From d57c07b6816309f5be46c5c4c4dbe78ea5d8c042 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Wed, 22 Nov 2023 22:52:19 +0100
Subject: [PATCH] Vorbereitung 23.11.2023

---
 20231116/hp-20231116.pdf                      |  Bin 199688 -> 191270 bytes
 20231116/hp-20231116.tex                      |   20 +-
 20231116/hp-musterloesung-20231116.pdf        |  Bin 101305 -> 101148 bytes
 20231116/hp-musterloesung-20231116.tex        |    4 +-
 20231116/sum-01.c                             |   15 +
 20231116/sum-02.c                             |   15 +
 20231116/sum-03.c                             |   15 +
 20231116/sum-04.c                             |   15 +
 20231116/sum-05.c                             |   14 +
 20231116/sum-06.c                             |   15 +
 20231116/sum-07.c                             |    8 +
 20231116/sum-09.c                             |   25 +
 20231123/aufgabe-2.c                          |   23 +
 20231123/aufgabe-3.c                          |   62 +
 20231123/hp-20231123.pdf                      |  Bin 0 -> 165231 bytes
 20231123/hp-20231123.tex                      |  883 +++++++++++
 20231123/hp-musterloesung-20231123.pdf        |  Bin 0 -> 202907 bytes
 20231123/hp-musterloesung-20231123.tex        |  394 +++++
 20231123/hp-uebung-20231123.pdf               |  Bin 0 -> 113904 bytes
 20231123/hp-uebung-20231123.tex               |  188 +++
 20231123/loesung-1a.c                         |   22 +
 20231123/loesung-1b.c                         |   22 +
 20231123/loesung-1c.c                         |   22 +
 20231123/loesung-1c.dat                       | 1324 +++++++++++++++++
 20231123/loesung-1c.tikz                      |  521 +++++++
 20231123/loesung-3.c                          |   28 +
 .../logo-hochschule-bochum-cvh-text-v2.pdf    |    1 +
 20231123/logo-hochschule-bochum.pdf           |    1 +
 20231123/pendulum.pdf                         |    1 +
 20231123/pgscript.sty                         |    1 +
 20231123/pgslides.sty                         |    1 +
 README.md                                     |    5 +-
 hp-slides-2023ws.pdf                          |  Bin 1839908 -> 2020462 bytes
 hp-slides-2023ws.tex                          |    4 +-
 34 files changed, 3638 insertions(+), 11 deletions(-)
 create mode 100644 20231116/sum-01.c
 create mode 100644 20231116/sum-02.c
 create mode 100644 20231116/sum-03.c
 create mode 100644 20231116/sum-04.c
 create mode 100644 20231116/sum-05.c
 create mode 100644 20231116/sum-06.c
 create mode 100644 20231116/sum-07.c
 create mode 100644 20231116/sum-09.c
 create mode 100644 20231123/aufgabe-2.c
 create mode 100644 20231123/aufgabe-3.c
 create mode 100644 20231123/hp-20231123.pdf
 create mode 100644 20231123/hp-20231123.tex
 create mode 100644 20231123/hp-musterloesung-20231123.pdf
 create mode 100644 20231123/hp-musterloesung-20231123.tex
 create mode 100644 20231123/hp-uebung-20231123.pdf
 create mode 100644 20231123/hp-uebung-20231123.tex
 create mode 100644 20231123/loesung-1a.c
 create mode 100644 20231123/loesung-1b.c
 create mode 100644 20231123/loesung-1c.c
 create mode 100644 20231123/loesung-1c.dat
 create mode 100644 20231123/loesung-1c.tikz
 create mode 100644 20231123/loesung-3.c
 create mode 120000 20231123/logo-hochschule-bochum-cvh-text-v2.pdf
 create mode 120000 20231123/logo-hochschule-bochum.pdf
 create mode 120000 20231123/pendulum.pdf
 create mode 120000 20231123/pgscript.sty
 create mode 120000 20231123/pgslides.sty

diff --git a/20231116/hp-20231116.pdf b/20231116/hp-20231116.pdf
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diff --git a/20231116/hp-20231116.tex b/20231116/hp-20231116.tex
index e10f6c2..d96bbf3 100644
--- a/20231116/hp-20231116.tex
+++ b/20231116/hp-20231116.tex
@@ -20,7 +20,7 @@
 % Attribution-ShareAlike 3.0 Unported License along with this
 % document.  If not, see <http://creativecommons.org/licenses/>.
 
-% README: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen, Speicherausrichtung
+% README: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen
 
 \documentclass[10pt,t]{beamer}
 
@@ -61,6 +61,7 @@
         \item[4.5] Byte-Reihenfolge -- Endianness
         \item[4.6] Binärdarstellung negativer Zahlen
         \item[4.7] Binärdarstellung von Gleitkommazahlen
+        \color{black}
         \item[4.8] Speicherausrichtung -- Alignment
       \end{itemize}
     \item[\textbf{5}] \textbf{Algorithmen}
@@ -547,6 +548,7 @@
         \item[4.5] Byte-Reihenfolge -- Endianness
         \item[4.6] Binärdarstellung negativer Zahlen
         \item[4.7] Binärdarstellung von Gleitkommazahlen
+        \color{black}
         \item[4.8] Speicherausrichtung -- Alignment
       \end{itemize}
     \item[\textbf{5}] \textbf{Algorithmen}
@@ -871,16 +873,18 @@
     \item
       Zahlen aufsummieren:\\
       vorher sortieren, mit der kleinsten Zahl beginnen
-    \item
-      Ableitungen bilden:\\
-      Beim Bilden von Differenzquotienten\\
-      verliert man notwendigerweise an Präzision!\\
-      \textarrow\ Die Differenzen sehr sorgfältig auswählen.\\
-      \textarrow\ Am besten gar nicht ableiten, sondern integrieren.
+%    \item
+%      Ableitungen bilden:\\
+%      Beim Bilden von Differenzquotienten\\
+%      verliert man notwendigerweise an Präzision!\\
+%      \textarrow\ Die Differenzen sehr sorgfältig auswählen.\\
+%      \textarrow\ Am besten gar nicht ableiten, sondern integrieren.
   \end{itemize}
 
 \end{frame}
 
+\iffalse
+
 \subsection{Speicherausrichtung -- Alignment}
 
 \begin{frame}[fragile]
@@ -947,4 +951,6 @@
 
 \end{frame}
 
+\fi
+
 \end{document}
diff --git a/20231116/hp-musterloesung-20231116.pdf b/20231116/hp-musterloesung-20231116.pdf
index e1a8b074f3e986af2da73bb1c7491cc74eb1a684..429cab8899551fd68e5c426323d1bdff75083470 100644
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diff --git a/20231116/hp-musterloesung-20231116.tex b/20231116/hp-musterloesung-20231116.tex
index 5e52b6f..e3bcfb3 100644
--- a/20231116/hp-musterloesung-20231116.tex
+++ b/20231116/hp-musterloesung-20231116.tex
@@ -1,4 +1,4 @@
-% hp-musterloesung-20231109.pdf - Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences
+% hp-musterloesung-20231116.pdf - Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences
 % Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  Peter Gerwinski
 %
 % This document is free software: you can redistribute it and/or
@@ -33,7 +33,7 @@
 \begin{document}
 
   \section*{Hardwarenahe Programmierung\\
-            Musterlösung zu den Übungsaufgaben -- 9.\ November 2023}
+            Musterlösung zu den Übungsaufgaben -- 16.\ November 2023}
 
   \exercise{Trickprogrammierung}
 
diff --git a/20231116/sum-01.c b/20231116/sum-01.c
new file mode 100644
index 0000000..0362b2f
--- /dev/null
+++ b/20231116/sum-01.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (float x = 1; x <= 100; x++)
+    S += 1.0 / (x * x);
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231116/sum-02.c b/20231116/sum-02.c
new file mode 100644
index 0000000..c0fabe8
--- /dev/null
+++ b/20231116/sum-02.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (float x = 1; x <= 1000000; x++)
+    S += 1.0 / (x * x);
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231116/sum-03.c b/20231116/sum-03.c
new file mode 100644
index 0000000..472d8b7
--- /dev/null
+++ b/20231116/sum-03.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (float x = 1; x <= 10000000; x++)  /* ca. 1/20 s Rechenzeit */
+    S += 1.0 / (x * x);
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231116/sum-04.c b/20231116/sum-04.c
new file mode 100644
index 0000000..c49d13a
--- /dev/null
+++ b/20231116/sum-04.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (float x = 1; x <= 100000000; x++)  /* erwarte: ca. 1/2 s Rechenzeit */
+    S += 1.0 / (x * x);
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231116/sum-05.c b/20231116/sum-05.c
new file mode 100644
index 0000000..8612524
--- /dev/null
+++ b/20231116/sum-05.c
@@ -0,0 +1,14 @@
+#include <stdio.h>
+
+int main (void)
+{
+  float x = 10000000;
+  printf ("%f\n", x);
+  x++;
+  printf ("%f\n", x);
+  x = 100000000;
+  printf ("%f\n", x);
+  x++;
+  printf ("%f\n", x);
+  return 0;
+}
diff --git a/20231116/sum-06.c b/20231116/sum-06.c
new file mode 100644
index 0000000..477e087
--- /dev/null
+++ b/20231116/sum-06.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (int i = 1; i <= 100000000; i++)  /* erwarte: ca. 1/2 s Rechenzeit */
+    S += 1.0 / (i * i);
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231116/sum-07.c b/20231116/sum-07.c
new file mode 100644
index 0000000..af48243
--- /dev/null
+++ b/20231116/sum-07.c
@@ -0,0 +1,8 @@
+#include <stdio.h>
+
+int main (void)
+{
+  int i = 65536;
+  printf ("%d\n", i * i);
+  return 0;
+}
diff --git a/20231116/sum-09.c b/20231116/sum-09.c
new file mode 100644
index 0000000..e2c732f
--- /dev/null
+++ b/20231116/sum-09.c
@@ -0,0 +1,25 @@
+#include <stdio.h>
+#include <math.h>
+
+/* 1/1² + 1/2² + 1/3² + ... = pi²/6 */
+
+int main (void)
+{
+  float pi = M_PI;
+  printf ("%0.9f\n", pi * pi / 6.0);
+  float S = 0.0;
+  for (int i = 1; i <= 100000000; i++)
+    {
+      float x = i;
+      S += 1.0 / (x * x);  /* kleine Zahl zu großer addieren: verschwindet */
+    }
+  printf ("%0.9f\n", S);
+  S = 0.0;
+  for (int i = 100000000; i >= 1; i--)  /* Zuerst die kleinen Zahlen addieren, dann die großen. */
+    {
+      float x = i;
+      S += 1.0 / (x * x);
+    }
+  printf ("%0.9f\n", S);
+  return 0;
+}
diff --git a/20231123/aufgabe-2.c b/20231123/aufgabe-2.c
new file mode 100644
index 0000000..47595ef
--- /dev/null
+++ b/20231123/aufgabe-2.c
@@ -0,0 +1,23 @@
+#include <stdio.h>
+#include <string.h>
+
+typedef struct
+{
+  char first_name[10];
+  char family_name[20];
+  char day, month;
+  int year;
+} person;
+
+int main (void)
+{
+  person sls;
+  sls.day = 26;
+  sls.month = 7;
+  sls.year = 1951;
+  strcpy (sls.first_name, "Sabine");
+  strcpy (sls.family_name, "Leutheusser-Schnarrenberger");
+  printf ("%s %s wurde am %d.%d.%d geboren.\n",
+          sls.first_name, sls.family_name, sls.day, sls.month, sls.year);
+  return 0;
+}
diff --git a/20231123/aufgabe-3.c b/20231123/aufgabe-3.c
new file mode 100644
index 0000000..5b0cb23
--- /dev/null
+++ b/20231123/aufgabe-3.c
@@ -0,0 +1,62 @@
+#include <gtk/gtk.h>
+
+#define WIDTH 320
+#define HEIGHT 240
+
+double t = 0.0;
+double dt = 0.2;
+
+int r = 5;
+
+double x = 10;
+double y = 200;
+double vx = 20;
+double vy = -60;
+double g = 9.81;
+
+gboolean draw (GtkWidget *widget, cairo_t *c, gpointer data)
+{
+  GdkRGBA blue = { 0.0, 0.5, 1.0, 1.0 };
+
+  gdk_cairo_set_source_rgba (c, &blue);
+  cairo_arc (c, x, y, r, 0, 2 * G_PI);
+  cairo_fill (c);
+
+  return FALSE;
+}
+
+gboolean timer (GtkWidget *widget)
+{
+  t += dt;
+  x += vx * dt;
+  y += vy * dt;
+  vx = vx;
+  vy = 0.5 * g * (t * t);
+  if (y + r >= HEIGHT)
+    vy = -vy * 0.9;
+  if (x + r >= WIDTH)
+    vx = -vx * 0.9;
+  if (x - r <= 0)
+    vx = -vx * 0.9;
+  gtk_widget_queue_draw_area (widget, 0, 0, WIDTH, HEIGHT);
+  g_timeout_add (50, (GSourceFunc) timer, widget);
+  return FALSE;
+}
+
+int main (int argc, char **argv)
+{
+  gtk_init (&argc, &argv);
+
+  GtkWidget *window = gtk_window_new (GTK_WINDOW_TOPLEVEL);
+  gtk_widget_show (window);
+  gtk_window_set_title (GTK_WINDOW (window), "Hello");
+  g_signal_connect (window, "destroy", G_CALLBACK (gtk_main_quit), NULL);
+
+  GtkWidget *drawing_area = gtk_drawing_area_new ();
+  gtk_widget_show (drawing_area);
+  gtk_container_add (GTK_CONTAINER (window), drawing_area);
+  gtk_widget_set_size_request (drawing_area, WIDTH, HEIGHT);
+
+  gtk_main ();
+  return 0;
+}
diff --git a/20231123/hp-20231123.pdf b/20231123/hp-20231123.pdf
new file mode 100644
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diff --git a/20231123/hp-20231123.tex b/20231123/hp-20231123.tex
new file mode 100644
index 0000000..1975ab6
--- /dev/null
+++ b/20231123/hp-20231123.tex
@@ -0,0 +1,883 @@
+% hp-20231123.pdf - Lecture Slides on Low-Level Programming
+% Copyright (C) 2012, 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Speicherausrichtung, Algorithmen: Differentialgleichungen
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{tikz}
+
+\newcommand{\redurl}[1]{\href{#1}{\color{red}\nolinkurl{#1}}}
+
+\title{Hardwarenahe Programmierung}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{23.\ November 2023}
+
+\begin{document}
+
+\maketitleframe
+
+\title{Hardwarenahe Programmierung}
+
+\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{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \item[4.4] volatile-Variable
+        \color{medgreen}
+        \item[4.5] Byte-Reihenfolge -- Endianness
+        \item[4.6] Binärdarstellung negativer Zahlen
+        \item[4.7] Binärdarstellung von Gleitkommazahlen
+        \color{red}
+        \item[4.8] Speicherausrichtung -- Alignment
+      \end{itemize}
+    \item[\textbf{5}] \textbf{Algorithmen}
+    \item[\textbf{6}] \textbf{Objektorientierte Programmierung}
+    \item[\textbf{7}] \textbf{Datenstrukturen}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{3}
+\section{Hardwarenahe Programmierung}
+\setcounter{subsection}{4}
+\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}{} & für Menschen leichter lesbar \\
+    \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}{} & 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<1->{, MSB first}
+    \item
+      XBM-Dateien: Little-Endian\only<1->{, LSB first}
+  \end{itemize}
+  \only<1->{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{Binärdarstellung von Gleitkommazahlen}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+%  (Diese Seite wurde unbewußt leer gelassen.)
+
+  Beispiel für Gleitkommazahl: $2{,}351\cdot10^5$ (oder: $2.351\times10^5$)
+
+  \smallskip
+
+  Bezeichnungen: $\text{Mantisse} \cdot 10^{\text{Exponent}}$
+
+  \smallskip
+
+  C-Schreibweise: \lstinline{2.351e5} (oder: \lstinline{2.351E5})
+
+%  \pause
+  \bigskip
+
+  Wie speichert man Gleitkommazahlen?
+
+  \smallskip
+
+  $m$-Bit-Zahl, davon
+  \begin{itemize}
+    \item
+      $e$ Bits für den Exponenten (einschließlich Vorzeichen),
+    \item
+      $1$ Bit für das Vorzeichen der Mantisse,
+    \item
+      $m - e - 1$ Bits für die Mantisse.
+  \end{itemize}
+
+%  \pause
+  \begin{picture}(0,0)
+    \color{red}
+    \put(1.95,0.65){\makebox(0,0){\tikz{\draw(0,0)--(0.5,0.25);}}}
+    \put(1.95,0.65){\makebox(0,0){\tikz{\draw(0,0.25)--(0.5,0);}}}
+  \end{picture}%
+  {\color{red}Trick: Mantisse als \newterm{normalisierte Zahl\/} abspeichern}
+
+%  \pause
+  \bigskip
+  Vorteil gegenüber ganzen Zahlen:\\
+  größerer Wertebereich bei vergleichbarem Speicherplatzbedarf
+
+  \medskip
+
+  Nachteil gegenüber ganzen Zahlen: Rundungsfehler\\
+  \textcolor{red}{\textarrow\
+  \textbf{ungeeignet} für Anwendungen, bei denen es auf jedes Bit ankommt\\
+  \phantom{\textarrow\ }(z.\,B.\ Verschlüsselung)}
+  \vspace*{-1cm}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Problem beim Arbeiten mit Gleitkommazahlen: Auslöschung von Ziffern
+  \begin{itemize}
+    \item
+      Zahlen aufsummieren:\\
+      vorher sortieren, mit der kleinsten Zahl beginnen
+    \pause
+    \item
+      Ableitungen bilden:\\
+      Beim Bilden von Differenzquotienten\\
+      verliert man notwendigerweise an Präzision!\\
+      \textarrow\ Die Differenzen sehr sorgfältig auswählen.\\
+      \textarrow\ Am besten gar nicht ableiten, sondern integrieren.
+  \end{itemize}
+
+\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}
+
+\section{Algorithmen}
+\subsection{Differentialgleichungen}
+
+\begin{frame}[fragile]
+
+  \showsection
+  \showsubsection
+
+  \textbf{Beispiel 1: Gleichmäßig beschleunigte Bewegung}
+
+  \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<2->{\hfill$\Rightarrow$\hfill}%
+  \begin{onlyenv}<2-8>
+    \begin{minipage}{8.3cm}
+      \begin{align*}
+        x(t) &= \int v_x(t)\,dt
+          \visible<4->{= \int v_{0x}\,dt}
+          \visible<5->{= x_0 + v_{0x}\cdot t}\\[\medskipamount]
+        y(t) &= \int v_y(t)\,dt
+          \visible<7->{= \int v_{0y} - g\cdot t\,dt}
+          \visible<8->{= y_0 + v_{0y}\cdot t
+                         - {\textstyle\frac12}gt^2}\\[\bigskipamount]
+        v_x(t) &= \int 0\,dt
+          \visible<3->{= v_{0x}} \\[\medskipamount]
+        v_y(t) &= \int -g\,dt
+          \visible<6->{= v_{0y} - g\cdot t}
+      \end{align*}
+    \end{minipage}%
+  \end{onlyenv}%
+  \begin{onlyenv}<9->
+    \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}
+      \strut
+    \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}
+
+\iffalse
+
+\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{4}] \textbf{Hardwarenahe Programmierung}
+      \begin{itemize}
+        \item[4.1] Bit-Operationen
+        \item[4.2] I/O-Ports
+        \item[4.3] Interrupts
+        \item[4.4] volatile-Variable
+        \color{medgreen}
+        \item[4.5] Byte-Reihenfolge -- Endianness
+        \item[4.6] Binärdarstellung negativer Zahlen
+        \item[4.7] Speicherausrichtung -- Alignment
+      \end{itemize}
+    \item[\textbf{5}] \textbf{Algorithmen}
+      \begin{itemize}
+        \color{medgreen}
+        \item[5.1] Differentialgleichungen
+        \color{red}
+        \item[5.2] Rekursion
+        \color{black}
+        \item[5.3] Aufwandsabschätzungen
+      \end{itemize}
+    \item[\textbf{6}] \textbf{Objektorientierte Programmierung}
+    \item[\textbf{7}] \textbf{Datenstrukturen}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{4}
+\section{Algorithmen}
+\setcounter{subsection}{1}
+\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}<2>
+    \begin{center}
+      \includegraphics[width=12.2cm]{Tower_of_Hanoi.jpeg}
+    \end{center}
+  \end{onlyenv}
+
+  \begin{onlyenv}<3->
+    \begin{itemize}
+      \item
+        64 Scheiben, 3 Plätze,
+        \only<3-4>{\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}<5>
+      \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}<6->
+%       \vspace{-5.0cm}
+%       \hspace*{7.4cm}\begin{minipage}[t]{5cm}
+%         32 Scheiben:
+%         \begin{lstlisting}[gobble=10,style=terminal]
+%           $ ¡time ./hanoi-9b¿
+%           ...
+%           real    0m30,672s
+%           user    0m30,662s
+%           sys     0m0,008s
+%         \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!
+%         % 30.672 * 2^32 / 3600 / 24 / 365.25 = 4174.43775518138261464750
+%         \begin{itemize}
+%           \arrowitem
+%             $\frac{30,672\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4174$
+%             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!
+      \begin{itemize}
+        \arrowitem
+          $\frac{30,672\,\text{s}\,\cdot\,2^{32}}{3600\,\cdot\,24\,\cdot\,365,25} \approx 4174$
+          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}
+
+\fi
+
+\end{document}
diff --git a/20231123/hp-musterloesung-20231123.pdf b/20231123/hp-musterloesung-20231123.pdf
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diff --git a/20231123/hp-musterloesung-20231123.tex b/20231123/hp-musterloesung-20231123.tex
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+% hp-musterloesung-20231116.pdf - Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Kondensator, Personen-Datenbank, Hexdumps
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gnuplot-lua-tikz}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 16.\ November 2023}
+
+  \exercise{Kondensator}
+
+  Ein Kondensator der Kapazität $C = 100\,\mu{\rm F}$
+  ist auf die Spannung $U_0 = 5\,{\rm V}$ aufgeladen
+  und wird über einen Widerstand $R = 33\,{\rm k}\Omega$ entladen.
+
+  \begin{enumerate}[(a)]
+    \item
+      Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.
+      \points{5}
+    \item
+      Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter $0.1\,{\rm V}$ gefallen ist.
+      \points{4}
+    \item
+      Vergleichen Sie die berechneten Werte mit der exakten theoretischen Entladekurve:
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}\\
+      \points{3}
+  \end{enumerate}
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Für die Simulation zerlegen wir den Entladevorgang in kurze Zeitintervalle $dt$.
+      Innerhalb jedes Zeitintervalls betrachten wir den Strom $I$ als konstant
+      und berechnen, wieviel Ladung $Q$ innerhalb des Zeitintervalls
+      aus dem Kondensator herausfließt.
+      Aus der neuen Ladung berechnen wir die Spannung am Ende des Zeitintervalls.
+    \item
+      Für den Vergleich mit der exakten theoretischen Entladekurve
+      benötigen Sie die Exponentialfunktion \lstinline{exp()}.
+      Diese finden Sie in der Mathematik-Bibliothek:
+      \lstinline{#include <math.h>} im Quelltext,
+      beim \lstinline[style=cmd]{gcc}-Aufruf \lstinline[style=cmd]{-lm} mit angeben.
+    \item
+      $Q = C \cdot U$,\quad $U = R \cdot I$,\quad $I = \frac{dQ}{dt}$
+  \end{itemize}
+
+  \solution
+
+  \begin{itemize}
+    \item
+      \textbf{Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.}
+
+      In dem Programm \gitfile{hp}{2023ws/20231123}{loesung-1a.c}
+      arbeiten wir, dem ersten Hinweis folgend,
+      mit einem Zeitintervall von \lstinline{dt = 0.01}.
+      Mit dieser Schrittweite lassen wir uns eine Tabelle ausgeben,
+      die jeweils die Zeit und durch die Simulation berechnete Spannung ausgibt.
+
+      Wir simulieren, wie die Ladung $Q = C \cdot U$ des Kondensators
+      im Laufe der Zeit abfließt.
+      Dazu berechnen wir in jedem Zeitschritt zunächst den Strom $I = U / R$,
+      der aus dem Kondensator fließt.
+      Dieser Strom bewirkt, daß innerhalb des Zeitintervalls $dt$
+      die Ladung $dQ = I \cdot dt$ aus dem Kondensator abfließt.
+      Am Ende des Zeitintervalls berechnen wir die zur neuen Ladung $Q$
+      gehörende neue Spannung $U = Q / C$.
+
+      Für eine einfache Ausgabe der Tabelle
+      verwenden wir die Formatspezifikationen \lstinline{%10.3lf} für drei 
+      bzw.\ \lstinline{%15.8lf} für acht Nachkommastellen Genauigkeit.
+      Damit schreiben wir jeweils eine \emph{lange Fließkommazahl\/} (\lstinline{%lf})
+      rechtsbündig in ein Feld der Breite 10 bzw.\ 15
+      und lassen uns 3 bzw.\ 8 Nachkommastellen ausgeben. 
+
+      Wir compilieren das Programm mit:
+      \lstinline[style=cmd]{gcc -Wall -O loesung-1a.c -o loesung-1a}
+
+    \item
+      \textbf{Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter \boldmath $0.1\,{\rm V}$ gefallen ist.}
+
+      Wir ändern das Programm \gitfile{hp}{2023ws/20231123}{loesung-1a.c} so ab,
+      daß zum einen die Schleife abbricht, sobald die Spannung 
+      den Wert $0.1\,{\rm V}$ unterschreitet (\gitfile{hp}{2023ws/20231123}{loesung-1b.c}),
+      und daß zum anderen nicht jedesmal eine Zeile für die Tabelle ausgegeben wird,
+      sondern erst am Ende die Zeit (und die Spannung).
+
+      Der Ausgabe entnehmen wir, daß die Spannung bei etwa $t = 12.90\,{\rm s}$
+      den Wert $0.1\,{\rm V}$ unterschreitet.
+
+    \item
+      \textbf{Vergleichen Sie die berechneten Werte
+      mit der exakten theoretischen Entladekurve:\\[0.5\smallskipamount]
+      \boldmath  
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}}
+
+      Wir ändern das Programm \gitfile{hp}{2023ws/20231123}{loesung-1a.c} so ab,
+      daß es zusätzlich zur Zeit und zur simulierten Spannung
+      die exakte Spannung $U_0 \cdot e^{-\frac{t}{RC}}$
+      gemäß der theoretischen Entladekurve ausgibt (\gitfile{hp}{2023ws/20231123}{loesung-1c.c}),
+
+      Da dieses Programm die Exponentialfunktion verwendet, müssen wir nun
+      beim Compilieren zusätzlich \lstinline[style=cmd]{-lm}\hspace{1pt}
+      für das Einbinden der Mathematik-Bibliothek angeben.
+
+      Der erweiterten Tabelle können wir entnehmen,
+      daß die durch die Simulation berechnete Spannung
+      mit der Spannung $U_0 \cdot e^{-\frac{t}{RC}}$
+      gemäß der theoretischen Entladekurve
+      bis auf wenige Prozent übereinstimmt.
+      Dies ist für viele praktische Anwendungen ausreichend,
+      wenn auch nicht für Präzisionsmessungen.
+
+      Wenn Sie die Ausgabe des Programms, z.\,B.\ mit
+      \lstinline[style=cmd]{./loesung-1c > loesung-1c.dat},
+      in einer Datei \gitfile{hp}{2023ws/20231123}{loesung-1c.dat} speichern,
+      können Sie sich die beiden Kurven graphisch darstellen lassen,
+      z.\,B.\ mit \file{gnuplot} und dem folgenden Befehl:
+      \begin{lstlisting}[style=cmd,gobble=8]
+        plot "loesung-1c.dat" using 1:2 with lines title "Simulation",
+             "loesung-1c.dat" using 1:3 with lines title "Theorie"
+      \end{lstlisting}
+      \vspace*{-\bigskipamount}
+      \begin{center}
+        \input{loesung-1c.tikz}
+      \end{center}
+      Der Unterschied zwischen der simulierten und der theoretischen Entladungskurve
+      ist mit bloßem Auge nicht sichtbar.
+  \end{itemize}
+
+  \exercise{Personen-Datenbank}
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231123}{aufgabe-2.c}):
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <string.h>
+
+    typedef struct
+    {
+      char first_name[10];
+      char family_name[20];
+      char day, month;
+      int year;
+    } person;
+
+    int main (void)
+    {
+      person sls;
+      sls.day = 26;
+      sls.month = 7;
+      sls.year = 1951;
+      strcpy (sls.first_name, "Sabine");
+      strcpy (sls.family_name, "Leutheusser-Schnarrenberger");
+      printf ("%s %s wurde am %d.%d.%d geboren.\n",
+              sls.first_name, sls.family_name, sls.day, sls.month, sls.year);
+      return 0;
+    }
+  \end{lstlisting}
+
+  Die Standard-Funktion \lstinline{strcpy()} bewirkt ein Kopieren eines Strings
+  von rechts nach links, hier also z.\,B.\ die Zuweisung der String-Konstanten
+  \lstinline{"Sabine"} an die String-Variable \lstinline{sls.first_name[]}.
+
+  Das Programm wird für einen 32-Bit-Rechner compiliert und ausgeführt.\\
+  (Die \lstinline[style=cmd]{gcc}-Option \lstinline[style=cmd]{-m32} sorgt dafür,
+  daß \lstinline[style=cmd]{gcc} Code für einen 32-Bit-Prozessor erzeugt.)
+
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -Wall -O -m32 aufgabe-2.c -o aufgabe-2¿
+    $ ¡./aufgabe-2¿
+    Sabine Leutheusser-Schnarrenberger wurde am 110.98.1701278309 geboren.
+    Speicherzugriffsfehler
+  \end{lstlisting}
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Erklären Sie die Ausgabe des Programms einschließlich der Zahlenwerte.
+      \points{4}
+    \item
+      Welche Endianness hat der verwendete Rechner?
+      Begründen Sie Ihre Antwort.
+      \points{1}
+    \item
+      Wie sähe die Ausgabe auf einem Rechner mit entgegengesetzter Endianness aus?
+      \points{2}
+    \item
+      Erklären Sie den Speicherzugriffsfehler.
+      (Es kann sein, daß sich der Fehler auf Ihrem Rechner nicht bemerkbar macht.
+      Er ist aber trotzdem vorhanden.)
+      \points{2}
+  \end{enumerate}
+
+  \goodbreak
+
+  \solution
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      \textbf{Erklären Sie die Ausgabe des Programms einschließlich der Zahlenwerte.}
+
+      Der String \lstinline{"Leutheusser-Schnarrenberger"}
+      hat 27 Zeichen und daher mehr als die in der Variablen
+      \lstinline{sls.family_name} vorgesehenen 20 Zeichen.
+      Das \lstinline{"nberger"} paßt nicht mehr in die String-Variable.
+      
+      Die Zuweisung \lstinline{strcpy (sls.family_name, "Leutheusser-Schnarrenberger")}
+      überschreibt daher 8 Speicherzellen außerhalb der String-Variablen
+      \lstinline{sls.family_name} mit dem String \lstinline{"nberger"}
+      (7 Buchstaben zzgl.\ String-Ende-Symbol) -- und damit insbesondere die Variablen
+      \lstinline{sls.day}, \lstinline{sls.month} und \lstinline{sls.year}.
+
+      Die überschriebenen Speicherzellen sehen demnach folgendermaßen aus:
+      \begin{center}
+        \begin{picture}(8,1.5)(0,-0.5)
+          \put(0,0){\line(1,0){8}}
+          \put(0,1){\line(1,0){8}}
+          \multiput(0,0)(1,0){9}{\line(0,1){1}}
+          \put(0.4,0.38){\lstinline{n}}
+          \put(1.4,0.38){\lstinline{b}}
+          \put(2.4,0.38){\lstinline{e}}
+          \put(3.4,0.38){\lstinline{r}}
+          \put(4.4,0.38){\lstinline{g}}
+          \put(5.4,0.38){\lstinline{e}}
+          \put(6.4,0.38){\lstinline{r}}
+          \put(7.5,0.5){\makebox(0,0){\lstinline{0x00}}}
+          \put(0.5,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{0.95cm}{0pt}}_{\mbox{\lstinline{day}}}$}}
+          \put(1.5,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{0.95cm}{0pt}}_{\mbox{\lstinline{month}}}$}}
+          \put(4.0,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{3.95cm}{0pt}}_{\mbox{\lstinline{year}}}$}}
+          \put(7.0,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{1.95cm}{0pt}}_{\mbox{?}}$}}
+        \end{picture}
+      \end{center}
+      ("`?"' steht für zwei Speicherzellen, von denen wir nicht wissen,
+      wofür sie genutzt werden.)
+
+      Wenn wir die ASCII-Zeichen in Hexadezimalzahlen umrechnen, entspricht dies:
+      \begin{center}
+        \begin{picture}(7,1.5)(0,-0.5)
+          \put(0,0){\line(1,0){8}}
+          \put(0,1){\line(1,0){8}}
+          \multiput(0,0)(1,0){9}{\line(0,1){1}}
+          \put(0.5,0.5){\makebox(0,0){\lstinline{0x6e}}}
+          \put(1.5,0.5){\makebox(0,0){\lstinline{0x62}}}
+          \put(2.5,0.5){\makebox(0,0){\lstinline{0x65}}}
+          \put(3.5,0.5){\makebox(0,0){\lstinline{0x72}}}
+          \put(4.5,0.5){\makebox(0,0){\lstinline{0x67}}}
+          \put(5.5,0.5){\makebox(0,0){\lstinline{0x65}}}
+          \put(6.5,0.5){\makebox(0,0){\lstinline{0x72}}}
+          \put(7.5,0.5){\makebox(0,0){\lstinline{0x00}}}
+          \put(0.5,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{0.95cm}{0pt}}_{\mbox{\lstinline{day}}}$}}
+          \put(1.5,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{0.95cm}{0pt}}_{\mbox{\lstinline{month}}}$}}
+          \put(4.0,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{3.95cm}{0pt}}_{\mbox{\lstinline{year}}}$}}
+          \put(7.0,-0.1){\makebox(0,0)[t]{$\underbrace{\rule{1.95cm}{0pt}}_{\mbox{?}}$}}
+        \end{picture}
+      \end{center}
+      Dies entspricht bereits genau den Werten \lstinline{110} und \lstinline{98}
+      für die Variablen \lstinline{sls.day} bzw.\ \lstinline{sls.month}.
+
+      Für die Variable \lstinline{sls.year} müssen wir ihre vier Speicherzellen
+      unter der Berücksichtigung der Endianness des Rechners zusammenziehen.
+      Für Big-Endian ergibt dies \lstinline{0x65726765 == 1701996389}.
+      Für Little-Endian ergibt sich der Wert \lstinline{0x65677265 == 1701278309},
+      der auch in der Ausgabe des Programms auftaucht.
+
+    \item
+      \textbf{Welche Endianness hat der verwendete Rechner?
+      Begründen Sie Ihre Antwort.}
+
+      Wie in (a) begründet, ergibt sich die Ausgabe von
+      \lstinline[style=terminal]{1701278309} für das Jahr
+      aus dem Speicherformat Little-Endian.
+
+    \item
+      \textbf{Wie sähe die Ausgabe auf einem Rechner mit entgegengesetzter Endianness aus?}
+
+      Wie in (a) begründet, ergäbe sich aus dem Speicherformat Big-Endian
+      die Ausgabe von \lstinline[style=terminal]{1701996389} für das Jahr.
+
+    \item
+      \textbf{Erklären Sie den Speicherzugriffsfehler.
+      (Es kann sein, daß sich der Fehler auf Ihrem Rechner nicht bemerkbar macht.
+      Er ist aber trotzdem vorhanden.)}
+
+      Die zwei in (a) mit "`?"' bezeichneten Speicherzellen
+      wurden ebenfalls überschrieben.
+      Dies ist in der Ausgabe zunächst nicht sichtbar,
+      bewirkt aber später den Speicherzugriffsfehler.
+
+      (Tatsächlich handelt es sich bei den überschriebenen Speicherzellen
+      um einen Teil der Rücksprungadresse, die \lstinline{main()} verwendet,
+      um mit \lstinline{return 0} an das Betriebssystem zurückzugeben.)
+
+  \end{enumerate}
+
+  \textbf{Hinweis 1:}
+  Um auf einen solchen Lösungsweg zu kommen, wird empfohlen,
+  "`geheimnisvolle"' Zahlen nach hexadezimal umzurechnen
+  und in Speicherzellen (Zweiergruppen von Hex-Ziffern) zu zerlegen.
+  Oft erkennt man dann direkt ASCII-Zeichen:
+  Großbuchstaben beginnen mit der Hex-Ziffer \lstinline{4} oder \lstinline{5},
+  Kleinbuchstaben mit \lstinline{6} oder \lstinline{7}.
+
+  \textbf{Hinweis 2:}
+  Um derartige Programmierfehler in der Praxis von vorneherein zu vermeiden,
+  wird empfohlen, anstelle von \lstinline{strcpy()}
+  grundsätzlich die Funktion \lstinline{strncpy()} zu verwenden.
+  Diese erwartet einen zusätzlichen Parameter,
+  der die maximal zulässige Länge des Strings enthält.
+  Ohne einen derartigen expliziten Parameter kann die Funktion nicht wissen,
+  wie lang die Variable ist, in der der String gespeichert werden soll.
+
+  \exercise{Hexdumps}
+
+  Das folgende Programm (\gitfile{hp}{2023ws/20231123}{aufgabe-4.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}{2023ws/20231123}{loesung-3.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/20231123/hp-uebung-20231123.pdf b/20231123/hp-uebung-20231123.pdf
new file mode 100644
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diff --git a/20231123/hp-uebung-20231123.tex b/20231123/hp-uebung-20231123.tex
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+% hp-uebung-20231123.pdf - Exercises on Low-Level Programming / Applied Computer Sciences
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020, 2021, 2022, 2023  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: Kondensator, Personen-Datenbank, Hexdumps
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gensymb}
+
+\newcommand{\ItwoC}{I\raisebox{0.5ex}{\footnotesize 2}C}
+\newcommand{\ITWOC}{I\raisebox{0.5ex}{\normalsize 2}C}
+
+\begin{document}
+
+  \thispagestyle{empty}
+
+  \section*{Hardwarenahe Programmierung\\
+            Übungsaufgaben -- 23.\ November 2023}
+
+  Diese Übung enthält Punkteangaben wie in einer Klausur.
+  Um zu "`bestehen"', müssen Sie innerhalb von 80 Minuten
+  unter Verwendung ausschließlich zugelassener Hilfsmittel
+  14 Punkte (von insgesamt \totalpoints) erreichen.
+
+  \exercise{Kondensator}
+
+  Ein Kondensator der Kapazität $C = 100\,\mu{\rm F}$
+  ist auf die Spannung $U_0 = 5\,{\rm V}$ aufgeladen
+  und wird über einen Widerstand $R = 33\,{\rm k}\Omega$ entladen.
+
+  \begin{enumerate}[(a)]
+    \item
+      Schreiben Sie ein C-Programm, das
+      den zeitlichen Spannungsverlauf in einer Tabelle darstellt.
+      \points{5}
+    \item
+      Schreiben Sie ein C-Programm, das ermittelt,
+      wie lange es dauert, bis die Spannung unter $0.1\,{\rm V}$ gefallen ist.
+      \points{4}
+    \item
+      Vergleichen Sie die berechneten Werte mit der exakten theoretischen Entladekurve:
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}\\
+      \points{3}
+  \end{enumerate}
+
+  Hinweise:
+  \begin{itemize}
+    \item
+      Für die Simulation zerlegen wir den Entladevorgang in kurze Zeitintervalle $dt$.
+      Innerhalb jedes Zeitintervalls betrachten wir den Strom $I$ als konstant
+      und berechnen, wieviel Ladung $Q$ innerhalb des Zeitintervalls
+      aus dem Kondensator herausfließt.
+      Aus der neuen Ladung berechnen wir die Spannung am Ende des Zeitintervalls.
+    \item
+      Für den Vergleich mit der exakten theoretischen Entladekurve
+      benötigen Sie die Exponentialfunktion \lstinline{exp()}.
+      Diese finden Sie in der Mathematik-Bibliothek:
+      \lstinline{#include <math.h>} im Quelltext,
+      beim \lstinline[style=cmd]{gcc}-Aufruf \lstinline[style=cmd]{-lm} mit angeben.
+    \item
+      $Q = C \cdot U$,\quad $U = R \cdot I$,\quad $I = \frac{dQ}{dt}$
+  \end{itemize}
+
+  \exercise{Personen-Datenbank}
+
+  Wir betrachten das folgende Programm (\gitfile{hp}{2023ws/20231123}{aufgabe-2.c}):
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <string.h>
+
+    typedef struct
+    {
+      char first_name[10];
+      char family_name[20];
+      char day, month;
+      int year;
+    } person;
+
+    int main (void)
+    {
+      person sls;
+      sls.day = 26;
+      sls.month = 7;
+      sls.year = 1951;
+      strcpy (sls.first_name, "Sabine");
+      strcpy (sls.family_name, "Leutheusser-Schnarrenberger");
+      printf ("%s %s wurde am %d.%d.%d geboren.\n",
+              sls.first_name, sls.family_name, sls.day, sls.month, sls.year);
+      return 0;
+    }
+  \end{lstlisting}
+
+  Die Standard-Funktion \lstinline{strcpy()} bewirkt ein Kopieren eines Strings
+  von rechts nach links, hier also z.\,B.\ die Zuweisung der String-Konstanten
+  \lstinline{"Sabine"} an die String-Variable \lstinline{sls.first_name[]}.
+
+  Das Programm wird für einen 32-Bit-Rechner compiliert und ausgeführt.\\
+  (Die \lstinline[style=cmd]{gcc}-Option \lstinline[style=cmd]{-m32} sorgt dafür,
+  daß \lstinline[style=cmd]{gcc} Code für einen 32-Bit-Prozessor erzeugt.)
+
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -Wall -O -m32 aufgabe-2.c -o aufgabe-2¿
+    $ ¡./aufgabe-2¿
+    Sabine Leutheusser-Schnarrenberger wurde am 110.98.1701278309 geboren.
+    Speicherzugriffsfehler
+  \end{lstlisting}
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Erklären Sie die Ausgabe des Programms einschließlich der Zahlenwerte.
+      \points{4}
+    \item
+      Welche Endianness hat der verwendete Rechner?
+      Begründen Sie Ihre Antwort.
+      \points{1}
+    \item
+      Wie sähe die Ausgabe auf einem Rechner mit entgegengesetzter Endianness aus?
+      \points{2}
+    \item
+      Erklären Sie den Speicherzugriffsfehler.
+      (Es kann sein, daß sich der Fehler auf Ihrem Rechner nicht bemerkbar macht.
+      Er ist aber trotzdem vorhanden.)
+      \points{2}
+  \end{enumerate}
+
+  \exercise{Hexdumps}
+
+  Das folgende Programm (\gitfile{hp}{2023ws/20231123}{aufgabe-4.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.
+
+  \begin{flushright}
+    \textit{Viel Erfolg!}
+  \end{flushright}
+
+  \makeatletter
+    \immediate\write\@mainaux{\string\gdef\string\totalpoints{\arabic{points}}}
+  \makeatother
+
+\end{document}
diff --git a/20231123/loesung-1a.c b/20231123/loesung-1a.c
new file mode 100644
index 0000000..f355706
--- /dev/null
+++ b/20231123/loesung-1a.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U > 0.09)
+    {
+      printf ("%10.3lf%15.8lf\n", t, U);
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  return 0;
+}
diff --git a/20231123/loesung-1b.c b/20231123/loesung-1b.c
new file mode 100644
index 0000000..f5fc220
--- /dev/null
+++ b/20231123/loesung-1b.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U >= 0.1)
+    {
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  printf ("%10.3lf%15.8lf\n", t, U);
+  return 0;
+}
diff --git a/20231123/loesung-1c.c b/20231123/loesung-1c.c
new file mode 100644
index 0000000..71802e0
--- /dev/null
+++ b/20231123/loesung-1c.c
@@ -0,0 +1,22 @@
+#include <stdio.h>
+#include <math.h>
+
+int main (void)
+{
+  double C = 0.0001;
+  double U0 = 5.0;
+  double U = U0;
+  double R = 33000.0;
+  double t = 0.0;
+  double dt = 0.01;
+  double Q = C * U;
+  while (U > 0.09)
+    {
+      printf ("%10.3lf%15.8lf%15.8lf\n", t, U, U0 * exp (-t / (R * C)));
+      double I = U / R;
+      Q -= I * dt;
+      U = Q / C;
+      t += dt;
+    }
+  return 0;
+}
diff --git a/20231123/loesung-1c.dat b/20231123/loesung-1c.dat
new file mode 100644
index 0000000..4df7062
--- /dev/null
+++ b/20231123/loesung-1c.dat
@@ -0,0 +1,1324 @@
+     0.000     5.00000000     5.00000000
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diff --git a/20231123/loesung-1c.tikz b/20231123/loesung-1c.tikz
new file mode 100644
index 0000000..e97073c
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+  --(3.441,3.638)--(3.449,3.629)--(3.457,3.620)--(3.465,3.610)--(3.472,3.601)--(3.480,3.592)%
+  --(3.488,3.584)--(3.496,3.574)--(3.504,3.565)--(3.511,3.556)--(3.519,3.547)--(3.527,3.539)%
+  --(3.535,3.529)--(3.543,3.520)--(3.550,3.512)--(3.558,3.503)--(3.566,3.494)--(3.574,3.486)%
+  --(3.582,3.477)--(3.590,3.469)--(3.597,3.460)--(3.605,3.450)--(3.613,3.442)--(3.621,3.433)%
+  --(3.629,3.425)--(3.636,3.416)--(3.644,3.408)--(3.652,3.401)--(3.660,3.391)--(3.668,3.383)%
+  --(3.675,3.374)--(3.683,3.366)--(3.691,3.359)--(3.699,3.349)--(3.707,3.342)--(3.715,3.334)%
+  --(3.722,3.324)--(3.730,3.317)--(3.738,3.309)--(3.746,3.300)--(3.754,3.292)--(3.761,3.284)%
+  --(3.769,3.276)--(3.777,3.269)--(3.785,3.259)--(3.793,3.251)--(3.800,3.244)--(3.808,3.236)%
+  --(3.816,3.228)--(3.824,3.220)--(3.832,3.213)--(3.839,3.205)--(3.847,3.197)--(3.855,3.189)%
+  --(3.863,3.182)--(3.871,3.174)--(3.879,3.166)--(3.886,3.158)--(3.894,3.150)--(3.902,3.143)%
+  --(3.910,3.135)--(3.918,3.127)--(3.925,3.119)--(3.933,3.112)--(3.941,3.104)--(3.949,3.096)%
+  --(3.957,3.088)--(3.964,3.082)--(3.972,3.074)--(3.980,3.067)--(3.988,3.059)--(3.996,3.051)%
+  --(4.004,3.045)--(4.011,3.037)--(4.019,3.029)--(4.027,3.023)--(4.035,3.015)--(4.043,3.008)%
+  --(4.050,3.001)--(4.058,2.994)--(4.066,2.986)--(4.074,2.980)--(4.082,2.972)--(4.089,2.964)%
+  --(4.097,2.958)--(4.105,2.950)--(4.113,2.944)--(4.121,2.936)--(4.128,2.930)--(4.136,2.922)%
+  --(4.144,2.916)--(4.152,2.908)--(4.160,2.902)--(4.168,2.894)--(4.175,2.888)--(4.183,2.880)%
+  --(4.191,2.874)--(4.199,2.866)--(4.207,2.860)--(4.214,2.854)--(4.222,2.846)--(4.230,2.840)%
+  --(4.238,2.834)--(4.246,2.826)--(4.253,2.820)--(4.261,2.813)--(4.269,2.806)--(4.277,2.800)%
+  --(4.285,2.793)--(4.293,2.787)--(4.300,2.779)--(4.308,2.773)--(4.316,2.767)--(4.324,2.761)%
+  --(4.332,2.754)--(4.339,2.747)--(4.347,2.741)--(4.355,2.734)--(4.363,2.728)--(4.371,2.722)%
+  --(4.378,2.716)--(4.386,2.709)--(4.394,2.703)--(4.402,2.695)--(4.410,2.689)--(4.417,2.683)%
+  --(4.425,2.677)--(4.433,2.671)--(4.441,2.664)--(4.449,2.658)--(4.457,2.652)--(4.464,2.646)%
+  --(4.472,2.640)--(4.480,2.633)--(4.488,2.629)--(4.496,2.622)--(4.503,2.616)--(4.511,2.610)%
+  --(4.519,2.604)--(4.527,2.598)--(4.535,2.591)--(4.542,2.585)--(4.550,2.579)--(4.558,2.574)%
+  --(4.566,2.568)--(4.574,2.562)--(4.581,2.556)--(4.589,2.549)--(4.597,2.545)--(4.605,2.539)%
+  --(4.613,2.532)--(4.621,2.526)--(4.628,2.522)--(4.636,2.515)--(4.644,2.509)--(4.652,2.504)%
+  --(4.660,2.498)--(4.667,2.492)--(4.675,2.487)--(4.683,2.481)--(4.691,2.475)--(4.699,2.470)%
+  --(4.706,2.464)--(4.714,2.458)--(4.722,2.453)--(4.730,2.447)--(4.738,2.442)--(4.746,2.436)%
+  --(4.753,2.430)--(4.761,2.425)--(4.769,2.419)--(4.777,2.414)--(4.785,2.408)--(4.792,2.404)%
+  --(4.800,2.397)--(4.808,2.393)--(4.816,2.386)--(4.824,2.382)--(4.831,2.377)--(4.839,2.371)%
+  --(4.847,2.366)--(4.855,2.360)--(4.863,2.355)--(4.870,2.349)--(4.878,2.344)--(4.886,2.340)%
+  --(4.894,2.334)--(4.902,2.329)--(4.910,2.324)--(4.917,2.318)--(4.925,2.313)--(4.933,2.309)%
+  --(4.941,2.303)--(4.949,2.298)--(4.956,2.293)--(4.964,2.289)--(4.972,2.282)--(4.980,2.278)%
+  --(4.988,2.273)--(4.995,2.268)--(5.003,2.262)--(5.011,2.258)--(5.019,2.253)--(5.027,2.248)%
+  --(5.035,2.244)--(5.042,2.237)--(5.050,2.233)--(5.058,2.228)--(5.066,2.223)--(5.074,2.219)%
+  --(5.081,2.214)--(5.089,2.209)--(5.097,2.203)--(5.105,2.199)--(5.113,2.194)--(5.120,2.189)%
+  --(5.128,2.185)--(5.136,2.180)--(5.144,2.175)--(5.152,2.171)--(5.159,2.166)--(5.167,2.161)%
+  --(5.175,2.157)--(5.183,2.152)--(5.191,2.147)--(5.199,2.143)--(5.206,2.138)--(5.214,2.133)%
+  --(5.222,2.129)--(5.230,2.124)--(5.238,2.119)--(5.245,2.115)--(5.253,2.110)--(5.261,2.105)%
+  --(5.269,2.101)--(5.277,2.096)--(5.284,2.093)--(5.292,2.088)--(5.300,2.084)--(5.308,2.079)%
+  --(5.316,2.074)--(5.324,2.070)--(5.331,2.065)--(5.339,2.062)--(5.347,2.057)--(5.355,2.053)%
+  --(5.363,2.048)--(5.370,2.043)--(5.378,2.040)--(5.386,2.035)--(5.394,2.031)--(5.402,2.026)%
+  --(5.409,2.023)--(5.417,2.018)--(5.425,2.014)--(5.433,2.009)--(5.441,2.006)--(5.448,2.001)%
+  --(5.456,1.997)--(5.464,1.994)--(5.472,1.989)--(5.480,1.984)--(5.488,1.980)--(5.495,1.976)%
+  --(5.503,1.972)--(5.511,1.969)--(5.519,1.964)--(5.527,1.959)--(5.534,1.956)--(5.542,1.952)%
+  --(5.550,1.947)--(5.558,1.944)--(5.566,1.939)--(5.573,1.936)--(5.581,1.931)--(5.589,1.927)%
+  --(5.597,1.924)--(5.605,1.919)--(5.613,1.916)--(5.620,1.911)--(5.628,1.908)--(5.636,1.903)%
+  --(5.644,1.900)--(5.652,1.896)--(5.659,1.893)--(5.667,1.888)--(5.675,1.885)--(5.683,1.880)%
+  --(5.691,1.877)--(5.698,1.872)--(5.706,1.869)--(5.714,1.865)--(5.722,1.862)--(5.730,1.858)%
+  --(5.737,1.854)--(5.745,1.851)--(5.753,1.846)--(5.761,1.843)--(5.769,1.840)--(5.777,1.835)%
+  --(5.784,1.832)--(5.792,1.827)--(5.800,1.824)--(5.808,1.821)--(5.816,1.816)--(5.823,1.813)%
+  --(5.831,1.810)--(5.839,1.806)--(5.847,1.802)--(5.855,1.799)--(5.862,1.795)--(5.870,1.792)%
+  --(5.878,1.789)--(5.886,1.785)--(5.894,1.781)--(5.902,1.778)--(5.909,1.775)--(5.917,1.770)%
+  --(5.925,1.767)--(5.933,1.764)--(5.941,1.761)--(5.948,1.756)--(5.956,1.753)--(5.964,1.750)%
+  --(5.972,1.747)--(5.980,1.743)--(5.987,1.739)--(5.995,1.736)--(6.003,1.733)--(6.011,1.730)%
+  --(6.019,1.726)--(6.026,1.723)--(6.034,1.719)--(6.042,1.716)--(6.050,1.712)--(6.058,1.709)%
+  --(6.066,1.706)--(6.073,1.703)--(6.081,1.700)--(6.089,1.695)--(6.097,1.692)--(6.105,1.689)%
+  --(6.112,1.686)--(6.120,1.683)--(6.128,1.680)--(6.136,1.677)--(6.144,1.674)--(6.151,1.670)%
+  --(6.159,1.667)--(6.167,1.664)--(6.175,1.661)--(6.183,1.658)--(6.191,1.655)--(6.198,1.650)%
+  --(6.206,1.647)--(6.214,1.644)--(6.222,1.641)--(6.230,1.638)--(6.237,1.635)--(6.245,1.632)%
+  --(6.253,1.629)--(6.261,1.625)--(6.269,1.624)--(6.276,1.621)--(6.284,1.618)--(6.292,1.615)%
+  --(6.300,1.611)--(6.308,1.608)--(6.315,1.605)--(6.323,1.602)--(6.331,1.599)--(6.339,1.596)%
+  --(6.347,1.593)--(6.355,1.590)--(6.362,1.587)--(6.370,1.584)--(6.378,1.582)--(6.386,1.579)%
+  --(6.394,1.576)--(6.401,1.573)--(6.409,1.570)--(6.417,1.566)--(6.425,1.563)--(6.433,1.560)%
+  --(6.440,1.559)--(6.448,1.556)--(6.456,1.552)--(6.464,1.549)--(6.472,1.546)--(6.480,1.545)%
+  --(6.487,1.542)--(6.495,1.538)--(6.503,1.535)--(6.511,1.532)--(6.519,1.531)--(6.526,1.528)%
+  --(6.534,1.525)--(6.542,1.521)--(6.550,1.518)--(6.558,1.517)--(6.565,1.514)--(6.573,1.511)%
+  --(6.581,1.507)--(6.589,1.506)--(6.597,1.503)--(6.604,1.500)--(6.612,1.497)--(6.620,1.495)%
+  --(6.628,1.492)--(6.636,1.489)--(6.644,1.487)--(6.651,1.484)--(6.659,1.481)--(6.667,1.479)%
+  --(6.675,1.476)--(6.683,1.473)--(6.690,1.470)--(6.698,1.469)--(6.706,1.465)--(6.714,1.464)%
+  --(6.722,1.461)--(6.729,1.458)--(6.737,1.456)--(6.745,1.453)--(6.753,1.450)--(6.761,1.448)%
+  --(6.768,1.445)--(6.776,1.442)--(6.784,1.441)--(6.792,1.438)--(6.800,1.436)--(6.808,1.433)%
+  --(6.815,1.430)--(6.823,1.428)--(6.831,1.425)--(6.839,1.424)--(6.847,1.420)--(6.854,1.419)%
+  --(6.862,1.416)--(6.870,1.413)--(6.878,1.411)--(6.886,1.408)--(6.893,1.406)--(6.901,1.403)%
+  --(6.909,1.402)--(6.917,1.399)--(6.925,1.397)--(6.933,1.394)--(6.940,1.393)--(6.948,1.389)%
+  --(6.956,1.388)--(6.964,1.385)--(6.972,1.383)--(6.979,1.380)--(6.987,1.379)--(6.995,1.375)%
+  --(7.003,1.374)--(7.011,1.371)--(7.018,1.369)--(7.026,1.366)--(7.034,1.365)--(7.042,1.361)%
+  --(7.050,1.360)--(7.057,1.357)--(7.065,1.355)--(7.073,1.352)--(7.081,1.351)--(7.089,1.349)%
+  --(7.097,1.346)--(7.104,1.344)--(7.112,1.341)--(7.120,1.340)--(7.128,1.337)--(7.136,1.335)%
+  --(7.143,1.333)--(7.151,1.330)--(7.159,1.329)--(7.167,1.326)--(7.175,1.324)--(7.182,1.323)%
+  --(7.190,1.320)--(7.198,1.318)--(7.206,1.316)--(7.214,1.313)--(7.222,1.312)--(7.229,1.309)%
+  --(7.237,1.307)--(7.245,1.306)--(7.253,1.302)--(7.261,1.301)--(7.268,1.299)--(7.276,1.296)%
+  --(7.284,1.295)--(7.292,1.293)--(7.300,1.290)--(7.307,1.288)--(7.315,1.287)--(7.323,1.285)%
+  --(7.331,1.282)--(7.339,1.281)--(7.346,1.279)--(7.354,1.276)--(7.362,1.274)--(7.370,1.273)%
+  --(7.378,1.270)--(7.386,1.268)--(7.393,1.267)--(7.401,1.265)--(7.409,1.262)--(7.417,1.260)%
+  --(7.425,1.259)--(7.432,1.257)--(7.440,1.254)--(7.448,1.253)--(7.456,1.251)--(7.464,1.250)%
+  --(7.471,1.247)--(7.479,1.245)--(7.487,1.243)--(7.495,1.242)--(7.503,1.239)--(7.511,1.237)%
+  --(7.518,1.236)--(7.526,1.234)--(7.534,1.233)--(7.542,1.229)--(7.550,1.228)--(7.557,1.226)%
+  --(7.565,1.225)--(7.573,1.223)--(7.581,1.220)--(7.589,1.219)--(7.596,1.217)--(7.604,1.215)%
+  --(7.612,1.214)--(7.620,1.212)--(7.628,1.209)--(7.635,1.208)--(7.643,1.206)--(7.651,1.205)%
+  --(7.659,1.203)--(7.667,1.201)--(7.675,1.200)--(7.682,1.197)--(7.690,1.195)--(7.698,1.194)%
+  --(7.706,1.192)--(7.714,1.191)--(7.721,1.189)--(7.729,1.188)--(7.737,1.186)--(7.745,1.183)%
+  --(7.753,1.181)--(7.760,1.180)--(7.768,1.178)--(7.776,1.177)--(7.784,1.175)--(7.792,1.174)%
+  --(7.800,1.172)--(7.807,1.170)--(7.815,1.169)--(7.823,1.167)--(7.831,1.164)--(7.839,1.163)%
+  --(7.846,1.161)--(7.854,1.160)--(7.862,1.158)--(7.870,1.156)--(7.878,1.155)--(7.885,1.153)%
+  --(7.893,1.152)--(7.901,1.150)--(7.909,1.149)--(7.917,1.147)--(7.924,1.146)--(7.932,1.144)%
+  --(7.940,1.142)--(7.948,1.141)--(7.956,1.139)--(7.964,1.138)--(7.971,1.136)--(7.979,1.135)%
+  --(7.987,1.133)--(7.995,1.132)--(8.003,1.130)--(8.010,1.128)--(8.018,1.127)--(8.026,1.125)%
+  --(8.034,1.124)--(8.042,1.122)--(8.049,1.121)--(8.057,1.119)--(8.065,1.118)--(8.073,1.116)%
+  --(8.081,1.115)--(8.089,1.113)--(8.096,1.111)--(8.104,1.110)--(8.112,1.108)--(8.120,1.107)%
+  --(8.128,1.105)--(8.135,1.104)--(8.143,1.102)--(8.151,1.101)--(8.159,1.099)--(8.167,1.097)%
+  --(8.174,1.096)--(8.182,1.094)--(8.190,1.093)--(8.198,1.091)--(8.206,1.091)--(8.213,1.090)%
+  --(8.221,1.088)--(8.229,1.087)--(8.237,1.085)--(8.245,1.083)--(8.253,1.082)--(8.260,1.080)%
+  --(8.268,1.079)--(8.276,1.077)--(8.284,1.076)--(8.292,1.074)--(8.299,1.074)--(8.307,1.073)%
+  --(8.315,1.071)--(8.323,1.069)--(8.331,1.068)--(8.338,1.066)--(8.346,1.065)--(8.354,1.063)%
+  --(8.362,1.063)--(8.370,1.062)--(8.378,1.060)--(8.385,1.059)--(8.393,1.057)--(8.401,1.055)%
+  --(8.409,1.054)--(8.417,1.052)--(8.424,1.052)--(8.432,1.051)--(8.440,1.049)--(8.448,1.048)%
+  --(8.456,1.046)--(8.463,1.045)--(8.471,1.045)--(8.479,1.043)--(8.487,1.042)--(8.495,1.040)%
+  --(8.502,1.038)--(8.510,1.037)--(8.518,1.037)--(8.526,1.035)--(8.534,1.034)--(8.542,1.032)%
+  --(8.549,1.031)--(8.557,1.031)--(8.565,1.029)--(8.573,1.028)--(8.581,1.026)--(8.588,1.024)%
+  --(8.596,1.024)--(8.604,1.023)--(8.612,1.021)--(8.620,1.020)--(8.627,1.018)--(8.635,1.018)%
+  --(8.643,1.017)--(8.651,1.015)--(8.659,1.014)--(8.667,1.012)--(8.674,1.012)--(8.682,1.010)%
+  --(8.690,1.009)--(8.698,1.007)--(8.706,1.007)--(8.713,1.006)--(8.721,1.004)--(8.729,1.003)%
+  --(8.737,1.003)--(8.745,1.001)--(8.752,1.000)--(8.760,0.998)--(8.768,0.998)--(8.776,0.996)%
+  --(8.784,0.995)--(8.791,0.993)--(8.799,0.993)--(8.807,0.992)--(8.815,0.990)--(8.823,0.989)%
+  --(8.831,0.989)--(8.838,0.987)--(8.846,0.986)--(8.854,0.984)--(8.862,0.984)--(8.870,0.983)%
+  --(8.877,0.981)--(8.885,0.981)--(8.893,0.979)--(8.901,0.978)--(8.909,0.978)--(8.916,0.976)%
+  --(8.924,0.975)--(8.932,0.973)--(8.940,0.973)--(8.948,0.972)--(8.955,0.970)--(8.963,0.970)%
+  --(8.971,0.969)--(8.979,0.967)--(8.987,0.967)--(8.995,0.965)--(9.002,0.964)--(9.010,0.964)%
+  --(9.018,0.962)--(9.026,0.961)--(9.034,0.959)--(9.041,0.959)--(9.049,0.958)--(9.057,0.956)%
+  --(9.065,0.956)--(9.073,0.955)--(9.080,0.953)--(9.088,0.953)--(9.096,0.951)--(9.104,0.951)%
+  --(9.112,0.950)--(9.120,0.948)--(9.127,0.948)--(9.135,0.947)--(9.143,0.945)--(9.151,0.945)%
+  --(9.159,0.944)--(9.166,0.942)--(9.174,0.942)--(9.182,0.941)--(9.190,0.939)--(9.198,0.939)%
+  --(9.205,0.937)--(9.213,0.937)--(9.221,0.936)--(9.229,0.934)--(9.237,0.934)--(9.244,0.933)%
+  --(9.252,0.931)--(9.260,0.931)--(9.268,0.930)--(9.276,0.930)--(9.284,0.928)--(9.291,0.927)%
+  --(9.299,0.927)--(9.307,0.925)--(9.315,0.925)--(9.323,0.923)--(9.330,0.922)--(9.338,0.922)%
+  --(9.346,0.920)--(9.354,0.920)--(9.362,0.919)--(9.369,0.917)--(9.377,0.917)--(9.385,0.916)%
+  --(9.393,0.916)--(9.401,0.914)--(9.409,0.913)--(9.416,0.913)--(9.424,0.911)--(9.432,0.911)%
+  --(9.440,0.910)--(9.448,0.910)--(9.455,0.908)--(9.463,0.906)--(9.471,0.906)--(9.479,0.905)%
+  --(9.487,0.905)--(9.494,0.903)--(9.502,0.903)--(9.510,0.902)--(9.518,0.900)--(9.526,0.900)%
+  --(9.533,0.899)--(9.541,0.899)--(9.549,0.897)--(9.557,0.897)--(9.565,0.896)--(9.573,0.896)%
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+  --(5.269,2.105)--(5.277,2.101)--(5.284,2.096)--(5.292,2.091)--(5.300,2.087)--(5.308,2.082)%
+  --(5.316,2.079)--(5.324,2.074)--(5.331,2.070)--(5.339,2.065)--(5.347,2.060)--(5.355,2.056)%
+  --(5.363,2.053)--(5.370,2.048)--(5.378,2.043)--(5.386,2.039)--(5.394,2.034)--(5.402,2.031)%
+  --(5.409,2.026)--(5.417,2.021)--(5.425,2.017)--(5.433,2.014)--(5.441,2.009)--(5.448,2.004)%
+  --(5.456,2.001)--(5.464,1.997)--(5.472,1.992)--(5.480,1.987)--(5.488,1.984)--(5.495,1.980)%
+  --(5.503,1.975)--(5.511,1.972)--(5.519,1.967)--(5.527,1.964)--(5.534,1.959)--(5.542,1.955)%
+  --(5.550,1.952)--(5.558,1.947)--(5.566,1.944)--(5.573,1.939)--(5.581,1.934)--(5.589,1.931)%
+  --(5.597,1.927)--(5.605,1.924)--(5.613,1.919)--(5.620,1.916)--(5.628,1.911)--(5.636,1.908)%
+  --(5.644,1.903)--(5.652,1.899)--(5.659,1.896)--(5.667,1.893)--(5.675,1.888)--(5.683,1.885)%
+  --(5.691,1.880)--(5.698,1.877)--(5.706,1.872)--(5.714,1.869)--(5.722,1.865)--(5.730,1.862)%
+  --(5.737,1.857)--(5.745,1.854)--(5.753,1.851)--(5.761,1.846)--(5.769,1.843)--(5.777,1.838)%
+  --(5.784,1.835)--(5.792,1.832)--(5.800,1.827)--(5.808,1.824)--(5.816,1.821)--(5.823,1.816)%
+  --(5.831,1.813)--(5.839,1.810)--(5.847,1.806)--(5.855,1.802)--(5.862,1.799)--(5.870,1.795)%
+  --(5.878,1.792)--(5.886,1.789)--(5.894,1.784)--(5.902,1.781)--(5.909,1.778)--(5.917,1.775)%
+  --(5.925,1.770)--(5.933,1.767)--(5.941,1.764)--(5.948,1.761)--(5.956,1.756)--(5.964,1.753)%
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+  --(6.019,1.730)--(6.026,1.726)--(6.034,1.722)--(6.042,1.719)--(6.050,1.716)--(6.058,1.712)%
+  --(6.066,1.709)--(6.073,1.706)--(6.081,1.703)--(6.089,1.698)--(6.097,1.695)--(6.105,1.692)%
+  --(6.112,1.689)--(6.120,1.686)--(6.128,1.683)--(6.136,1.680)--(6.144,1.677)--(6.151,1.674)%
+  --(6.159,1.670)--(6.167,1.667)--(6.175,1.664)--(6.183,1.661)--(6.191,1.658)--(6.198,1.655)%
+  --(6.206,1.652)--(6.214,1.647)--(6.222,1.644)--(6.230,1.641)--(6.237,1.638)--(6.245,1.635)%
+  --(6.253,1.632)--(6.261,1.630)--(6.269,1.627)--(6.276,1.624)--(6.284,1.621)--(6.292,1.618)%
+  --(6.300,1.615)--(6.308,1.611)--(6.315,1.608)--(6.323,1.605)--(6.331,1.602)--(6.339,1.599)%
+  --(6.347,1.596)--(6.355,1.593)--(6.362,1.590)--(6.370,1.587)--(6.378,1.585)--(6.386,1.582)%
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+  --(6.440,1.562)--(6.448,1.559)--(6.456,1.556)--(6.464,1.552)--(6.472,1.549)--(6.480,1.546)%
+  --(6.487,1.545)--(6.495,1.542)--(6.503,1.538)--(6.511,1.535)--(6.519,1.532)--(6.526,1.531)%
+  --(6.534,1.528)--(6.542,1.525)--(6.550,1.521)--(6.558,1.520)--(6.565,1.517)--(6.573,1.514)%
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+  --(6.628,1.495)--(6.636,1.492)--(6.644,1.489)--(6.651,1.487)--(6.659,1.484)--(6.667,1.481)%
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+  --(11.314,0.759)--(11.322,0.759)--(11.330,0.757)--(11.338,0.757)--(11.346,0.757);
+\gpcolor{color=gp lt color border}
+\draw[gp path] (1.012,8.381)--(1.012,0.616)--(11.947,0.616)--(11.947,8.381)--cycle;
+%% coordinates of the plot area
+\gpdefrectangularnode{gp plot 1}{\pgfpoint{1.012cm}{0.616cm}}{\pgfpoint{11.947cm}{8.381cm}}
+\end{tikzpicture}
+%% gnuplot variables
diff --git a/20231123/loesung-3.c b/20231123/loesung-3.c
new file mode 100644
index 0000000..872058a
--- /dev/null
+++ b/20231123/loesung-3.c
@@ -0,0 +1,28 @@
+#include <stdio.h>
+
+int read_hex (char c)
+{
+  if (c >= '0' && c <= '9')
+    return c - '0';
+  else if (c >= 'A' && c <= 'F')
+    return c - 'A' + 10;
+  else if (c >= 'a' && c <= 'f')
+    return c - 'a' + 10;
+  else
+    {
+      fprintf (stderr, "invalid hex digit '%c'\n", c);
+      return 0;
+    }
+}
+
+int main (void)
+{
+  char buffer[100];
+  fgets (buffer, 100, stdin);
+  for (char *p = buffer; p[0] && p[1]; p += 2)
+    {
+      char c = 16 * read_hex (p[0]) + read_hex (p[1]);
+      printf ("%c", c);
+    }
+  printf ("\n");
+}
diff --git a/20231123/logo-hochschule-bochum-cvh-text-v2.pdf b/20231123/logo-hochschule-bochum-cvh-text-v2.pdf
new file mode 120000
index 0000000..4aa99b8
--- /dev/null
+++ b/20231123/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/20231123/logo-hochschule-bochum.pdf b/20231123/logo-hochschule-bochum.pdf
new file mode 120000
index 0000000..b6b9491
--- /dev/null
+++ b/20231123/logo-hochschule-bochum.pdf
@@ -0,0 +1 @@
+../common/logo-hochschule-bochum.pdf
\ No newline at end of file
diff --git a/20231123/pendulum.pdf b/20231123/pendulum.pdf
new file mode 120000
index 0000000..7d1d873
--- /dev/null
+++ b/20231123/pendulum.pdf
@@ -0,0 +1 @@
+../common/pendulum.pdf
\ No newline at end of file
diff --git a/20231123/pgscript.sty b/20231123/pgscript.sty
new file mode 120000
index 0000000..95c8884
--- /dev/null
+++ b/20231123/pgscript.sty
@@ -0,0 +1 @@
+../common/pgscript.sty
\ No newline at end of file
diff --git a/20231123/pgslides.sty b/20231123/pgslides.sty
new file mode 120000
index 0000000..5be1416
--- /dev/null
+++ b/20231123/pgslides.sty
@@ -0,0 +1 @@
+../common/pgslides.sty
\ No newline at end of file
diff --git a/README.md b/README.md
index 492885f..e381558 100644
--- a/README.md
+++ b/README.md
@@ -23,7 +23,8 @@ Vortragsfolien und Beispiele:
  * [26.10.2023: Einführung in C: String-Operationen; Bibliotheken](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231026/hp-20231026.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231026/)
  * [02.11.2023: Bibliotheken](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231102/hp-20231102.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231102/)
  * [09.11.2023: Hardwarenahe Programmierung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-20231109.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231109/)
- * [16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen, Speicherausrichtung](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-20231116.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231116/)
+ * [16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-20231116.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231116/)
+ * [23.11.2023: Speicherausrichtung, Algorithmen: Differentialgleichungen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-20231123.pdf) [**(Beispiele)**](https://gitlab.cvh-server.de/pgerwinski/hp/tree/2023ws/20231123/)
  * [alle in 1 Datei](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/hp-slides-2023ws.pdf)
 
 Übungsaufgaben:
@@ -35,6 +36,7 @@ Vortragsfolien und Beispiele:
  * [02.11.2023: Zahlensysteme, Ausgabe von Hexadezimalzahlen, Einfügen in Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231102/hp-uebung-20231102.pdf)
  * [09.11.2023: Text-Grafik-Bibliothek, Mikrocontroller, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-uebung-20231109.pdf)
  * [16.11.2023: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, Speicherformate von Zahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-uebung-20231116.pdf)
+ * [23.11.2023: Kondensator, Personen-Datenbank, Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-uebung-20231123.pdf)
 
 Musterlösungen:
 ---------------
@@ -44,6 +46,7 @@ Musterlösungen:
  * [02.11.2023: Zahlensysteme, Ausgabe von Hexadezimalzahlen, Einfügen in Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231102/hp-musterloesung-20231102.pdf)
  * [09.11.2023: Text-Grafik-Bibliothek, Mikrocontroller, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231109/hp-musterloesung-20231109.pdf)
  * [16.11.2023: Trickprogrammierung, Thermometer-Baustein an I²C-Bus, Speicherformate von Zahlen](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231116/hp-musterloesung-20231116.pdf)
+ * [23.11.2023: Kondensator, Personen-Datenbank, Hexdumps](https://gitlab.cvh-server.de/pgerwinski/hp/raw/2023ws/20231123/hp-musterloesung-20231123.pdf)
 
 Praktikumsunterlagen:
 ---------------------
diff --git a/hp-slides-2023ws.pdf b/hp-slides-2023ws.pdf
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CAdIR2

diff --git a/hp-slides-2023ws.tex b/hp-slides-2023ws.tex
index f7cd9bd..f577a24 100644
--- a/hp-slides-2023ws.tex
+++ b/hp-slides-2023ws.tex
@@ -23,6 +23,8 @@
   \includepdf[pages=-]{20231102/hp-20231102.pdf}
   \pdfbookmark[1]{09.11.2023: Hardwarenahe Programmierung}{20231109}
   \includepdf[pages=-]{20231109/hp-20231109.pdf}
-  \pdfbookmark[1]{16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen, Speicherausrichtung}{20231116}
+  \pdfbookmark[1]{16.11.2023: Byte-Reihenfolge, Darstellung negativer Zahlen, Darstellung von Gleitkommazahlen}{20231116}
   \includepdf[pages=-]{20231116/hp-20231116.pdf}
+  \pdfbookmark[1]{23.11.2023: Speicherausrichtung}{20231123}
+  \includepdf[pages=-]{20231123/hp-20231123.pdf}
 \end{document}
-- 
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