-v2.pdf
 create mode 120000 20210114/logo-hochschule-bochum.pdf
 create mode 120000 20210114/pendulum.pdf
 create mode 120000 20210114/pgscript.sty
 create mode 120000 20210114/pgslides.sty

diff --git a/20210107/InstallationUndVerwendungGTKWin10.pdf b/20210107/InstallationUndVerwendungGTKWin10.pdf
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literal 0
HcmV?d00001

diff --git a/20210114/Tower_of_Hanoi.jpeg b/20210114/Tower_of_Hanoi.jpeg
new file mode 120000
index 0000000..a1a794a
--- /dev/null
+++ b/20210114/Tower_of_Hanoi.jpeg
@@ -0,0 +1 @@
+../common/Tower_of_Hanoi.jpeg
\ No newline at end of file
diff --git a/20210114/aufgabe-2.c b/20210114/aufgabe-2.c
new file mode 100644
index 0000000..1afa7b1
--- /dev/null
+++ b/20210114/aufgabe-2.c
@@ -0,0 +1,15 @@
+#include <avr/io.h>
+
+int main (void)
+{
+  DDRA = 0xff;
+  DDRB = 0xff;
+  DDRC = 0xff;
+  DDRD = 0xff;
+  PORTA = 0x1f;
+  PORTB = 0x10;
+  PORTD = 0x10;
+  PORTC = 0xfc;
+  while (1);
+  return 0;
+}
diff --git a/20210114/aufgabe-3.c b/20210114/aufgabe-3.c
new file mode 100644
index 0000000..4c95eb6
--- /dev/null
+++ b/20210114/aufgabe-3.c
@@ -0,0 +1,33 @@
+#include <stdint.h>
+#include <avr/io.h>
+#include <avr/interrupt.h>
+
+uint8_t counter = 1;
+uint8_t leds = 0;
+
+ISR (TIMER0_COMP_vect)
+{
+  if (counter == 0)
+    {
+      leds = (leds + 1) % 8;
+      PORTC = leds << 4;
+    }
+  counter++;
+}
+
+void init (void)
+{
+  cli ();
+  TCCR0 = (1 << CS01) | (1 << CS00);
+  TIMSK = 1 << OCIE0;
+  sei ();
+  DDRC = 0x70;
+}
+
+int main (void)
+{
+  init ();
+  while (1)
+    ; /* do nothing */
+  return 0;
+}
diff --git a/20210114/hp-2020ws-p3.pdf b/20210114/hp-2020ws-p3.pdf
new file mode 100644
index 0000000000000000000000000000000000000000..95e1f2fb877e9e32d0f8d5709938bd291ae1ca09
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diff --git a/20210114/hp-2020ws-p3.tex b/20210114/hp-2020ws-p3.tex
new file mode 100644
index 0000000..4202686
--- /dev/null
+++ b/20210114/hp-2020ws-p3.tex
@@ -0,0 +1,195 @@
+% hp-2020ws-p3.pdf - Labor Notes on Low-Level Programming
+% Copyright (C) 2014, 2015, 2016, 2017, 2018, 2019, 2021  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: Versuch 3: Druckknopfampel
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{multicol}
+\usepackage{amsmath}
+\usepackage{sfmath}
+
+\sloppy
+\raggedcolumns
+\pagestyle{empty}
+\addtolength{\textheight}{1cm}
+\newcommand{\sep}{~$\cdot$~}
+\newcommand{\mylicense}{CC BY-SA (Version 4.0) oder GNU GPL (Version 3 oder höher)}
+
+\begin{document}
+
+  \makebox(0,0.005)[tl]{\includegraphics[scale=0.72]{logo-hochschule-bochum-cvh-text-v2.pdf}}\hfill
+  \makebox(0,0)[tr]{\includegraphics[scale=0.5]{logo-hochschule-bochum.pdf}}
+  \par\bigskip\bigskip
+  \begin{center}
+    \Large\textbf{Praktikumsversuch 2: Druckknopfampel}
+    \par\medskip
+    \normalsize Hardwarenahe Programmierung\sep
+    Wintersemester 2020/21\sep
+    Prof.~Dr.~Peter Gerwinski
+  \end{center}
+
+  Aufgabe: Programmieren Sie in C einen Mikrocontroller so,
+  daß er eine Druckknopfampel steuern kann.
+
+  \begin{multicols}{2}
+
+    \begin{itemize}
+      \item
+        Normalerweise zeigt eine Druckknopfampel rotes Licht für die
+        Fußgänger und grünes Licht für die Straße.
+      \item
+        Nach Knopfdruck wechselt die Straße über Gelb nach Rot.
+        Danach bekommen die Fußgänger Grün.
+        Nach einer gewissen Zeit bekommen die Fußgänger wieder Rot,
+        und die Straße wechselt über Rot-Gelb wieder zu Grün.
+
+      \medskip
+      \item
+        Als Mikrocontroller-Entwicklungsplattform eignet sich u.\,a.\
+        ein \emph{Arduino Uno\/}. \textbf{Wenn Sie keinen Zugang zu einer
+        geeigneten Mi\-kro\-con\-trol\-ler-Ent\-wick\-lungs\-platt\-form haben,
+        sprechen Sie uns an.}
+      \item
+        Software-Entwiklung für den Arduino geschieht üblicherweise
+        mit Hilfe der Entwicklungswerkzeuge \emph{GCC, binutils und
+        glibc für AVR} sowie \emph{avrdude\/} für das Herunterladen
+        des geschriebenen Programms vom PC auf den Mikrocontroller.
+
+        Die Arduino-Entwicklungsumgebung (siehe z.\,B.\
+        \url{https://www.arduino.cc/en/Main/Software}) integriert
+        alle diese Komponenten.
+      \item
+        Wir schreiben unser Programm \textbf{in C und nicht in der INO-Sprache}.
+        Wenn die Quelltext-Dateien in der Arduino-Entwicklungsumgebung
+        die Endung \file{.ino} haben, ist das kein Problem,
+        sofern der Inhalt der Datei in C geschrieben ist.
+      \item
+        Den Schaltplan des Arduino Uno sowie das Datenblatt des
+        ATmega328p finden Sie per Web-Recherche.
+
+      \columnbreak
+
+      \item
+        Sie können Ihr Programm direkt aus der Arduino-Entwicklungsumgebung heraus
+        compilieren und auf den Mikrocontroller herunterladen.
+        Wenn Sie dies von der Kommandozeile aus machen möchten,
+        geht dies folgendermaßen:
+
+        \lstinline[style=cmd]{avr-gcc -Wall -Os -mmcu=atmega328p \}\\
+        \lstinline[style=cmd]{dateiname.c -o dateiname.elf}
+
+        \lstinline[style=cmd]{avr-objcopy -O ihex \}\\
+        \lstinline[style=cmd]{dateiname-4.elf dateiname-4.hex}
+
+        \lstinline[style=cmd]{avrdude -P /dev/ttyACM0 -c arduino \}\\
+        \lstinline[style=cmd]{-p m328p -U flash:w:dateiname.hex}
+
+        Bei Zugriffsproblemen auf die Schnittstelle
+        (hier: \lstinline[style=terminal]{/dev/ttyACM0}) fügen Sie Ihr
+        Benutzerkonto der entsprechenden Gruppe hinzu (normalerweise:
+        \lstinline[style=terminal]{dialout}).
+
+        Notfalls: \lstinline[style=cmd]{sudo chmod 666 /dev/ttyACM0}
+
+      \medskip
+      \item
+        Die Verdrahtung erfolgt üblicherweise auf einer Steckplatine
+        -- siehe Abb.~\ref{Steckplatine}.
+        Die mit roten und blauen Streifen markierten Lochreihen sind
+        in Längsrichtung elektrisch verbunden, alle anderen in
+        Querrichtung mit einer Trennung in der Mitte. Üblicherweise
+        verwendet man die Längsrichtung für die Stromversorgung: Rot
+        = Versorgungsspannung, Blau = 0\,V.
+      \item
+        LEDs sind keine Glühlampen! Sie haben einen Pluspol (länger)
+        und einen Minuspol (kürzer, Gehäuse abgeflacht), und sie dürfen
+        \textbf{nur mit Vorwiderstand} betrieben werden,
+        andernfalls besteht die Gefahr einer Zerstörung der LED
+        und/oder des Arduino.
+      \item
+        Anstelle eines Drucktasters kann man auch ein Stück Draht verwenden.
+      \item
+        \textbf{Abgabe:}
+        Ihre Quelltexte mit den Lösungen der Praktikumsaufgabe schicken Sie bitte
+        per E-Mail an \file{peter.gerwinski@hs-bochum.de}
+        mit dem \textbf{Betreff:} \lstinline[style=terminal]{PaoJ6nae}
+        unter Angabe von Name, Matrikel-Nummer,
+        Studiengang (MI/MP/TI) und Studienmodell (KIA/KIS/GS).
+
+    \end{itemize}
+
+    \vspace*{-\medskipamount}
+
+    \strut\hfill\emph{Viel Erfolg!}\\[-3.5cm]
+
+  \end{multicols}
+
+  \vspace*{-5\bigskipamount}
+
+  \begin{figure}[h]
+    \begin{minipage}{7.3cm}
+      \includegraphics[width=8cm]{400_points_breadboard.jpg}
+      \vspace*{-1cm}
+      \caption{Steckplatine\label{Steckplatine}\hspace*{1.2cm}}
+      \vspace*{1cm}
+    \end{minipage}%
+    \begin{picture}(0,0)
+      \put(-1.6,0.0){\makebox(0,0)[tl]{%
+        \begin{minipage}{9cm}
+          \small\raggedright
+          \vspace*{1cm}
+          Bildquelle:
+          \href{https://commons.wikimedia.org/wiki/File:400_points_breadboard.jpg}%
+               {\nolinkurl{https://commons.wikimedia.org/}\\
+                \nolinkurl{wiki/File:400_points_breadboard.jpg}}\\
+          Autor: \url{https://www.flickr.com/people/33504192@N00}\\
+          Lizenz: CC-BY-SA 2.0 Generic
+        \end{minipage}}}
+    \end{picture}
+  \end{figure}
+
+  \vspace*{-1.5\bigskipamount}
+
+  \vfill
+
+  \begingroup
+
+    \small
+
+    \setlength{\leftskip}{3cm}
+
+    Stand: 14.\ Januar 2021
+
+%    Soweit nicht anders angegeben:\\
+    Copyright \copyright\ 2014, 2015, 2016, 2017, 2018, 2019, 2021\quad Peter Gerwinski\\
+    Lizenz: \mylicense
+
+    Sie können diese Praktikumsunterlagen einschließlich \LaTeX-Quelltext
+%    und Beispielprogramme\\
+    herunterladen unter:\\
+    \url{https://gitlab.cvh-server.de/pgerwinski/hp}
+
+  \endgroup
+
+\end{document}
diff --git a/20210114/hp-20210114.pdf b/20210114/hp-20210114.pdf
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diff --git a/20210114/hp-20210114.tex b/20210114/hp-20210114.tex
new file mode 100644
index 0000000..8146672
--- /dev/null
+++ b/20210114/hp-20210114.tex
@@ -0,0 +1,1223 @@
+% hp-20210114.pdf - Lecture Slides on Low-Level Programming
+% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  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: Hardwarenahe Programmierung
+
+\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{14.\ Januar 2021}
+
+\begin{document}
+
+\maketitleframe
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \item[5.1] Differentialgleichungen
+        \color{medgreen}
+        \item[5.2] Rekursion
+        \item[5.3] Aufwandsabschätzungen
+      \end{itemize}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{red}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \item[4.4] volatile-Variable
+        \item[4.6] Byte-Reihenfolge -- Endianness
+        \item[4.7] Binärdarstellung negativer Zahlen
+        \item[4.8] Speicherausrichtung -- Alignment
+      \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: Gleichmäßig 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-13.c}
+    \end{minipage}
+  \end{onlyenv}%
+  \hfill\strut
+
+\end{frame}
+
+\begin{frame}[fragile]
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig 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: Weltraum-Simulation}
+
+  Praktikumsaufgabe
+  \vspace*{-1cm}
+
+\end{frame}
+
+\subsection{Rekursion}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Vollständige Induktion:
+  \vspace*{-0.725cm}
+  \begin{displaymath}
+    \hspace*{4cm}
+    \left.
+      \begin{array}{r}
+        \mbox{Aussage gilt für $n = 1$}\\[2pt]
+        \mbox{Schluß von $n - 1$ auf $n$}
+      \end{array}
+    \right\}
+    \mbox{Aussage gilt für alle $n\in\mathbb{N}$}
+  \end{displaymath}
+  \vspace*{-0.5cm}
+
+%  \pause
+
+  Türme von Hanoi
+
+%  \begin{onlyenv}<1>
+%    \begin{center}
+%      \includegraphics[width=12.2cm]{Tower_of_Hanoi.jpeg}
+%    \end{center}
+%  \end{onlyenv}
+
+  \begin{onlyenv}<1->
+    \begin{itemize}
+      \item
+        64 Scheiben, 3 Plätze,
+        \only<1>{\hfill\makebox(0,0)[rt]{\includegraphics[width=6cm]{Tower_of_Hanoi.jpeg}}}\\
+        immer 1 Scheibe verschieben
+      \item
+        Ziel: Turm verschieben
+      \item
+        Es dürfen nur kleinere Scheiben\\
+        auf größeren liegen.
+      \bigskip
+%      \pause
+%      \pause
+      \item
+        $n = 1$ Scheibe: fertig
+      \item
+        Wenn $n - 1$ Scheiben verschiebbar:\\
+        schiebe $n - 1$ Scheiben auf Hilfsplatz,\\
+        verschiebe die darunterliegende,\\
+        hole $n - 1$ Scheiben von Hilfsplatz
+    \end{itemize}
+    \begin{onlyenv}<2>
+      \vspace{-4.3cm}
+      \begin{lstlisting}[gobble=8,xleftmargin=6.4cm]
+        void move (int from, int to, int disks)
+        {
+          if (disks == 1)
+            move_one_disk (from, to);
+          else
+            {
+              int help = 0 + 1 + 2 - from - to;
+              move (from, help, disks - 1);
+              move (from, to, 1);
+              move (help, to, disks - 1);
+            }
+        }
+      \end{lstlisting}
+    \end{onlyenv}
+    \begin{onlyenv}<3->
+      \vspace{-5.0cm}
+      \hspace*{7.4cm}\begin{minipage}[t]{5cm}
+        32 Scheiben:
+        \begin{lstlisting}[gobble=10,style=terminal]
+          $ ¡time ./hanoi-9a¿
+          ...
+          real    0m32,712s
+          user    0m32,708s
+          sys     0m0,000s
+        \end{lstlisting}
+%        \pause[7]
+        \begin{itemize}
+          \arrowitem
+            etwas über 1 Minute\\
+            für 64 Scheiben
+        \end{itemize}
+%        \pause
+        \vspace*{-0.5cm}
+        \begin{picture}(0,0)
+          \color{red}
+          \put(0,0){\makebox(0,0)[bl]{\tikz[line width=1pt]{\draw(0,0)--(4,0.8);}}}
+          \put(0,0.8){\makebox(0,0)[tl]{\tikz[line width=1pt]{\draw(0,0)--(4,-0.8);}}}
+        \end{picture}
+
+        Für jede zusätzliche Scheibe\\verdoppelt sich die Rechenzeit!
+        % 32.712 * 2^32 / 3600 / 24 / 365.25 = 4452.08032888280477602859
+        \begin{itemize}
+          \arrowitem
+            $\frac{32,712\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4452$
+            Jahre\\[\smallskipamount]
+            für 64 Scheiben
+        \end{itemize}
+      \end{minipage}
+    \end{onlyenv}
+  \end{onlyenv}
+
+\end{frame}
+
+\subsection{Aufwandsabschätzungen \protect\color{gray}-- Komplexitätsanalyse}
+
+\begin{frame}[fragile]
+
+%  \newcommand{\w}{\hspace*{0.75pt}}
+
+  \showsubsection
+
+  \begin{picture}(0,0)
+    \put(7.6,-0.5){%
+      \begin{minipage}[t]{5.3cm}
+%        \vspace*{-1.0cm}\includegraphics{landau-symbols.pdf}
+        \vspace*{-1.0cm}\alt<16->{\includegraphics{landau-symbols-3.pdf}}%
+                       {\alt<15->{\includegraphics{landau-symbols-2.pdf}}%
+                                 {\includegraphics{landau-symbols.pdf}}}
+        \small
+        \begin{description}\itemsep0pt\leftskip-0.5cm
+          \item[$n$:] Eingabedaten
+          \item[$g(n)$:] Rechenzeit
+        \end{description}
+      \end{minipage}}
+  \end{picture}
+
+  \vspace*{-\bigskipamount}
+
+  Wann ist ein Programm "`schnell"'?
+
+  \medskip
+
+  \begin{onlyenv}<1-2>
+      Türme von Hanoi: $\mathcal{O}(2^n)$
+      \par\medskip
+      Für jede zusätzliche Scheibe\\verdoppelt sich die Rechenzeit!
+      % 32.712 * 2^32 / 3600 / 24 / 365.25 = 4452.08032888280477602859
+      \begin{itemize}
+        \arrowitem
+          $\frac{32,712\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4452$
+          Jahre\\[\smallskipamount]
+          für 64 Scheiben
+      \end{itemize}
+
+      \bigskip
+  \end{onlyenv}
+
+  \begin{onlyenv}<2->
+    Faustregel:\\Schachtelung der Schleifen zählen\\
+    $k$ Schleifen ineinander \textarrow\ $\mathcal{O}(n^k)$
+
+    \bigskip
+  \end{onlyenv}
+
+  \begin{onlyenv}<3-13>
+    \textbf{Beispiel: Sortieralgorithmen}
+
+    \smallskip
+
+    Anzahl der Vergleiche bei $n$ Strings
+    \begin{itemize}
+      \item
+        Maximum suchen \pause[4]mit Schummeln\pause: $\mathcal{O}(1)$
+      \pause
+      \item
+        Maximum suchen\pause: $\mathcal{O}(n)$
+      \pause
+      \item
+        Selection-Sort\pause: $\mathcal{O}(n^2)$
+      \pause
+      \item
+        Bubble-Sort\pause: $\mathcal{O}(n)$ bis $\mathcal{O}(n^2)$
+      \pause
+      \item
+        Quicksort\pause: $\mathcal{O}(n\log n)$ bis $\mathcal{O}(n^2)$
+    \end{itemize}
+
+  \end{onlyenv}
+
+  \begin{onlyenv}<14>
+    \textbf{Wie schnell ist RSA-Verschlüsselung?}
+
+    \smallskip
+
+    \begin{math}
+      c = m^e\,\%\,N
+    \end{math}
+    \quad
+    ("`$\%$"' = "`modulo"')
+
+    \medskip
+
+    \begin{lstlisting}[gobble=6,xleftmargin=2em]
+      int c = 1;
+      for (int i = 0; i < e; i++)
+        c = (c * m) % N;
+    \end{lstlisting}
+
+    \smallskip
+
+    \begin{itemize}
+      \item
+        $\mathcal{O}(e)$ Iterationen
+%      \item
+%        wenn $n$ die Anzahl der Binärziffern (Bits) von $e$ ist:
+%        $\mathcal{O}(2^n)$ Iterationen
+      \item
+        mit Trick:
+        $\mathcal{O}(\log e)$ Iterationen ($\log e$ = Anzahl der Ziffern von $e$)
+    \end{itemize}
+
+    \smallskip
+
+    Jede Iteration enthält eine Multiplikation und eine Division.\\
+    Aufwand dafür: $\mathcal{O}(\log e)$\\
+    \textarrow\ Gesamtaufwand: $\mathcal{O}\bigl((\log e)^2\bigr)$
+
+  \end{onlyenv}
+
+  \begin{onlyenv}<15->
+
+    \textbf{Wie schnell ist RSA?}\\
+
+    \smallskip
+
+    ($n$ = typische beteiligte Zahl, z.\,B. $e,p,q$)
+
+    \begin{itemize}
+      \item
+        Ver- und Entschlüsselung (Exponentiation):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\!\left((\log n)^2\right)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}(n^2)$}}
+      \item
+        Schlüsselerzeugung (Berechnung von $d$):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\!\left((\log n)^2\right)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}(n^2)$}}
+      \item
+        Verschlüsselung brechen (Primfaktorzerlegung):\\
+        \strut\hbox to 3.5cm{\color{red}$\mathcal{O}\bigl(2^{\sqrt{\log n\,\cdot\,\log\log n}}\bigr)$\hss}
+        \only<16->{{\color{magenta}$\mathcal{O}\bigl(2^{\sqrt{n\log n}}\bigr)$}}
+    \end{itemize}
+
+    \vspace{0cm plus 1filll}
+
+    \textbf{Die Sicherheit von RSA beruht darauf,
+    daß das Brechen der Verschlüsselung aufwendiger ist als
+    \boldmath$\mathcal{O}\bigl((\log n)^k\bigr)$ (für beliebiges $k$).}
+
+    \vspace*{0.65cm}
+
+  \end{onlyenv}
+
+\end{frame}
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \item[5.1] Differentialgleichungen
+        \color{medgreen}
+        \item[5.2] Rekursion
+        \item[5.3] Aufwandsabschätzungen
+      \end{itemize}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{red}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \item[4.4] volatile-Variable
+        \item[4.6] Byte-Reihenfolge -- Endianness
+        \item[4.7] Binärdarstellung negativer Zahlen
+        \item[4.8] Speicherausrichtung -- Alignment
+      \end{itemize}
+    \vspace*{-\smallskipamount}
+    \item[\textbf{\dots}]
+  \end{itemize}
+  \vspace*{-1cm}
+
+\end{frame}
+
+\section{Hardwarenahe Programmierung}
+\subsection{Bit-Operationen}
+\subsubsection{Zahlensysteme}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \vspace*{-\smallskipamount}
+  \showsubsection
+  \vspace*{-\medskipamount}
+  \showsubsubsection
+
+  \begin{tabular}{rlrl}
+    Basis & Name & Beispiel & Anwendung \\[\smallskipamount]
+      2 & Binärsystem & 1\,0000\,0011 & Bit-Operationen \\
+      8 & Oktalsystem & \lstinline,0403, & Dateizugriffsrechte (Unix) \\
+     10 & Dezimalsystem & \lstinline,259, & Alltag \\
+     16 & Hexadezimalsystem & \lstinline,0x103, & Bit-Operationen \\
+    256 & (keiner gebräuchlich) & 0.0.1.3 & IP-Adressen (IPv4)
+  \end{tabular}
+
+  \bigskip
+
+  \begin{itemize}
+    \item
+      Computer rechnen im Binärsystem.
+    \item
+      Für viele Anwendungen (z.\,B.\ I/O-Ports, Grafik, \dots) ist es notwendig,\\
+      Bits in Zahlen einzeln ansprechen zu können.
+  \end{itemize}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  \begin{tabular}{rlrlrc}
+    \qquad 000 & \bf 0 \hspace*{1.5cm} & 0000 & \bf 0 & \quad 1000 & \bf 8\\
+           001 & \bf 1                 & 0001 & \bf 1 &       1001 & \bf 9\\
+           010 & \bf 2                 & 0010 & \bf 2 &       1010 & \bf A\\
+           011 & \bf 3                 & 0011 & \bf 3 &       1011 & \bf B\\[\smallskipamount]
+           100 & \bf 4                 & 0100 & \bf 4 &       1100 & \bf C\\
+           101 & \bf 5                 & 0101 & \bf 5 &       1101 & \bf D\\
+           110 & \bf 6                 & 0110 & \bf 6 &       1110 & \bf E\\
+           111 & \bf 7                 & 0111 & \bf 7 &       1111 & \bf F\\
+  \end{tabular}
+
+  \medskip
+
+  \begin{itemize}
+    \item
+      Oktal- und Hexadezimalzahlen lassen sich ziffernweise\\
+      in Binär-Zahlen umrechnen.
+    \item
+      Hexadezimalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+      gruppiert zu jeweils 4 Bits.
+    \item
+      Oktalzahlen sind eine Kurzschreibweise für Binärzahlen,\\
+      gruppiert zu jeweils 3 Bits.
+    \item
+      Trotz Taschenrechner u.\,ä.\ lohnt es sich,\\
+      die o.\,a.\ Umrechnungstabelle \textbf{auswendig} zu kennen.
+  \end{itemize}
+
+\end{frame}
+
+\subsubsection{Bit-Operationen in C}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  \begin{tabular}{lll}
+    C-Operator     & Verknüpfung              & Anwendung                \\[\smallskipamount]
+    \lstinline,&,  & Und                      & Bits gezielt löschen     \\
+    \lstinline,|,  & Oder                     & Bits gezielt setzen      \\
+    \lstinline,^,  & Exklusiv-Oder            & Bits gezielt invertieren \\
+    \lstinline,~,  & Nicht                    & Alle Bits invertieren    \\[\smallskipamount]
+    \lstinline,<<, & Verschiebung nach links  & Maske generieren         \\
+    \lstinline,>>, & Verschiebung nach rechts & Bits isolieren
+  \end{tabular}
+
+  \bigskip
+
+  Numerierung der Bits: von rechts ab 0
+
+  \medskip
+
+  \begin{tabular}{ll}
+    Bit Nr.\ 3 auf 1 setzen: &
+    \lstinline,a |= 1 << 3;, \\
+    Bit Nr.\ 4 auf 0 setzen: &
+    \lstinline,a &= ~(1 << 4);, \\
+    Bit Nr.\ 0 invertieren: &
+    \lstinline,a ^= 1 << 0;,
+  \end{tabular}
+
+  \smallskip
+
+  ~~Abfrage, ob Bit Nr.\ 1 gesetzt ist:\quad
+  \lstinline{if (a & (1 << 1))}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsubsection
+
+  C-Datentypen für Bit-Operationen:
+  \smallskip\par
+  \lstinline{#include <stdint.h>}
+  \medskip\par
+  \begin{tabular}{lllll}
+                    & 8 Bit & 16 Bit & 32 Bit & 64 Bit \\
+    mit Vorzeichen  & \lstinline,int8_t,
+                    & \lstinline,int16_t,
+                    & \lstinline,int32_t,
+                    & \lstinline,int64_t, \\
+    ohne Vorzeichen & \lstinline,uint8_t,
+                    & \lstinline,uint16_t,
+                    & \lstinline,uint32_t,
+                    & \lstinline,uint64_t,
+  \end{tabular}
+
+  \bigskip
+  \bigskip
+
+  Ausgabe:
+  \smallskip\par
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <stdint.h>
+    #include <inttypes.h>
+    ...
+    uint64_t x = 42;
+    printf ("Die Antwort lautet: %" PRIu64 "\n", x);
+  \end{lstlisting}
+
+\iffalse
+
+  \bigskip
+
+  Aufgabe: Schreiben Sie C-Funktionen, die ein "`Array von Bits"' realisieren, z.\,B.
+
+  \smallskip
+
+  \begin{tabular}[t]{ll}
+    \lstinline|void set_bit (int i);|   & Bei Index $i$ auf 1 setzen \\
+    \lstinline|void clear_bit (int i);| & Bei Index $i$ auf 0 setzen \\
+    \lstinline|int get_bit (int i);|    & Bei Index $i$ lesen
+  \end{tabular}
+
+  \medskip
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Die Größe des Bit-"`Arrays"' (z.\,B.\ 1000) dürfen Sie als \emph{vorher bekannt\/} voraussetzen.
+    \item
+      Sie benötigen ein Array, z.\,B.\ von \lstinline|char|- oder \lstinline|int|-Variablen.
+    \item
+      Sie benötigen eine Division (\lstinline|/|) sowie den Divisionsrest (Modulo: \lstinline|%|).
+  \end{itemize}
+
+\fi
+
+\end{frame}
+
+\subsection{I/O-Ports}
+
+\begin{frame}[fragile]
+
+%  \showsection
+  \showsubsection
+  \vspace*{-1.5\medskipamount}
+  {\large\textbf{\color{structure}4.3\quad Interrupts}}
+
+  \bigskip
+
+  Kommunikation mit externen Geräten
+
+  \bigskip
+
+  \begin{center}
+    \includegraphics{io-ports-and-interrupts.pdf}
+  \end{center}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  In Output-Port schreiben = Aktoren ansteuern
+
+  Beispiel: LED
+
+  \medskip
+
+  \begin{lstlisting}
+    #include <avr/io.h>
+    ...
+    DDRC = 0x70;
+    PORTC = 0x40;
+  \end{lstlisting}
+  \begin{picture}(0,0)
+    \put(3,0.67){\begin{minipage}{3cm}
+                \color{red}%
+                binär: 0111\,0000\\
+                binär: 0100\,0000
+              \end{minipage}}
+    \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+  \end{picture}
+
+  \bigskip
+
+  \lstinline{DDR} = Data Direction Register\\
+  Bit = 1 für Output-Port\\
+  Bit = 0 für Input-Port
+
+  \bigskip
+
+  \emph{Details: siehe Datenblatt und Schaltplan}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Aus Input-Port lesen = Sensoren abfragen
+
+  Beispiel: Taster
+
+  \medskip
+
+  \begin{lstlisting}
+    #include <avr/io.h>
+    ...
+    DDRC = 0xfd;
+    while ((PINC & 0x02) == 0)
+      ; /* just wait */
+  \end{lstlisting}
+  \begin{picture}(0,0)(-1.5,-0.42)
+    \put(3,0.67){\begin{minipage}{3cm}
+                \color{red}%
+                binär: 1111\,1101\\
+                binär: 0000\,0010
+              \end{minipage}}
+    \put(10,0.67){\makebox(0,0)[r]{\color{red}Herstellerspezifisch!}}
+  \end{picture}
+
+  \bigskip
+
+  \lstinline{DDR} = Data Direction Register\\
+  Bit = 1 für Output-Port\\
+  Bit = 0 für Input-Port
+
+  \bigskip
+
+  \emph{Details: siehe Datenblatt und Schaltplan}
+  
+  \bigskip
+
+  Praktikumsaufgabe: Druckknopfampel
+
+\end{frame}
+
+\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 über 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 "`großes Ende zuerst"' \\\cline{1-2}
+    \multicolumn{2}{c}{} & \pause für 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\ außer bei Datenaustausch!}
+
+%  \pause
+%  \bigskip
+%
+%  Aber: nicht verwechseln! \qquad $0304_{16} = 772$
+
+\end{frame}
+
+\begin{frame}
+
+  \showsubsection
+  \showsubsubsection
+
+  Eine Zahl geht über mehrere Speicherzellen.\\
+  Beispiel: 16-Bit-Zahl in 2 8-Bit-Speicherzellen
+
+  \smallskip
+
+  Welche Bits liegen wo?
+
+  \medskip
+
+  \textarrow\ Geschmackssache\\
+  \textbf{\dots\ außer bei Datenaustausch!}
+
+  \begin{itemize}
+    \item
+      Dateiformate
+    \item
+      Datenübertragung
+  \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{Datenübertragung}
+
+\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 "`natürliche"' Schreibweise für $-1$.\\
+  \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 "`natürliche"' Schreibweise für $-1$.\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{Für 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 größer: & $37027$
+      & (zusätzliche Bytes mit Nullen aufgefüllt)
+  \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 aufgefüllt)\\
+    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}
+
+\nosectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \shownosectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \hfill\makebox(0,0)[br]{\raisebox{2.25ex}{\url{https://gitlab.cvh-server.de/pgerwinski/hp}}}
+    \item[\textbf{2}] \textbf{Einführung in C}
+    \item[\textbf{3}] \textbf{Bibliotheken}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \item[5.1] Differentialgleichungen
+        \item[5.2] Rekursion
+        \item[5.3] Aufwandsabschätzungen
+      \end{itemize}
+    \item[\textbf{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \color{medgreen}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \item[4.4] volatile-Variable
+        \item[4.6] Byte-Reihenfolge -- Endianness
+        \item[4.7] Binärdarstellung negativer Zahlen
+        \item[4.8] Speicherausrichtung -- Alignment
+      \end{itemize}
+    \item[\textbf{\dots}]
+  \end{itemize}
+
+\end{frame}
+
+\end{document}
diff --git a/20210114/hp-musterloesung-20210114.pdf b/20210114/hp-musterloesung-20210114.pdf
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diff --git a/20210114/hp-musterloesung-20210114.tex b/20210114/hp-musterloesung-20210114.tex
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+% hp-musterloesung-20210107.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  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: Fakultät, Länge von Strings (Neuauflage), Hexdumps
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gnuplot-lua-tikz}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 7.\ Januar 2021}
+
+  \exercise{Fakultät}
+
+  Die Fakultät $n!$ einer ganzen Zahl $n \ge 0$ ist definiert als:
+  \begin{eqnarray*}
+    1 & \mbox{für} & n = 0, \\
+    n \cdot (n-1)! & \mbox{für} & n > 0.
+  \end{eqnarray*}
+
+  Mit anderen Worten: $n! = 1\cdot2\cdot3\cdot\dots\cdot n$.
+
+  Die folgende Funktion \lstinline{fak()} berechnet die Fakultät \emph{rekursiv}
+  (Datei: \gitfile{hp}{2020ws/20210107}{aufgabe-1.c}):
+
+  \begin{lstlisting}
+    int fak (int n)
+    {
+      if (n <= 0)
+        return 1;
+      else
+        return n * fak (n - 1);
+    }
+  \end{lstlisting}
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Schreiben Sie eine Funktion, die die Fakultät \emph{iterativ} berechnet,\\
+      d.\,h.\ mit Hilfe einer Schleife anstelle von Rekursion.
+      \points{3}
+    \item
+      Wie viele Multiplikationen (Landau-Symbol)
+      erfordern beide Versionen der Fakultätsfunktion\\
+      in Abhängigkeit von \lstinline$n$?
+      Begründen Sie Ihre Antwort.
+      \points{2}
+    \item
+      Wieviel Speicherplatz (Landau-Symbol)
+      erfordern beide Versionen der Fakultätsfunktion\\
+      in Abhängigkeit von \lstinline$n$?
+      Begründen Sie Ihre Antwort.
+      \points{3}
+  \end{enumerate}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Schreiben Sie eine Funktion, die die Fakultät \emph{iterativ} berechnet,\\
+      d.\,h.\ mit Hilfe einer Schleife anstelle von Rekursion.}
+
+      Datei: \gitfile{hp}{2020ws/20210107}{loesung-1.c}
+      \begin{lstlisting}[gobble=8]
+        int fak (int n)
+        {
+          int f = 1;
+          for (int i = 2; i <= n; i++)
+            f *= i;
+          return f;
+        }
+      \end{lstlisting}
+
+    \item[(b)]
+      \textbf{Wie viele Multiplikationen (Landau-Symbol)
+      erfordern beide Versionen der Fakultätsfunktion\\
+      in Abhängigkeit von \lstinline$n$?
+      Begründen Sie Ihre Antwort.}
+
+      In beiden Fällen werden $n$ Zahlen miteinander multipliziert --
+      oder $n - 1$, wenn man Multiplikationen mit 1 ausspart.
+      In jedem Fall hängt die Anzahl der Multiplikationen
+      linear von $n$ ab; es sind $\mathcal{O}(n)$ Multiplikationen.
+      Insbesondere arbeiten also beide Versionen gleich schnell.
+
+    \item[(c)]
+      \textbf{Wieviel Speicherplatz (Landau-Symbol)
+      erfordern beide Versionen der Fakultätsfunktion\\
+      in Abhängigkeit von \lstinline$n$?
+      Begründen Sie Ihre Antwort.}
+
+      Die iterative Version der Funktion benötigt 2 Variable vom Typ \lstinline{int},
+      nämlich \lstinline{n} und \lstinline{f}.
+      Dies ist eine konstante Zahl;
+      der Speicherplatzverbrauch ist daher $\mathcal{O}(1)$.
+
+      Die rekursive Version der Funktion erzeugt
+      jedesmal, wenn sie sich selbst aufruft,
+      eine zusätzliche Variable \lstinline{n}.
+      Es sind $n + 1$ Aufrufe; die Anzahl der Variablen \lstinline{n}
+      hängt linear von $n$ ab; der Speicherplatzverbrauch ist also $\mathcal{O}(n)$.
+  \end{itemize}
+
+  \exercise{Länge von Strings}
+
+  Diese Aufgabe ist eine Neuauflage von Aufgabe 3 der
+  Übung vom 14.\ November 2019,\\
+  ergänzt um die Teilaufgaben (f) und (g).
+
+  \medskip
+
+  Strings werden in der Programmiersprache C durch Zeiger auf \lstinline{char}-Variable realisiert.
+
+  Beispiel: \lstinline{char *hello_world = "Hello, world!\n"}
+
+  Die Systembibliothek stellt eine Funktion \lstinline{strlen()} zur Ermittlung der Länge von Strings\\
+  zur Verfügung (\lstinline{#include <string.h>}).
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Auf welche Weise ist die Länge eines Strings gekennzeichnet?
+      \points{1}
+    \item
+      Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?\\
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.\\
+      \points{3}
+  \end{enumerate}
+
+  \goodbreak
+
+  Wir betrachten nun die folgenden Funktionen (Datei: \gitfile{hp}{2020ws/20210107}{aufgabe-2.c}):
+  \begin{center}
+    \begin{minipage}{8cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_1 (char *s)
+        {
+          int x = 0;
+          for (int i = 0; i < strlen (s); i++)
+            x += s[i];
+          return x;
+        }
+      \end{lstlisting}
+    \end{minipage}%
+    \begin{minipage}{6cm}
+      \vspace*{-1cm}
+      \begin{lstlisting}[gobble=8]
+        int fun_2 (char *s)
+        {
+          int i = 0, x = 0;
+          int len = strlen (s);
+          while (i < len)
+            x += s[i++];
+          return x;
+        }
+      \end{lstlisting}
+      \vspace*{-1cm}
+    \end{minipage}
+  \end{center}
+  \begin{enumerate}[\quad(a)]\setcounter{enumi}{3}
+    \item
+      Was bewirken die beiden Funktionen?
+      \points{2}
+    \item
+      Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},\\
+      nur effizienter.
+      \points{4}
+    \item
+      Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String?
+      Begründen Sie Ihre Antwort.
+      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.
+       \points{3}
+    \item
+      Von welcher Ordnung (Landau-Symbol) ist Ihre effizientere Funktion?\\
+      Begründen Sie Ihre Antwort.
+      \points{1}
+  \end{enumerate}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Auf welche Weise ist die Länge eines Strings gekennzeichnet?}
+
+      Ein String ist ein Array von \lstinline{char}s.
+      Nach den eigentlichen Zeichen des Strings enthält das Array
+      \textbf{ein Null-Symbol} (Zeichen mit Zahlenwert 0,
+      nicht zu verwechseln mit der Ziffer \lstinline{'0'}) als Ende-Markierung.
+      Die Länge eines Strings ist die Anzahl der Zeichen
+      \emph{vor\/} diesem Symbol.
+
+    \item[(b)]
+      {\bf Wie lang ist die Beispiel-String-Konstante \lstinline{"Hello, world!\n"},
+      und wieviel Speicherplatz belegt sie?}
+
+      Sie ist 14 Zeichen lang (\lstinline{'\n'} ist nur 1 Zeichen;
+      das Null-Symbol, das das Ende markiert, zählt hier nicht mit)
+      und belegt Speicherplatz für 15 Zeichen
+      (15 Bytes -- einschließlich Null-Symbol / Ende-Markierung).
+
+    \item[(c)]
+      \textbf{Schreiben Sie eine eigene Funktion \lstinline{int strlen (char *s)},
+      die die Länge eines Strings zurückgibt.}
+
+      Siehe die Dateien \gitfile{hp}{2020ws/20210107}{loesung-2c-1.c} (mit Array-Index)
+      und \gitfile{hp}{2020ws/20210107}{loesung-2c-2.c} (mit Zeiger-Arithmetik).
+      Beide Lösungen sind korrekt und arbeiten gleich schnell.
+
+      Die Warnung \lstinline[style=terminal]{conflicting types for built-in function "strlen"}
+      kann normalerweise ignoriert werden;
+      auf manchen Systemen (z.\,B.\ MinGW) hat jedoch die eingebaute Funktion \lstinline{strlen()}
+      beim Linken Vorrang vor der selbstgeschriebenen,
+      so daß die selbstgeschriebene Funktion nie aufgerufen wird.
+      In solchen Fällen ist es zulässig, die selbstgeschriebene Funktion
+      anders zu nennen (z.\,B.\ \lstinline{my_strlen()}).
+
+    \item[(d)]
+      \textbf{Was bewirken die beiden Funktionen?}
+
+      Beide addieren die Zahlenwerte der im String enthaltenen Zeichen
+      und geben die Summe als Funktionsergebnis zurück.
+
+      Im Falle des Test-Strings \lstinline{"Hello, world!\n"}
+      lautet der Rückgabewert 1171 (siehe \gitfile{hp}{2020ws/20210107}{loesung-2d-1.c} und \gitfile{hp}{2020ws/20210107}{loesung-2d-2.c}).
+
+    \item[(e)]
+      \textbf{Schreiben Sie eine eigene Funktion,
+      die dieselbe Aufgabe erledigt wie \lstinline{fun_2()},
+      nur effizienter.}
+
+      Die Funktion wird effizienter,
+      wenn man auf den Aufruf von \lstinline{strlen()} verzichtet
+      und stattdessen die Ende-Prüfung in derselben Schleife vornimmt,
+      in der man auch die Zahlenwerte der Zeichen des Strings aufsummiert.
+
+      Die Funktion \lstinline{fun_3()} in der Datei \gitfile{hp}{2020ws/20210107}{loesung-2e-1.c}
+      realisiert dies mit einem Array-Index,
+      Die Funktion \lstinline{fun_4()} in der Datei \gitfile{hp}{2020ws/20210107}{loesung-2e-2.c}
+      mit Zeiger-Arithmetik.
+      Beide Lösungen sind korrekt und arbeiten gleich schnell.
+
+      \textbf{Bemerkung:} Die effizientere Version der Funktion
+      arbeitet doppelt so schnell wie die ursprüngliche,
+      hat aber ebenfalls die Ordnung $\mathcal{O}(n)$ -- siehe unten.
+
+    \item[(f)]
+      \textbf{Von welcher Ordnung (Landau-Symbol) sind die beiden Funktionen
+      hinsichtlich der Anzahl ihrer Zugriffe auf die Zeichen im String?
+      Begründen Sie Ihre Antwort.
+      Sie dürfen für \lstinline{strlen()} Ihre eigene Version der Funktion voraussetzen.}
+
+      Vorüberlegung: \lstinline{strlen()} greift in einer Schleife
+      auf alle Zeichen des Strings der Länge $n$ zu,
+      hat also $\mathcal{O}(n)$.
+
+      \lstinline{fun_1()} ruft in jedem Schleifendurchlauf
+      (zum Prüfen der \lstinline{while}-Bedingung) einmal \lstinline{strlen()} auf
+      und greift anschließend auf ein Zeichen des Strings zu,
+      hat also $\mathcal{O}\bigl(n\cdot(n+1)\bigr) = \mathcal{O}(n^2)$.
+
+      \lstinline{fun_2()} ruft einmalig \lstinline{strlen()} auf
+      und greift anschließend in einer Schleife auf alle Zeichen des Strings zu,
+      hat also $\mathcal{O}(n+n) = \mathcal{O}(n)$.
+
+    \item[(g)]
+      \textbf{Von welcher Ordnung (Landau-Symbol) ist Ihre effizientere Funktion?\\
+      Begründen Sie Ihre Antwort.}
+
+      In beiden o.\,a.\ Lösungsvarianten
+      -- \gitfile{hp}{2020ws/20210107}{loesung-2e-1.c}
+      und \gitfile{hp}{2020ws/20210107}{loesung-2e-2.c} --
+      arbeitet die Funktion mit einer einzigen Schleife,
+      die gleichzeitig die Zahlenwerte addiert und das Ende des Strings sucht.
+
+      Mit jeweils einer einzigen Schleife
+      haben beide Funktionen die Ordnung $\mathcal{O}(n)$.
+
+  \end{itemize}
+
+  \exercise{Hexdumps}
+
+  Das folgende Programm (\gitfile{hp}{2020ws/20210107}{aufgabe-2.c}) liest
+  einen String ein und gibt die ASCII-Werte der Buchstaben hexadezimal aus.
+  (Anders als z.\,B.\ \lstinline{scanf()}
+  akzeptiert die Funktion \lstinline{fgets()} zum Lesen von Strings auch Leerzeichen,
+  und sie vermeidet Pufferüberläufe.)
+  \begin{lstlisting}[style=numbered]
+    #include <stdio.h>
+
+    int main (void)
+    {
+      char buffer[100];
+      fgets (buffer, 100, stdin);
+      for (char *p = buffer; *p; p++)
+        printf ("%02x", *p);
+      printf ("\n");
+    }
+  \end{lstlisting}
+  Beispiel: Bei der Eingabe von \lstinline[style=cmd]{Dies ist ein Test.}
+  erscheint die Ausgabe\\
+  \lstinline[style=terminal]{44696573206973742065696e20546573742e0a}.
+
+  Schreiben Sie ein Programm, das diese Umwandlung in umgekehrter Richtung vornimmt,
+  also z.\,B.\ bei Eingabe von \lstinline[style=cmd]{44696573206973742065696e20546573742e0a}
+  wieder \lstinline[style=terminal]{Dies ist ein Test.} ausgibt.
+
+  \points{6}
+
+  Hinweis für die Klausur:
+  Abgabe in digitaler Form ist erwünscht, aber nicht zwingend.
+
+  \solution
+
+  Siehe \gitfile{hp}{2020ws/20210107}{loesung-2.c}.
+
+  Das Programm macht mehrfach davon Gebrauch,
+  daß in C Zeichen und Zahlen äquivalent sind.
+  Wenn z.\,B.\ die \lstinline{char}-Variable \lstinline{c}
+  den Wert \lstinline{'3'} (Ziffer 3) enthält,
+  dann hat der Ausdruck \lstinline{c - '0'} den Wert \lstinline{3} (Zahlenwert 3).
+  Hierfür ist es insbesondere nicht nötig, vorauszusetzen,
+  daß wir den ASCII-Zeichensatz verwenden und \lstinline{'0'}
+  den Wert \lstinline{48} hat.
+
+  Bei Eingabe von \lstinline[style=cmd]{44696573206973742065696e20546573742e0a}
+  gibt das Programm zusätzlich eine Leerzeile aus.
+  Die liegt daran, daß das \lstinline[style=cmd]{0a} am Ende
+  bereits eine Zeilenschaltung enthält und das Programm mit
+  \lstinline{printf ("\n")} eine zusätzliche Zeilenschaltung ausgibt.
+
+\end{document}
diff --git a/20210114/hp-uebung-20210114.pdf b/20210114/hp-uebung-20210114.pdf
new file mode 100644
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diff --git a/20210114/hp-uebung-20210114.tex b/20210114/hp-uebung-20210114.tex
new file mode 100644
index 0000000..c1af612
--- /dev/null
+++ b/20210114/hp-uebung-20210114.tex
@@ -0,0 +1,271 @@
+% hp-uebung-20210114.pdf - Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021  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: Zahlensysteme, Mikrocontroller, LED-Blinkmuster
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+
+\begin{document}
+
+%  \thispagestyle{empty}
+
+  \section*{Hardwarenahe Programmierung\\
+            Übungsaufgaben -- 14.\ Januar 2021}
+
+  Diese Übung enthält Punkteangaben wie in einer Klausur.
+  Um zu "`bestehen"', müssen Sie innerhalb von 85 Minuten
+  unter Verwendung ausschließlich zugelassener Hilfsmittel
+  17 Punkte (von insgesamt \totalpoints) erreichen.
+
+  \exercise{Zahlensysteme}
+
+  Wandeln Sie ohne Hilfsmittel
+
+  \begin{minipage}[t]{0.3\textwidth}
+    \begin{itemize}
+      \item
+        nach Dezimal:
+        \begin{itemize}
+          \item[(a)]
+            0010\,0000$_2$
+          \item[(b)]
+            42$_{16}$
+          \item[(c)]
+            17$_8$
+        \end{itemize}
+    \end{itemize}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.3\textwidth}
+    \begin{itemize}
+      \item
+        nach Hexadezimal:
+        \begin{itemize}
+          \item[(d)]
+            0010\,0000$_2$
+          \item[(e)]
+            42$_{10}$
+          \item[(f)]
+            192.168.20.254$_{256}$
+        \end{itemize}
+    \end{itemize}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{0.3\textwidth}
+    \begin{itemize}
+      \item
+        nach Binär:
+        \begin{itemize}
+          \item[(g)]
+            750$_8$
+          \item[(h)]
+            42$_{10}$
+          \item[(i)]
+            AFFE$_{16}$
+        \end{itemize}
+    \end{itemize}
+  \end{minipage}
+  
+  \medskip
+
+  Berechnen Sie ohne Hilfsmittel:
+  \begin{itemize}
+    \item[(j)]
+      750$_8$ \& 666$_8$
+    \item[(k)]
+      A380$_{16}$ + B747$_{16}$
+    \item[(l)]
+      AFFE$_{16} >> 1$
+  \end{itemize}
+
+  Die tiefgestellte Zahl steht für die Basis des Zahlensystems.
+  Jede Teilaufgabe zählt 1 Punkt. \addtocounter{points}{12}
+
+  (In der Klausur sind Hilfsmittel zugelassen,
+  daher ist dies \emph{keine\/} typische Klausuraufgabe.)
+
+  \exercise{Mikrocontroller}
+
+  \begin{minipage}[t]{10cm}
+    An die vier Ports eines ATmega16-Mikrocontrollers sind Leuchtdioden angeschlossen:
+    \begin{itemize}
+      \item
+        von links nach rechts an die Ports A, B, C und D,
+      \item
+        von oben nach unten an die Bits Nr.\ 0 bis 7.
+    \end{itemize}
+
+    Wir betrachten das folgende Programm (\gitfile{hp}{2019ws/20191121}{aufgabe-2.c}):
+
+    \begin{lstlisting}[gobble=6]
+      #include <avr/io.h>
+
+      int main (void)
+      {
+        DDRA = 0xff;
+        DDRB = 0xff;
+        DDRC = 0xff;
+        DDRD = 0xff;
+        PORTA = 0x1f;
+        PORTB = 0x10;
+        PORTD = 0x10;
+        PORTC = 0xfc;
+        while (1);
+        return 0;
+      }
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{3cm}
+    \strut\\[-\baselineskip]
+    \includegraphics[width=3cm]{leds.jpg}
+  \end{minipage}
+
+  \vspace*{-3cm}
+
+  \strut\hfill
+  \begin{minipage}{11.8cm}
+    \begin{itemize}
+      \item[(a)]
+        Was bewirkt dieses Programm? \points{4}
+      \item[(b)]
+        Wozu dienen die ersten vier Zeilen des Hauptprogramms? \points{2}
+      \item[(c)]
+        Was würde stattdessen die Zeile \lstinline{DDRA, DDRB, DDRC, DDRD = 0xff;} bewirken?
+        \points{2}
+      \item[(d)]
+        Schreiben Sie das Programm so um,
+        daß die durch das Programm dargestellte Figur spiegelverkehrt erscheint. \points{3}
+      \item[(e)]
+        Wozu dient das \lstinline{while (1)}? \points{2}
+      \item
+        Alle Antworten bitte mit Begründung.
+    \end{itemize}
+  \end{minipage}
+
+  \exercise{LED-Blinkmuster}
+
+  Wir betrachten das folgende Programm für einen ATmega32-Mikro-Controller
+  (Datei: \gitfile{hp}{2019ws/20191128}{aufgabe-3.c}).
+
+  \begin{minipage}[t]{7cm}
+    \begin{lstlisting}[gobble=6]
+      #include <stdint.h>
+      #include <avr/io.h>
+      #include <avr/interrupt.h>
+
+      uint8_t counter = 1;
+      uint8_t leds = 0;
+
+      ISR (TIMER0_COMP_vect)
+      {
+        if (counter == 0)
+          {
+            leds = (leds + 1) % 8;
+            PORTC = leds << 4;
+          }
+        counter++;
+      }
+    \end{lstlisting}
+  \end{minipage}\hfill\begin{minipage}[t]{8.5cm}
+    \begin{lstlisting}[gobble=6]
+      void init (void)
+      {
+        cli ();
+        TCCR0 = (1 << CS01) | (1 << CS00);
+        TIMSK = 1 << OCIE0;
+        sei ();
+        DDRC = 0x70;
+      }
+
+      int main (void)
+      {
+        init ();
+        while (1)
+          ; /* do nothing */
+        return 0;
+      }
+    \end{lstlisting}
+  \end{minipage}
+
+  An die Bits Nr.\ 4, 5 und 6 des Output-Ports C des Mikro-Controllers sind LEDs angeschlossen.\\
+  Sobald das Programm läuft, blinken diese in charakteristischer Weise:
+  \begin{quote}
+    \newcommand{\tdn}[1]{\raisebox{-2pt}{#1}}
+    \begin{tabular}{|c|c|c|c|}\hline
+      \tdn{Phase} & \tdn{LED oben (rot)} & \tdn{LED Mitte (gelb)} & \tdn{LED unten (grün)} \\[2pt]\hline
+      1 & aus & aus & an  \\\hline
+      2 & aus & an  & aus \\\hline
+      3 & aus & an  & an  \\\hline
+      4 & an  & aus & aus \\\hline
+      5 & an  & aus & an  \\\hline
+      6 & an  & an  & aus \\\hline
+      7 & an  & an  & an  \\\hline
+      8 & aus & aus & aus \\\hline
+    \end{tabular}
+  \end{quote}
+  Jede Phase dauert etwas länger als eine halbe Sekunde.
+  Nach 8 Phasen wiederholt sich das Schema.
+
+  Erklären Sie das Verhalten des Programms anhand des Quelltextes:
+  \vspace{-\medskipamount}
+  \begin{itemize}\itemsep0pt
+    \item[(a)]
+      Wieso macht das Programm überhaupt etwas,
+      wenn doch das Hauptprogramm nach dem Initialisieren lediglich eine Endlosschleife ausführt,
+      in der \emph{nichts} passiert?
+      \points{1}
+    \item[(b)]
+      Wieso wird die Zeile \lstinline|PORTC = leds << 4;| überhaupt aufgerufen,
+      wenn dies doch nur unter der Bedingung \lstinline|counter == 0| passiert,
+      wobei die Variable \lstinline|counter| auf 1 initialisiert,
+      fortwährend erhöht und nirgendwo zurückgesetzt wird?
+      \points{2}
+    \item[(c)]
+      Wie kommt das oben beschriebene Blinkmuster zustande?
+      \points{2}
+    \item[(d)]
+      Wieso dauert eine Phase ungefähr eine halbe Sekunde?
+      \points{2}
+    \item[(e)]
+      Was bedeutet "`\lstinline|ISR (TIMER0_COMP_vect)|"'?
+      \points{1}
+  \end{itemize}
+
+  Hinweis:
+  \vspace{-\medskipamount}
+  \begin{itemize}\itemsep0pt
+    \item
+      Die Funktion \lstinline|init()| sorgt dafür, daß der Timer-Interrupt Nr.\ 0 des Mikro-Controllers
+      etwa 488mal pro Sekunde aufgerufen wird.
+      Außerdem initialisiert sie die benötigten Bits an Port C als Output-Ports.
+      Sie selbst brauchen die Funktion \lstinline|init()| nicht weiter zu erklären.
+  \end{itemize}
+
+  \begin{flushright}
+    \textit{Viel Erfolg!}
+  \end{flushright}
+
+  \makeatletter
+    \immediate\write\@mainaux{\string\gdef\string\totalpoints{\arabic{points}}}
+  \makeatother
+
+\end{document}
diff --git a/20210114/io-ports-and-interrupts.pdf b/20210114/io-ports-and-interrupts.pdf
new file mode 120000
index 0000000..bcd46f7
--- /dev/null
+++ b/20210114/io-ports-and-interrupts.pdf
@@ -0,0 +1 @@
+../common/io-ports-and-interrupts.pdf
\ No newline at end of file
diff --git a/20210114/landau-symbols-2.pdf b/20210114/landau-symbols-2.pdf
new file mode 120000
index 0000000..6b458b6
--- /dev/null
+++ b/20210114/landau-symbols-2.pdf
@@ -0,0 +1 @@
+../common/landau-symbols-2.pdf
\ No newline at end of file
diff --git a/20210114/landau-symbols-3.pdf b/20210114/landau-symbols-3.pdf
new file mode 120000
index 0000000..46efa40
--- /dev/null
+++ b/20210114/landau-symbols-3.pdf
@@ -0,0 +1 @@
+../common/landau-symbols-3.pdf
\ No newline at end of file
diff --git a/20210114/landau-symbols.pdf b/20210114/landau-symbols.pdf
new file mode 120000
index 0000000..ca14542
--- /dev/null
+++ b/20210114/landau-symbols.pdf
@@ -0,0 +1 @@
+../common/landau-symbols.pdf
\ No newline at end of file
diff --git a/20210114/leds.jpg b/20210114/leds.jpg
new file mode 120000
index 0000000..5e66b77
--- /dev/null
+++ b/20210114/leds.jpg
@@ -0,0 +1 @@
+../common/leds.jpg
\ No newline at end of file
diff --git a/20210114/logo-hochschule-bochum-cvh-text-v2.pdf b/20210114/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20210114/logo-hochschule-bochum-cvh-text-v2.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum-cvh-text-v2.pdf
\ No newline at end of file
diff --git a/20210114/logo-hochschule-bochum.pdf b/20210114/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20210114/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20210114/pendulum.pdf b/20210114/pendulum.pdf
new file mode 120000
index 0000000..7d1d873
--- /dev/null
+++ b/20210114/pendulum.pdf
@@ -0,0 +1 @@
+../common/pendulum.pdf
\ No newline at end of file
diff --git a/20210114/pgscript.sty b/20210114/pgscript.sty
new file mode 120000
index 0000000..95c8884
--- /dev/null
+++ b/20210114/pgscript.sty
@@ -0,0 +1 @@
+../common/pgscript.sty
\ No newline at end of file
diff --git a/20210114/pgslides.sty b/20210114/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20210114/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/README.md b/README.md
index 2cd6792..3132476 100644
--- a/README.md
+++ b/README.md
@@ -24,6 +24,8 @@ Vortragsfolien und Beispiele:
  * [03.12.2020: Parameter des Hauptprogramms, String-Operationen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201203/hp-20201203.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20201203/)
  * [10.12.2020: Präprozessor, Bibliotheken einbinden und verwenden](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201210/hp-20201210.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20201210/)
  * [17.12.2020: make, Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-20201217.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20201217/)
+ * [07.01.2021: Rekursion, Aufwandsabschätzungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-20210107.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210107/)
+ * [14.01.2021: Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-20210114.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2020ws/20210114/)
  * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/hp-slides-2020ws.pdf)
 
 Übungsaufgaben:
@@ -35,6 +37,8 @@ Vortragsfolien und Beispiele:
  * [03.12.2020: Arrays mit Zahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201203/hp-uebung-20201203.pdf)
  * [10.12.2020: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201210/hp-uebung-20201210.pdf)
  * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-uebung-20201217.pdf)
+ * [07.01.2021: Fakultät, Länge von Strings (Neuauflage), Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-uebung-20210107.pdf)
+ * [14.01.2021: Zahlensysteme, Mikrocontroller, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-uebung-20210114.pdf)
 
 Musterlösungen:
 ---------------
@@ -44,6 +48,8 @@ Musterlösungen:
  * [03.12.2020: Arrays mit Zahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201203/hp-musterloesung-20201203.pdf)
  * [10.12.2020: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201210/hp-musterloesung-20201210.pdf)
  * [17.12.2020: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-musterloesung-20201217.pdf)
+ * [07.01.2021: Fakultät, Länge von Strings (Neuauflage), Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210107/hp-musterloesung-20210107.pdf)
+ * [14.01.2021: Fakultät, Länge von Strings (Neuauflage), Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-musterloesung-20210114.pdf)
 
 Tafelbilder:
 ------------
@@ -53,6 +59,7 @@ Praktikumsunterlagen:
 ---------------------
  * [Versuch 1: RSA-Verschlüsselung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201112/hp-2020ws-p1.pdf)
  * [Versuch 2: Weltraum-Simulation](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20201217/hp-2020ws-p2.pdf)
+ * [Versuch 3: Druckknopfampel](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2020ws/20210114/hp-2020ws-p3.pdf)
 
 Alte Klausuren:
 ---------------
diff --git a/hp-slides-2020ws.pdf b/hp-slides-2020ws.pdf
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diff --git a/hp-slides-2020ws.tex b/hp-slides-2020ws.tex
index 7d3efec..1bca6b8 100644
--- a/hp-slides-2020ws.tex
+++ b/hp-slides-2020ws.tex
@@ -20,8 +20,12 @@
   \includepdf[pages=-]{20201126/hp-20201126.pdf}
   \pdfbookmark[1]{03.12.2020: Parameter des Hauptprogramms, String-Operationen}{20201203}
   \includepdf[pages=-]{20201203/hp-20201203.pdf}
-  \pdfbookmark[1]{10.12.2020: Parameter des Hauptprogramms, String-Operationen}{20201210}
+  \pdfbookmark[1]{10.12.2020: Präprozessor, Bibliotheken einbinden und verwenden}{20201210}
   \includepdf[pages=-]{20201210/hp-20201210.pdf}
-  \pdfbookmark[1]{17.12.2020: Parameter des Hauptprogramms, String-Operationen}{20201217}
+  \pdfbookmark[1]{17.12.2020: make, Differentialgleichungen}{20201217}
   \includepdf[pages=-]{20201217/hp-20201217.pdf}
+  \pdfbookmark[1]{07.01.2021: Rekursion, Aufwandsabschätzungen}{20210107}
+  \includepdf[pages=-]{20210107/hp-20210107.pdf}
+  \pdfbookmark[1]{14.01.2021: Hardwarenahe Programmierung}{20210114}
+  \includepdf[pages=-]{20210114/hp-20210114.pdf}
 \end{document}
diff --git a/update b/update
index c7d95a3..b2addb6 100755
--- a/update
+++ b/update
@@ -5,8 +5,8 @@ course=hp
 date_mask="20[12][0-9][01][0-9][0-3][0-9]"
 
 time_mask="[0-2][0-9][0-5][0-9][0-5][0-9]"
-base_url="https://gitlab.cvh-server.de/pgerwinski/$course/tree/master/"
-raw_base_url="https://gitlab.cvh-server.de/pgerwinski/$course/raw/master/"
+base_url="https://gitlab.cvh-server.de/pgerwinski/$course/tree/$sem/"
+raw_base_url="https://gitlab.cvh-server.de/pgerwinski/$course/raw/$sem/"
 pattern="README:"
 
 if [ "$1" = "--no-slides" ]; then
@@ -122,17 +122,17 @@ Copyright © 2012–2020  Peter Gerwinski
 
 **Diese Lehrmaterialien sind freie Software.**  
 Sie dürfen diese gemäß den jeweils angegebenen Lizenzen  
-([CC-BY-SA 3.0](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/CC-BY-SA-3.0),
-[GNU GPL 3+](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/GNU-GPL-3),
-[modified BSD License](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/BSD-MODIFIED))  
+([CC-BY-SA 3.0](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/CC-BY-SA-3.0),
+[GNU GPL 3+](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/GNU-GPL-3),
+[modified BSD License](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/BSD-MODIFIED))  
 studieren, kopieren, modifizieren und/oder weitergeben.  
-Für Details siehe [common/README](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/README).
+Für Details siehe [common/README](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/README).
 EOF
 
 collect --with-examples "Vortragsfolien und Beispiele:" tex pdf $date_mask/hp-$date_mask.tex $date_mask/verschluesselung-$date_mask.tex
 
 cat >> $readme << EOF
- * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/hp-slides-$sem.pdf)
+ * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/hp-slides-$sem.pdf)
 EOF
 
 collect "Übungsaufgaben:" tex pdf $date_mask/hp-uebung-$date_mask.tex
@@ -145,13 +145,13 @@ cat >> $readme << EOF
 
 Skript:
 -------
- * [Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/script/hp-$sem.pdf)
+ * [Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/script/hp-$sem.pdf)
 
 Original-Materialien einschließlich Beispiel-Programme und LaTeX-Quelltexte:
 ----------------------------------------------------------------------------
- * [common – gemeinsame Dateien für Skript und Vortragsfolien](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/common)
- * [script – Skript zur Lehrveranstaltung](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/script)
- * [201????? – Vortragsfolien und Beispiele](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master)
+ * [common – gemeinsame Dateien für Skript und Vortragsfolien](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem/common)
+ * [script – Skript zur Lehrveranstaltung](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem/script)
+ * [201????? – Vortragsfolien und Beispiele](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem)
  * [branch 2018ws – vollständige Lehrmaterialien vom Wintersemester 2018/19](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2018ws)
 
 
@@ -167,15 +167,15 @@ Copyright © 2012–2020  Peter Gerwinski
 **These teaching materials are Free Software.**  
 You may study, copy, modify, and/or distribute them  
 according to their respective licences  
-([CC-BY-SA 3.0](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/CC-BY-SA-3.0),
-[GNU GPL 3+](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/GNU-GPL-3),
-[modified BSD License](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/BSD-MODIFIED)).  
-See the file [common/README](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/common/README) for details.
-
- * [common – common files for lecture notes and slides](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/common)
- * [script – lecture notes](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master/script)
- * [201????? – slides and examples](https://gitlab.cvh-server.de/pgerwinski/hp/tree/master)
- * [hp-slides-2020ws.pdf – all slides in 1 file](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/hp-slides-2020ws.pdf)
+([CC-BY-SA 3.0](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/CC-BY-SA-3.0),
+[GNU GPL 3+](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/GNU-GPL-3),
+[modified BSD License](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/BSD-MODIFIED)).  
+See the file [common/README](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/common/README) for details.
+
+ * [common – common files for lecture notes and slides](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem/common)
+ * [script – lecture notes](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem/script)
+ * [201????? – slides and examples](https://gitlab.cvh-server.de/pgerwinski/hp/tree/$sem)
+ * [hp-slides-2020ws.pdf – all slides in 1 file](https://gitlab.cvh-server.de/pgerwinski/hp/raw/$sem/hp-slides-2020ws.pdf)
  * [branch 2018ws – complete teaching materials from winter semester 2018–19](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2018ws)
 EOF
 
-- 
GitLab