From 783b0e9c746ddd2d50c5fb623885e126d788bc18 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Sat, 3 Oct 2020 21:02:14 +0200
Subject: [PATCH] =?UTF-8?q?Musterl=C3=B6sungen=2012.=20und=2019.12.2019?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 20191212/hp-musterloesung-20191212.pdf |  Bin 0 -> 177117 bytes
 20191212/hp-musterloesung-20191212.tex |  325 ++++++
 20191212/loesung-1a.c                  |   22 +
 20191212/loesung-1b.c                  |   22 +
 20191212/loesung-1c.c                  |   22 +
 20191212/loesung-1c.dat                | 1324 ++++++++++++++++++++++++
 20191212/loesung-1c.tikz               |  521 ++++++++++
 20191219/hp-musterloesung-20191219.pdf |  Bin 0 -> 75955 bytes
 20191219/hp-musterloesung-20191219.tex |  265 +++++
 20191219/loesung-1-1.c                 |   13 +
 20191219/loesung-1-2.c                 |   15 +
 20191219/loesung-1-3.c                 |   11 +
 20191219/loesung-2.c                   |   26 +
 README.md                              |    2 +
 14 files changed, 2568 insertions(+)
 create mode 100644 20191212/hp-musterloesung-20191212.pdf
 create mode 100644 20191212/hp-musterloesung-20191212.tex
 create mode 100644 20191212/loesung-1a.c
 create mode 100644 20191212/loesung-1b.c
 create mode 100644 20191212/loesung-1c.c
 create mode 100644 20191212/loesung-1c.dat
 create mode 100644 20191212/loesung-1c.tikz
 create mode 100644 20191219/hp-musterloesung-20191219.pdf
 create mode 100644 20191219/hp-musterloesung-20191219.tex
 create mode 100644 20191219/loesung-1-1.c
 create mode 100644 20191219/loesung-1-2.c
 create mode 100644 20191219/loesung-1-3.c
 create mode 100644 20191219/loesung-2.c

diff --git a/20191212/hp-musterloesung-20191212.pdf b/20191212/hp-musterloesung-20191212.pdf
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diff --git a/20191212/hp-musterloesung-20191212.tex b/20191212/hp-musterloesung-20191212.tex
new file mode 100644
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@@ -0,0 +1,325 @@
+% hp-musterloesung-20191212.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020  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, hüpfender Ball
+
+\documentclass[a4paper]{article}
+
+\usepackage{pgscript}
+\usepackage{gnuplot-lua-tikz}
+
+\begin{document}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 12.\ Dezember 2019}
+
+  \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}{20191212}{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}{20191212}{loesung-1a.c} so ab,
+      daß zum einen die Schleife abbricht, sobald die Spannung 
+      den Wert $0.1\,{\rm V}$ unterschreitet (\gitfile{hp}{20191212}{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:\\
+      \boldmath  
+      \begin{math}
+        U(t) = U_0 \cdot e^{-\frac{t}{RC}}
+      \end{math}}
+
+      Wir ändern das Programm \gitfile{hp}{20191212}{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}{20191212}{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{./loesung-1c > loesung-1c.dat},
+      in einer Datei \gitfile{hp}{20191212}{loesung-1c.dat} speichern,
+      können Sie sich die beiden Kurven graphisch darstellen lassen,
+      z.\,B.\ mit \file{gnuplot} und dem folgenden Befehl:\\
+      \lstinline[style=cmd]{plot "loesung-1c.dat" using 1:2 with lines title "Simulation",}\\
+      \lstinline[style=cmd]{     "loesung-1c.dat" using 1:3 with lines title "Theorie"}
+
+      \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}
+
+  \vfill
+
+  \exercise{Fehlerhaftes Programm: Hüpfender Ball}
+
+  Das auf der nächsten Seite abgedruckte GTK+-Programm
+  (Datei: \gitfile{hp}{20191212}{aufgabe-2.c}) soll einen
+  hüpfenden Ball darstellen, ist jedoch fehlerhaft.
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      Warum sieht man lediglich ein leeres Fenster?
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben?
+      \points{3}
+    \item
+      Nach der Fehlerbehebung in Aufgabenteil (a)
+      zeigt das Programm einen unbeweglichen Ball.
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben, und warum?
+      \points{2}
+    \item
+      Erklären Sie das merkwürdige Hüpfverhalten des Balls.
+      Wie kommt es zustande?
+      Was an diesem Verhalten ist korrekt, und was ist fehlerhaft? \points{5}
+    \item
+      Welche Befehle muß man in welcher Weise ändern,
+      um ein realistischeres Hüpf-Verhalten zu bekommen? \points{2}
+  \end{enumerate}
+
+  Hinweis: Das Hinzuziehen von Beispiel-Programmen aus der Vorlesung
+  ist ausdrücklich erlaubt -- auch in der Klausur.
+
+  Allgemeiner Hinweis:
+  Wenn Sie die Übungsaufgaben zu dieser Lehrveranstaltung
+  als PDF-Datei betrachten und darin auf die Dateinamen klicken,
+  können Sie die Beispiel-Programme direkt herunterladen.
+  Dadurch vermeiden Sie Übertragungsfehler.
+
+  \clearpage
+
+  \vbox to \textheight{\vspace*{-0.5cm}\begin{lstlisting}
+    #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;
+    }
+  \end{lstlisting}\vss}
+
+  \solution
+
+  \begin{enumerate}[\quad(a)]
+    \item
+      \textbf{Warum sieht man lediglich ein leeres Fenster?
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben?}
+
+      Die für das Zeichnen zuständige Callback-Funktion wurde zwar geschrieben,
+      aber nicht installiert.
+      Um dies zu beheben, ergänze man den folgenden Befehl im Hauptprogramm:
+
+      \lstinline{g_signal_connect (drawing_area, "draw", G_CALLBACK (draw), NULL);}
+
+      Dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20191205}{gtk-16.c}.
+
+    \item
+      \textbf{Nach der Fehlerbehebung in Aufgabenteil (a)
+      zeigt das Programm einen unbeweglichen Ball.
+      Welchen Befehl muß man ergänzen, um diesen Fehler zu beheben, und warum?}
+
+      Die Timer-Callback-Funktion wurde zwar geschrieben, aber nicht installiert.
+      Um dies zu beheben, ergänze man den folgenden Befehl im Hauptprogramm:
+
+      \lstinline{g_timeout_add (50, (GSourceFunc) timer, drawing_area);}
+
+      Auch dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20191205}{gtk-16.c}.
+
+    \item
+      \textbf{Erklären Sie das merkwürdige Hüpfverhalten des Balls.
+      Wie kommt es zustande?
+      Was an diesem Verhalten ist korrekt, und was ist fehlerhaft?}
+
+      Die Geschwindigkeit in $y$-Richtung wächst immer weiter.
+      Der Grund dafür ist, daß die $y$-Komponente der Geschwindigkeit
+      nicht auf physikalisch sinnvolle Weise berechnet wird.
+      In der dafür zuständigen Zeile
+      \lstinline{vy = 0.5 * g * (t * t);}
+      wird stattdessen der Weg in $y$-Richtung bei einer gleichmäßig
+      beschleunigten Bewegung berechnet und als Geschwindigkeit verwendet.
+
+    \item
+      \textbf{Welche Befehle muß man in welcher Weise ändern,
+      um ein realistischeres Hüpf-Verhalten zu bekommen?}
+
+      Da der Ball am Boden abprallen soll, ist es \emph{nicht\/} sinnvoll,
+      die $y$-Komponente der Geschwindigkeit über die bekannte physikalische
+      Formel $v_y = -g\cdot t$ für die Geschwindigkeit in einer
+      gleichmäßig beschleunigten Bewegung zu berechnen.
+
+      Stattdessen ist es sinnvoll, die \emph{Geschwindigkeitsänderung\/}
+      innerhalb des Zeitintervalls \lstinline{dt}
+      zur Geschwindigkeitskomponente zu addieren:
+      \lstinline{vy += g * dt;}
+
+      Auch dies erkennt man sehr schnell durch Vergleich mit dem Beispiel-Programm
+      \gitfile{hp}{20191205}{gtk-16.c}.
+  \end{enumerate}
+
+\end{document}
diff --git a/20191212/loesung-1a.c b/20191212/loesung-1a.c
new file mode 100644
index 0000000..f355706
--- /dev/null
+++ b/20191212/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/20191212/loesung-1b.c b/20191212/loesung-1b.c
new file mode 100644
index 0000000..f5fc220
--- /dev/null
+++ b/20191212/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/20191212/loesung-1c.c b/20191212/loesung-1c.c
new file mode 100644
index 0000000..71802e0
--- /dev/null
+++ b/20191212/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/20191212/loesung-1c.dat b/20191212/loesung-1c.dat
new file mode 100644
index 0000000..4df7062
--- /dev/null
+++ b/20191212/loesung-1c.dat
@@ -0,0 +1,1324 @@
+     0.000     5.00000000     5.00000000
+     0.010     4.98484848     4.98487142
+     0.020     4.96974288     4.96978861
+     0.030     4.95468306     4.95475144
+     0.040     4.93966887     4.93975977
+     0.050     4.92470017     4.92481346
+     0.060     4.90977684     4.90991237
+     0.070     4.89489873     4.89505637
+     0.080     4.88006570     4.88024532
+     0.090     4.86527762     4.86547908
+     0.100     4.85053436     4.85075752
+     0.110     4.83583577     4.83608050
+     0.120     4.82118172     4.82144789
+     0.130     4.80657208     4.80685956
+     0.140     4.79200671     4.79231537
+     0.150     4.77748548     4.77781518
+     0.160     4.76300825     4.76335887
+     0.170     4.74857489     4.74894630
+     0.180     4.73418527     4.73457733
+     0.190     4.71983925     4.72025184
+     0.200     4.70553671     4.70596970
+     0.210     4.69127751     4.69173077
+     0.220     4.67706151     4.67753493
+     0.230     4.66288860     4.66338203
+     0.240     4.64875864     4.64927196
+     0.250     4.63467149     4.63520458
+     0.260     4.62062703     4.62117977
+     0.270     4.60662513     4.60719739
+     0.280     4.59266566     4.59325732
+     0.290     4.57874849     4.57935942
+     0.300     4.56487349     4.56550358
+     0.310     4.55104054     4.55168966
+     0.320     4.53724951     4.53791754
+     0.330     4.52350027     4.52418709
+     0.340     4.50979269     4.51049818
+     0.350     4.49612666     4.49685070
+     0.360     4.48250203     4.48324450
+     0.370     4.46891869     4.46967948
+     0.380     4.45537651     4.45615549
+     0.390     4.44187537     4.44267243
+     0.400     4.42841514     4.42923016
+     0.410     4.41499570     4.41582857
+     0.420     4.40161693     4.40246753
+     0.430     4.38827870     4.38914691
+     0.440     4.37498088     4.37586660
+     0.450     4.36172336     4.36262646
+     0.460     4.34850602     4.34942639
+     0.470     4.33532873     4.33626626
+     0.480     4.32219137     4.32314595
+     0.490     4.30909382     4.31006534
+     0.500     4.29603596     4.29702430
+     0.510     4.28301767     4.28402273
+     0.520     4.27003883     4.27106049
+     0.530     4.25709932     4.25813747
+     0.540     4.24419901     4.24525356
+     0.550     4.23133781     4.23240862
+     0.560     4.21851557     4.21960256
+     0.570     4.20573219     4.20683524
+     0.580     4.19298755     4.19410655
+     0.590     4.18028152     4.18141637
+     0.600     4.16761400     4.16876459
+     0.610     4.15498487     4.15615109
+     0.620     4.14239401     4.14357576
+     0.630     4.12984130     4.13103847
+     0.640     4.11732663     4.11853912
+     0.650     4.10484988     4.10607759
+     0.660     4.09241094     4.09365377
+     0.670     4.08000970     4.08126753
+     0.680     4.06764603     4.06891877
+     0.690     4.05531983     4.05660738
+     0.700     4.04303098     4.04433324
+     0.710     4.03077937     4.03209623
+     0.720     4.01856489     4.01989625
+     0.730     4.00638742     4.00773319
+     0.740     3.99424685     3.99560692
+     0.750     3.98214307     3.98351735
+     0.760     3.97007597     3.97146436
+     0.770     3.95804544     3.95944783
+     0.780     3.94605136     3.94746767
+     0.790     3.93409363     3.93552375
+     0.800     3.92217214     3.92361597
+     0.810     3.91028677     3.91174422
+     0.820     3.89843741     3.89990839
+     0.830     3.88662397     3.88810838
+     0.840     3.87484632     3.87634406
+     0.850     3.86310436     3.86461535
+     0.860     3.85139798     3.85292212
+     0.870     3.83972708     3.84126427
+     0.880     3.82809154     3.82964169
+     0.890     3.81649127     3.81805428
+     0.900     3.80492614     3.80650193
+     0.910     3.79339606     3.79498454
+     0.920     3.78190092     3.78350199
+     0.930     3.77044062     3.77205419
+     0.940     3.75901504     3.76064102
+     0.950     3.74762408     3.74926239
+     0.960     3.73626765     3.73791819
+     0.970     3.72494562     3.72660831
+     0.980     3.71365791     3.71533265
+     0.990     3.70240440     3.70409110
+     1.000     3.69118499     3.69288357
+     1.010     3.67999958     3.68170996
+     1.020     3.66884807     3.67057015
+     1.030     3.65773035     3.65946404
+     1.040     3.64664632     3.64839154
+     1.050     3.63559587     3.63735255
+     1.060     3.62457892     3.62634695
+     1.070     3.61359534     3.61537465
+     1.080     3.60264506     3.60443555
+     1.090     3.59172795     3.59352955
+     1.100     3.58084393     3.58265655
+     1.110     3.56999288     3.57181645
+     1.120     3.55917472     3.56100915
+     1.130     3.54838934     3.55023454
+     1.140     3.53763665     3.53949254
+     1.150     3.52691654     3.52878304
+     1.160     3.51622891     3.51810594
+     1.170     3.50557367     3.50746115
+     1.180     3.49495072     3.49684857
+     1.190     3.48435996     3.48626810
+     1.200     3.47380130     3.47571964
+     1.210     3.46327463     3.46520310
+     1.220     3.45277985     3.45471838
+     1.230     3.44231689     3.44426538
+     1.240     3.43188562     3.43384401
+     1.250     3.42148597     3.42345417
+     1.260     3.41111783     3.41309577
+     1.270     3.40078111     3.40276871
+     1.280     3.39047571     3.39247290
+     1.290     3.38020154     3.38220824
+     1.300     3.36995851     3.37197464
+     1.310     3.35974651     3.36177200
+     1.320     3.34956546     3.35160023
+     1.330     3.33941526     3.34145924
+     1.340     3.32929582     3.33134893
+     1.350     3.31920705     3.32126921
+     1.360     3.30914885     3.31122000
+     1.370     3.29912112     3.30120118
+     1.380     3.28912378     3.29121269
+     1.390     3.27915674     3.28125441
+     1.400     3.26921990     3.27132626
+     1.410     3.25931318     3.26142816
+     1.420     3.24943647     3.25156000
+     1.430     3.23958969     3.24172171
+     1.440     3.22977276     3.23191317
+     1.450     3.21998557     3.22213432
+     1.460     3.21022803     3.21238506
+     1.470     3.20050007     3.20266529
+     1.480     3.19080158     3.19297494
+     1.490     3.18113249     3.18331390
+     1.500     3.17149269     3.17368209
+     1.510     3.16188211     3.16407943
+     1.520     3.15230065     3.15450583
+     1.530     3.14274822     3.14496119
+     1.540     3.13322474     3.13544543
+     1.550     3.12373012     3.12595846
+     1.560     3.11426427     3.11650019
+     1.570     3.10482711     3.10707055
+     1.580     3.09541854     3.09766944
+     1.590     3.08603849     3.08829677
+     1.600     3.07668685     3.07895246
+     1.610     3.06736356     3.06963642
+     1.620     3.05806852     3.06034857
+     1.630     3.04880164     3.05108882
+     1.640     3.03956285     3.04185710
+     1.650     3.03035206     3.03265330
+     1.660     3.02116917     3.02347735
+     1.670     3.01201411     3.01432917
+     1.680     3.00288680     3.00520866
+     1.690     2.99378714     2.99611575
+     1.700     2.98471506     2.98705036
+     1.710     2.97567047     2.97801239
+     1.720     2.96665328     2.96900177
+     1.730     2.95766343     2.96001841
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diff --git a/20191212/loesung-1c.tikz b/20191212/loesung-1c.tikz
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+  --(2.598,4.814)--(2.605,4.801)--(2.613,4.787)--(2.621,4.775)--(2.629,4.763)--(2.637,4.750)%
+  --(2.644,4.738)--(2.652,4.725)--(2.660,4.713)--(2.668,4.700)--(2.676,4.688)--(2.683,4.676)%
+  --(2.691,4.663)--(2.699,4.651)--(2.707,4.640)--(2.715,4.627)--(2.723,4.615)--(2.730,4.603)%
+  --(2.738,4.590)--(2.746,4.579)--(2.754,4.567)--(2.762,4.554)--(2.769,4.542)--(2.777,4.531)%
+  --(2.785,4.519)--(2.793,4.508)--(2.801,4.495)--(2.808,4.483)--(2.816,4.472)--(2.824,4.460)%
+  --(2.832,4.449)--(2.840,4.436)--(2.848,4.426)--(2.855,4.415)--(2.863,4.402)--(2.871,4.391)%
+  --(2.879,4.379)--(2.887,4.368)--(2.894,4.357)--(2.902,4.346)--(2.910,4.334)--(2.918,4.323)%
+  --(2.926,4.312)--(2.933,4.301)--(2.941,4.289)--(2.949,4.278)--(2.957,4.267)--(2.965,4.256)%
+  --(2.972,4.245)--(2.980,4.234)--(2.988,4.224)--(2.996,4.213)--(3.004,4.202)--(3.012,4.191)%
+  --(3.019,4.180)--(3.027,4.169)--(3.035,4.158)--(3.043,4.148)--(3.051,4.137)--(3.058,4.126)%
+  --(3.066,4.115)--(3.074,4.106)--(3.082,4.095)--(3.090,4.084)--(3.097,4.073)--(3.105,4.064)%
+  --(3.113,4.053)--(3.121,4.042)--(3.129,4.031)--(3.137,4.022)--(3.144,4.011)--(3.152,4.002)%
+  --(3.160,3.991)--(3.168,3.980)--(3.176,3.970)--(3.183,3.960)--(3.191,3.950)--(3.199,3.939)%
+  --(3.207,3.930)--(3.215,3.919)--(3.222,3.910)--(3.230,3.901)--(3.238,3.890)--(3.246,3.880)%
+  --(3.254,3.870)--(3.261,3.860)--(3.269,3.851)--(3.277,3.840)--(3.285,3.831)--(3.293,3.821)%
+  --(3.301,3.812)--(3.308,3.801)--(3.316,3.792)--(3.324,3.783)--(3.332,3.773)--(3.340,3.764)%
+  --(3.347,3.755)--(3.355,3.744)--(3.363,3.734)--(3.371,3.725)--(3.379,3.716)--(3.386,3.706)%
+  --(3.394,3.697)--(3.402,3.688)--(3.410,3.679)--(3.418,3.669)--(3.426,3.660)--(3.433,3.651)%
+  --(3.441,3.641)--(3.449,3.633)--(3.457,3.624)--(3.465,3.615)--(3.472,3.606)--(3.480,3.596)%
+  --(3.488,3.587)--(3.496,3.579)--(3.504,3.570)--(3.511,3.560)--(3.519,3.551)--(3.527,3.543)%
+  --(3.535,3.534)--(3.543,3.525)--(3.550,3.515)--(3.558,3.508)--(3.566,3.498)--(3.574,3.491)%
+  --(3.582,3.481)--(3.590,3.472)--(3.597,3.464)--(3.605,3.455)--(3.613,3.447)--(3.621,3.438)%
+  --(3.629,3.430)--(3.636,3.421)--(3.644,3.413)--(3.652,3.404)--(3.660,3.396)--(3.668,3.387)%
+  --(3.675,3.379)--(3.683,3.371)--(3.691,3.362)--(3.699,3.354)--(3.707,3.346)--(3.715,3.337)%
+  --(3.722,3.329)--(3.730,3.321)--(3.738,3.312)--(3.746,3.304)--(3.754,3.296)--(3.761,3.289)%
+  --(3.769,3.281)--(3.777,3.272)--(3.785,3.264)--(3.793,3.256)--(3.800,3.248)--(3.808,3.241)%
+  --(3.816,3.233)--(3.824,3.225)--(3.832,3.216)--(3.839,3.208)--(3.847,3.200)--(3.855,3.192)%
+  --(3.863,3.185)--(3.871,3.177)--(3.879,3.169)--(3.886,3.161)--(3.894,3.154)--(3.902,3.146)%
+  --(3.910,3.138)--(3.918,3.132)--(3.925,3.124)--(3.933,3.116)--(3.941,3.109)--(3.949,3.101)%
+  --(3.957,3.093)--(3.964,3.085)--(3.972,3.079)--(3.980,3.071)--(3.988,3.064)--(3.996,3.056)%
+  --(4.004,3.048)--(4.011,3.042)--(4.019,3.034)--(4.027,3.026)--(4.035,3.020)--(4.043,3.012)%
+  --(4.050,3.005)--(4.058,2.998)--(4.066,2.991)--(4.074,2.983)--(4.082,2.977)--(4.089,2.969)%
+  --(4.097,2.963)--(4.105,2.955)--(4.113,2.947)--(4.121,2.941)--(4.128,2.933)--(4.136,2.927)%
+  --(4.144,2.919)--(4.152,2.913)--(4.160,2.905)--(4.168,2.899)--(4.175,2.891)--(4.183,2.885)%
+  --(4.191,2.879)--(4.199,2.871)--(4.207,2.865)--(4.214,2.857)--(4.222,2.851)--(4.230,2.845)%
+  --(4.238,2.837)--(4.246,2.831)--(4.253,2.824)--(4.261,2.817)--(4.269,2.810)--(4.277,2.804)%
+  --(4.285,2.798)--(4.293,2.790)--(4.300,2.784)--(4.308,2.778)--(4.316,2.772)--(4.324,2.764)%
+  --(4.332,2.758)--(4.339,2.751)--(4.347,2.745)--(4.355,2.739)--(4.363,2.733)--(4.371,2.727)%
+  --(4.378,2.719)--(4.386,2.713)--(4.394,2.706)--(4.402,2.700)--(4.410,2.694)--(4.417,2.688)%
+  --(4.425,2.681)--(4.433,2.675)--(4.441,2.669)--(4.449,2.663)--(4.457,2.657)--(4.464,2.650)%
+  --(4.472,2.644)--(4.480,2.638)--(4.488,2.632)--(4.496,2.626)--(4.503,2.619)--(4.511,2.613)%
+  --(4.519,2.608)--(4.527,2.602)--(4.535,2.596)--(4.542,2.590)--(4.550,2.584)--(4.558,2.577)%
+  --(4.566,2.571)--(4.574,2.567)--(4.581,2.560)--(4.589,2.554)--(4.597,2.548)--(4.605,2.542)%
+  --(4.613,2.537)--(4.621,2.531)--(4.628,2.525)--(4.636,2.520)--(4.644,2.514)--(4.652,2.508)%
+  --(4.660,2.501)--(4.667,2.497)--(4.675,2.490)--(4.683,2.484)--(4.691,2.480)--(4.699,2.473)%
+  --(4.706,2.469)--(4.714,2.463)--(4.722,2.456)--(4.730,2.452)--(4.738,2.445)--(4.746,2.441)%
+  --(4.753,2.435)--(4.761,2.430)--(4.769,2.424)--(4.777,2.417)--(4.785,2.413)--(4.792,2.407)%
+  --(4.800,2.402)--(4.808,2.396)--(4.816,2.391)--(4.824,2.386)--(4.831,2.380)--(4.839,2.376)%
+  --(4.847,2.369)--(4.855,2.365)--(4.863,2.358)--(4.870,2.354)--(4.878,2.349)--(4.886,2.343)%
+  --(4.894,2.338)--(4.902,2.334)--(4.910,2.327)--(4.917,2.323)--(4.925,2.318)--(4.933,2.312)%
+  --(4.941,2.307)--(4.949,2.303)--(4.956,2.296)--(4.964,2.292)--(4.972,2.287)--(4.980,2.282)%
+  --(4.988,2.276)--(4.995,2.271)--(5.003,2.267)--(5.011,2.262)--(5.019,2.256)--(5.027,2.251)%
+  --(5.035,2.247)--(5.042,2.242)--(5.050,2.237)--(5.058,2.233)--(5.066,2.226)--(5.074,2.222)%
+  --(5.081,2.217)--(5.089,2.212)--(5.097,2.208)--(5.105,2.203)--(5.113,2.199)--(5.120,2.194)%
+  --(5.128,2.189)--(5.136,2.183)--(5.144,2.178)--(5.152,2.174)--(5.159,2.169)--(5.167,2.164)%
+  --(5.175,2.160)--(5.183,2.155)--(5.191,2.150)--(5.199,2.146)--(5.206,2.141)--(5.214,2.136)%
+  --(5.222,2.132)--(5.230,2.127)--(5.238,2.122)--(5.245,2.119)--(5.253,2.115)--(5.261,2.110)%
+  --(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)%
+  --(5.972,1.750)--(5.980,1.747)--(5.987,1.743)--(5.995,1.739)--(6.003,1.736)--(6.011,1.733)%
+  --(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)%
+  --(6.394,1.579)--(6.401,1.576)--(6.409,1.573)--(6.417,1.570)--(6.425,1.566)--(6.433,1.563)%
+  --(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)%
+  --(6.581,1.511)--(6.589,1.509)--(6.597,1.506)--(6.604,1.503)--(6.612,1.500)--(6.620,1.498)%
+  --(6.628,1.495)--(6.636,1.492)--(6.644,1.489)--(6.651,1.487)--(6.659,1.484)--(6.667,1.481)%
+  --(6.675,1.479)--(6.683,1.476)--(6.690,1.473)--(6.698,1.472)--(6.706,1.469)--(6.714,1.465)%
+  --(6.722,1.464)--(6.729,1.461)--(6.737,1.458)--(6.745,1.456)--(6.753,1.453)--(6.761,1.450)%
+  --(6.768,1.448)--(6.776,1.445)--(6.784,1.444)--(6.792,1.441)--(6.800,1.438)--(6.808,1.436)%
+  --(6.815,1.433)--(6.823,1.431)--(6.831,1.428)--(6.839,1.425)--(6.847,1.424)--(6.854,1.420)%
+  --(6.862,1.419)--(6.870,1.416)--(6.878,1.414)--(6.886,1.411)--(6.893,1.408)--(6.901,1.406)%
+  --(6.909,1.403)--(6.917,1.402)--(6.925,1.399)--(6.933,1.397)--(6.940,1.394)--(6.948,1.393)%
+  --(6.956,1.389)--(6.964,1.388)--(6.972,1.385)--(6.979,1.383)--(6.987,1.380)--(6.995,1.379)%
+  --(7.003,1.375)--(7.011,1.374)--(7.018,1.371)--(7.026,1.369)--(7.034,1.366)--(7.042,1.365)%
+  --(7.050,1.361)--(7.057,1.360)--(7.065,1.358)--(7.073,1.355)--(7.081,1.354)--(7.089,1.351)%
+  --(7.097,1.349)--(7.104,1.346)--(7.112,1.344)--(7.120,1.343)--(7.128,1.340)--(7.136,1.338)%
+  --(7.143,1.335)--(7.151,1.333)--(7.159,1.332)--(7.167,1.329)--(7.175,1.327)--(7.182,1.324)%
+  --(7.190,1.323)--(7.198,1.321)--(7.206,1.318)--(7.214,1.316)--(7.222,1.313)--(7.229,1.312)%
+  --(7.237,1.310)--(7.245,1.307)--(7.253,1.306)--(7.261,1.304)--(7.268,1.301)--(7.276,1.299)%
+  --(7.284,1.298)--(7.292,1.295)--(7.300,1.293)--(7.307,1.292)--(7.315,1.288)--(7.323,1.287)%
+  --(7.331,1.285)--(7.339,1.284)--(7.346,1.281)--(7.354,1.279)--(7.362,1.278)--(7.370,1.274)%
+  --(7.378,1.273)--(7.386,1.271)--(7.393,1.268)--(7.401,1.267)--(7.409,1.265)--(7.417,1.264)%
+  --(7.425,1.260)--(7.432,1.259)--(7.440,1.257)--(7.448,1.256)--(7.456,1.253)--(7.464,1.251)%
+  --(7.471,1.250)--(7.479,1.248)--(7.487,1.245)--(7.495,1.243)--(7.503,1.242)--(7.511,1.240)%
+  --(7.518,1.239)--(7.526,1.236)--(7.534,1.234)--(7.542,1.233)--(7.550,1.231)--(7.557,1.229)%
+  --(7.565,1.226)--(7.573,1.225)--(7.581,1.223)--(7.589,1.222)--(7.596,1.220)--(7.604,1.217)%
+  --(7.612,1.215)--(7.620,1.214)--(7.628,1.212)--(7.635,1.211)--(7.643,1.209)--(7.651,1.206)%
+  --(7.659,1.205)--(7.667,1.203)--(7.675,1.201)--(7.682,1.200)--(7.690,1.198)--(7.698,1.197)%
+  --(7.706,1.194)--(7.714,1.192)--(7.721,1.191)--(7.729,1.189)--(7.737,1.188)--(7.745,1.186)%
+  --(7.753,1.184)--(7.760,1.183)--(7.768,1.181)--(7.776,1.178)--(7.784,1.177)--(7.792,1.175)%
+  --(7.800,1.174)--(7.807,1.172)--(7.815,1.170)--(7.823,1.169)--(7.831,1.167)--(7.839,1.166)%
+  --(7.846,1.164)--(7.854,1.163)--(7.862,1.161)--(7.870,1.160)--(7.878,1.156)--(7.885,1.155)%
+  --(7.893,1.153)--(7.901,1.152)--(7.909,1.150)--(7.917,1.149)--(7.924,1.147)--(7.932,1.146)%
+  --(7.940,1.144)--(7.948,1.142)--(7.956,1.141)--(7.964,1.139)--(7.971,1.138)--(7.979,1.136)%
+  --(7.987,1.135)--(7.995,1.133)--(8.003,1.132)--(8.010,1.130)--(8.018,1.128)--(8.026,1.127)%
+  --(8.034,1.125)--(8.042,1.124)--(8.049,1.122)--(8.057,1.121)--(8.065,1.119)--(8.073,1.118)%
+  --(8.081,1.116)--(8.089,1.115)--(8.096,1.113)--(8.104,1.111)--(8.112,1.110)--(8.120,1.108)%
+  --(8.128,1.107)--(8.135,1.105)--(8.143,1.104)--(8.151,1.102)--(8.159,1.101)--(8.167,1.101)%
+  --(8.174,1.099)--(8.182,1.097)--(8.190,1.096)--(8.198,1.094)--(8.206,1.093)--(8.213,1.091)%
+  --(8.221,1.090)--(8.229,1.088)--(8.237,1.087)--(8.245,1.085)--(8.253,1.083)--(8.260,1.082)%
+  --(8.268,1.080)--(8.276,1.080)--(8.284,1.079)--(8.292,1.077)--(8.299,1.076)--(8.307,1.074)%
+  --(8.315,1.073)--(8.323,1.071)--(8.331,1.069)--(8.338,1.068)--(8.346,1.068)--(8.354,1.066)%
+  --(8.362,1.065)--(8.370,1.063)--(8.378,1.062)--(8.385,1.060)--(8.393,1.059)--(8.401,1.057)%
+  --(8.409,1.057)--(8.417,1.055)--(8.424,1.054)--(8.432,1.052)--(8.440,1.051)--(8.448,1.049)%
+  --(8.456,1.048)--(8.463,1.048)--(8.471,1.046)--(8.479,1.045)--(8.487,1.043)--(8.495,1.042)%
+  --(8.502,1.040)--(8.510,1.040)--(8.518,1.038)--(8.526,1.037)--(8.534,1.035)--(8.542,1.034)%
+  --(8.549,1.034)--(8.557,1.032)--(8.565,1.031)--(8.573,1.029)--(8.581,1.028)--(8.588,1.026)%
+  --(8.596,1.026)--(8.604,1.024)--(8.612,1.023)--(8.620,1.021)--(8.627,1.021)--(8.635,1.020)%
+  --(8.643,1.018)--(8.651,1.017)--(8.659,1.015)--(8.667,1.015)--(8.674,1.014)--(8.682,1.012)%
+  --(8.690,1.010)--(8.698,1.010)--(8.706,1.009)--(8.713,1.007)--(8.721,1.006)--(8.729,1.004)%
+  --(8.737,1.004)--(8.745,1.003)--(8.752,1.001)--(8.760,1.000)--(8.768,1.000)--(8.776,0.998)%
+  --(8.784,0.996)--(8.791,0.995)--(8.799,0.995)--(8.807,0.993)--(8.815,0.992)--(8.823,0.992)%
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+%% 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/20191219/hp-musterloesung-20191219.pdf b/20191219/hp-musterloesung-20191219.pdf
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diff --git a/20191219/hp-musterloesung-20191219.tex b/20191219/hp-musterloesung-20191219.tex
new file mode 100644
index 0000000..1f82cc4
--- /dev/null
+++ b/20191219/hp-musterloesung-20191219.tex
@@ -0,0 +1,265 @@
+% hp-musterloesung-20191219.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019, 2020  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: Trickprogrammierung, Thermometer-Baustein an I²C-Bus
+
+\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}
+
+  \section*{Hardwarenahe Programmierung\\
+            Musterlösung zu den Übungsaufgaben -- 19.\ Dezember 2019}
+
+  \exercise{Trickprogrammierung}
+
+  Wir betrachten das folgende Programm (Datei: \gitfile{hp}{20191219}{aufgabe-1.c}):
+  \begin{lstlisting}
+    #include <stdio.h>
+    #include <stdint.h>
+
+    int main (void)
+    {
+      uint64_t x = 4262939000843297096;
+      char *s = &x;
+      printf ("%s\n", s);
+      return 0;
+    }
+  \end{lstlisting}
+  Das Programm wird compiliert und auf einem 64-Bit-Little-Endian-Computer ausgeführt:
+  \begin{lstlisting}[style=terminal]
+    $ ¡gcc -Wall -O aufgabe-1.c -o aufgabe-1¿
+    aufgabe-1.c: In function `main':
+    aufgabe-1.c:7:13: warning: initialization from incompatible pointer type [...]
+    $ ¡./aufgabe-1¿
+    Hallo
+  \end{lstlisting}
+
+  \begin{itemize}
+    \item[(a)]
+      Erklären Sie die Warnung beim Compilieren. \points{2}
+    \item[(b)]
+      Erklären Sie die Ausgabe des Programms. \points{5}
+    \item[(c)]
+      Wie würde die Ausgabe des Programms auf einem 64-Bit-Big-Endian-Computer lauten? \points{3}
+  \end{itemize}
+  Hinweis: Modifizieren Sie das Programm
+  und lassen Sie sich Speicherinhalte ausgeben.
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Erklären Sie die Warnung beim Compilieren.}
+
+      Zeile 7 des Programms enthält eine Zuweisung von \lstinline{&x}
+      an die Variable \lstinline{s}.
+      Der Ausdruck \lstinline{&x} steht für die Speicheradresse der Variablen \lstinline{x},
+      ist also ein Zeiger auf \lstinline{x},
+      also ein Zeiger auf eine \lstinline{uint64_t}.
+      Die Variable \lstinline{s} hingegen ist ein Zeiger auf \lstinline{char},
+      also ein Zeiger auf eine viel kleinere Zahl,
+      also ein anderer Zeigertyp.
+
+    \item[(b)]
+      \textbf{Erklären Sie die Ausgabe des Programms.}
+
+      Die 64-Bit-Zahl (\lstinline{uint64_t}) \lstinline{x}
+      belegt 8 Speicherzellen (Bytes) von jeweils 8 Bit.
+      Um herauszufinden, was diese enthalten,
+      lassen wir uns \lstinline{x} als Hexadezimalzahl ausgeben,
+      z.\,B.\ mittels \lstinline{printf ("%lx\n", x)}
+      (auf 32-Bit-Rechnern: \lstinline{"%llx\n"})
+      oder mittels \lstinline{printf ("%" PRIx64 "\n", x)}
+      (erfordert \lstinline{#include <inttypes.h>}
+      -- siehe die Datei \gitfile{hp}{20191219}{loesung-1-1.c}).
+      Das Ergebnis lautet:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        3b29006f6c6c6148
+      \end{lstlisting}
+      Auf einzelne Bytes verteilt:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        3b 29 00 6f 6c 6c 61 48
+      \end{lstlisting}
+      Auf einem Little-Endian-Rechner
+      ist die Reihenfolge der Bytes in den Speicherzellen genau umgekehrt:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        48 61 6c 6c 6f 00 29 3b
+      \end{lstlisting}
+      Wenn wir uns diese Bytes als Zeichen ausgeben lassen
+      (\lstinline{printf()} mit \lstinline{%c} -- siehe die Datei \gitfile{hp}{20191219}{loesung-1-2.c}),
+      erhalten wir:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        H a l l o  ) ;
+      \end{lstlisting}
+      Das Zeichen hinter "`Hallo"' ist ein Null-Symbol (Zahlenwert 0)
+      und wird von \lstinline{printf ("%s")} als Ende des Strings erkannt.
+      Damit ist die Ausgabe \lstinline[style=terminal]{Hallo}
+      des Programms erklärt.
+
+    \goodbreak
+    \item[(c)]
+      \textbf{Wie würde die Ausgabe des Programms auf einem 64-Bit-Big-Endian-Computer lauten?}
+
+      Auf einem Big-Endian-Computer (egal, wieviele Bits die Prozessorregister haben)
+      ist die Reihenfolge der Bytes in den Speicherzellen genau umgekehrt
+      wie auf einem Little-Endian-Computer, hier also:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        3b 29 00 6f 6c 6c 61 48
+      \end{lstlisting}
+      \lstinline{printf ("%s")} gibt in diesem Fall die Hexadezimalzahlen
+      \lstinline[style=terminal]{3b} und \lstinline[style=terminal]{29}
+      als Zeichen aus. Danach steht das String-Ende-Symbol mit Zahlenwert 0,
+      und die Ausgabe bricht ab.
+      Da, wie oben ermittelt, die Hexadezimalzahl \lstinline[style=terminal]{3b}
+      für das Zeichen \lstinline[style=terminal]{;}
+      und \lstinline[style=terminal]{29}
+      für das Zeichen \lstinline[style=terminal]{)} steht,
+      lautet somit die Ausgabe:
+      \begin{lstlisting}[style=terminal,gobble=8]
+        ;)
+      \end{lstlisting}
+      Um die Aufgabe zu lösen, können Sie übrigens auch
+      auf einem Little-Endian-Computer (Standard-Notebook)
+      einen Big-Endian-Computer simulieren,
+      indem Sie die Reihenfolge der Bytes in der Zahl \lstinline{x} umdrehen
+      -- siehe die Datei \gitfile{hp}{20191219}{loesung-1-3.c}.
+  \end{itemize}
+
+  \exercise{Thermometer-Baustein an \ITWOC-Bus}
+
+  Eine Firma stellt einen elektronischen Thermometer-Baustein her,
+  den man über die serielle Schnittstelle (RS-232) an einen PC anschließen kann,
+  um die Temperatur auszulesen.
+  Nun wird eine Variante des Thermo"-meter-Bausteins entwickelt,
+  die die Temperatur zusätzlich über einen \ItwoC-Bus bereitstellt.
+
+  Um das neue Thermometer zu testen, wird es in ein Gefäß mit heißem Wasser gelegt,
+  das langsam auf Zimmertemperatur abkühlt.
+  Alle 10 Minuten liest ein Programm, das auf dem PC läuft,
+  die gemessene Temperatur über beide Schnittstellen aus
+  und erzeugt daraus die folgende Tabelle:
+
+  \begin{center}
+    \renewcommand{\arraystretch}{1.2}
+    \begin{tabular}{|c|c|c|}\hline
+      Zeit /\,min. & Temperatur per RS-232 /\,\degree C & Temperatur per \ItwoC\ /\,\degree C \\\hline\hline
+      \phantom{0}0 & 94 & 122 \\\hline
+      10 & 47 & 244 \\\hline
+      20 & 30 & 120 \\\hline
+      30 & 24 & \phantom{0}24 \\\hline
+      40 & 21 & 168 \\\hline
+    \end{tabular}
+  \end{center}
+
+  \begin{itemize}
+    \item[(a)]
+      Aus dem Vergleich der Meßdaten läßt sich
+      auf einen Fehler bei der \ItwoC-Übertragung schließen.\\
+      Um welchen Fehler handelt es sich,
+      und wie ergibt sich dies aus den Meßdaten?
+      \points{5}
+    \item[(b)]
+      Schreiben Sie eine C-Funktion \lstinline{uint8_t repair (uint8_t data)},
+      die eine über den \ItwoC-Bus empfangene fehlerhafte Temperatur \lstinline{data} korrigiert.
+      \points{5}
+  \end{itemize}
+
+  \solution
+
+  \begin{itemize}
+    \item[(a)]
+      \textbf{Aus dem Vergleich der Meßdaten läßt sich
+      auf einen Fehler bei der \ItwoC-Übertragung schließen.
+      Um welchen Fehler handelt es sich,
+      und wie ergibt sich dies aus den Meßdaten?}
+
+      Sowohl RS-232 als auch \ItwoC\ übertragen die Daten Bit für Bit.
+      Für die Fehlersuche ist es daher sinnvoll,
+      die Meßwerte als Binärzahlen zu betrachten:
+
+      \begin{center}
+        \renewcommand{\arraystretch}{1.2}
+        \begin{tabular}{|c|c|c|}\hline
+          Zeit /\,min. & Temperatur per RS-232 /\,\degree C & Temperatur per \ItwoC\ /\,\degree C \\\hline\hline
+          \phantom{0}0 & 94$_{10}$ = 01011110$_2$ & 122$_{10}$           = 01111010$_2$ \\\hline
+          10           & 47$_{10}$ = 00101111$_2$ & 244$_{10}$           = 11110100$_2$ \\\hline
+          20           & 30$_{10}$ = 00011110$_2$ & 120$_{10}$           = 01111000$_2$ \\\hline
+          30           & 24$_{10}$ = 00011000$_2$ & \phantom{0}24$_{10}$ = 00011000$_2$ \\\hline
+          40           & 21$_{10}$ = 00010101$_2$ & 168$_{10}$           = 10101000$_2$ \\\hline
+        \end{tabular}
+      \end{center}
+
+      Man erkennt, daß die Reihenfolge der Bits in den (fehlerhaften) \ItwoC-Meßwerten
+      genau die umgekehrte Reihenfolge der Bits in den (korrekten) RS-232-Mewßwerten ist.
+      Der Übertragungsfehler besteht also darin,
+      daß die Bits in der falschen Reihenfolge übertragen wurden.
+
+      Dies paßt gut damit zusammen,
+      daß die Bit-Reihenfolge von \ItwoC\ \emph{MSB First}, die von RS-232 hingegen \emph{LSB First\/} ist.
+      Offenbar haben die Entwickler der \ItwoC-Schnittstelle dies übersehen
+      und die \ItwoC-Daten ebenfalls \emph{LSB First\/} übertragen.
+
+    \goodbreak
+    \item[(b)]
+      \textbf{Schreiben Sie eine C-Funktion \lstinline{uint8_t repair (uint8_t data)},
+      die eine über den \ItwoC-Bus empfangene fehlerhafte Temperatur \lstinline{data} korrigiert.}
+
+      Die Aufgabe der Funktion besteht darin,
+      eine 8-Bit-Zahl \lstinline{data} entgegenzunehmen,
+      die Reihenfolge der 8 Bits genau umzudrehen
+      und das Ergebnis mittels \lstinline{return} zurückzugeben.
+
+      Zu diesem Zweck gehen wir die 8 Bits in einer Schleife durch
+      -- siehe die Datei \gitfile{hp}{20191219}{loesung-2.c}.
+      Wir lassen eine Lese-Maske \lstinline{mask_data} von rechts nach links
+      und gleichzeitig eine Schreib-Maske \lstinline{mask_result}
+      von links nach rechts wandern.
+      Immer wenn die Lese-Maske in \lstinline{data} eine 1 findet,
+      schreibt die Schreib-Maske diese in die Ergebnisvariable \lstinline{result}.
+
+      Da \lstinline{result} auf 0 initialisiert wurde,
+      brauchen wir Nullen nicht hineinzuschreiben.
+      Ansonsten wäre dies mit \lstinline{result &= ~mask_result} möglich.
+
+      Um die Schleife bis 8 zählen zu lassen,
+      könnte man eine weitere Zähler-Variable von 0 bis 7 zählen lassen,
+      z.\,B.\ \lstinline{for (int i = 0; i < 8; i++)}.
+      Dies ist jedoch nicht nötig, wenn man beachtet,
+      daß die Masken den Wert 0 annehmen,
+      sobald das Bit aus der 8-Bit-Variablen herausgeschoben wurde.
+      In \gitfile{hp}{20191219}{loesung-2.c} wird \lstinline{mask_data} auf 0 geprüft;
+      genausogut könnte man auch \lstinline{mask_result} prüfen.
+
+      Das \lstinline{return result} ist notwendig.
+      Eine Ausgabe des Ergebnisses per \lstinline{printf()} o.\,ä.\
+      erfüllt \emph{nicht\/} die Aufgabenstellung.
+      (In \gitfile{hp}{20191219}{loesung-2.c} erfolgt entsprechend \lstinline{printf()}
+      nur im Testprogramm \lstinline{main()}.)
+  \end{itemize}
+
+\end{document}
diff --git a/20191219/loesung-1-1.c b/20191219/loesung-1-1.c
new file mode 100644
index 0000000..26fcc81
--- /dev/null
+++ b/20191219/loesung-1-1.c
@@ -0,0 +1,13 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+
+int main (void)
+{
+  uint64_t x = 4262939000843297096;
+  char *s = &x;
+  printf ("%lx\n", x);
+  printf ("%" PRIx64 "\n", x);
+  printf ("%s\n", s);
+  return 0;
+}
diff --git a/20191219/loesung-1-2.c b/20191219/loesung-1-2.c
new file mode 100644
index 0000000..7151db6
--- /dev/null
+++ b/20191219/loesung-1-2.c
@@ -0,0 +1,15 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+
+int main (void)
+{
+  uint64_t x = 4262939000843297096;
+  char *s = &x;
+  printf ("%lx\n", x);
+  printf ("%" PRIx64 "\n", x);
+  printf ("%c %c %c %c %c %c %c %c\n",
+          0x48, 0x61, 0x6c, 0x6c, 0x6f, 0x00, 0x29, 0x3b);
+  printf ("%s\n", s);
+  return 0;
+}
diff --git a/20191219/loesung-1-3.c b/20191219/loesung-1-3.c
new file mode 100644
index 0000000..fadccde
--- /dev/null
+++ b/20191219/loesung-1-3.c
@@ -0,0 +1,11 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+
+int main (void)
+{
+  uint64_t x = 0x48616c6c6f00293b;
+  char *s = &x;
+  printf ("%s\n", s);
+  return 0;
+}
diff --git a/20191219/loesung-2.c b/20191219/loesung-2.c
new file mode 100644
index 0000000..b02d98b
--- /dev/null
+++ b/20191219/loesung-2.c
@@ -0,0 +1,26 @@
+#include <stdio.h>
+#include <stdint.h>
+
+uint8_t repair (uint8_t data)
+{
+  uint8_t result = 0;
+  uint8_t mask_data = 0x01;
+  uint8_t mask_result = 0x80;
+  while (mask_data)
+    {
+      if (data & mask_data)
+        result |= mask_result;
+      mask_data <<= 1;
+      mask_result >>= 1;
+    }
+  return result;
+}
+
+int main (void)
+{
+  int data[] = { 122, 244, 120, 24, 168, -1 };
+  int i = 0;
+  while (data[i] >= 0)
+    printf ("%d\n", repair (data[i++]));
+  return 0;
+}
diff --git a/README.md b/README.md
index 08ba7fa..ee2e6d2 100644
--- a/README.md
+++ b/README.md
@@ -60,6 +60,8 @@ Musterlösungen:
  * [14.11.2019: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191114/hp-musterloesung-20191114.pdf)
  * [21.11.2019: Zahlensysteme, Mikrocontroller](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191121/hp-musterloesung-20191121.pdf)
  * [28.11.2019: Datum-Bibliothek, Text-Grafik-Bibliothek, LED-Blinkmuster](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191128/hp-musterloesung-20191128.pdf)
+ * [12.12.2019: Kondensator, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191212/hp-musterloesung-20191212.pdf)
+ * [19.12.2019: Trickprogrammierung, Thermometer-Baustein an I²C-Bus](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191219/hp-musterloesung-20191219.pdf)
  * [09.01.2020: Speicherformate von Zahlen, Zeigerarithmetik, Personen-Datenbank](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20200109/hp-musterloesung-20200109.pdf)
  * [16.01.2020: Fakultät, Länge von Strings (Neuauflage), objektorientierte Tier-Datenbank](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20200116/hp-musterloesung-20200116.pdf)
  * [23.01.2020: Stack-Operationen, Iteratorfunktionen, dynamisches Bit-Array](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20200123/hp-musterloesung-20200123.pdf)
-- 
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