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 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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 + 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--(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)% + 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--(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)% + --(8.831,0.990)--(8.838,0.989)--(8.846,0.987)--(8.854,0.987)--(8.862,0.986)--(8.870,0.984)% + --(8.877,0.983)--(8.885,0.983)--(8.893,0.981)--(8.901,0.979)--(8.909,0.979)--(8.916,0.978)% + --(8.924,0.976)--(8.932,0.975)--(8.940,0.975)--(8.948,0.973)--(8.955,0.972)--(8.963,0.972)% + --(8.971,0.970)--(8.979,0.969)--(8.987,0.969)--(8.995,0.967)--(9.002,0.965)--(9.010,0.965)% + --(9.018,0.964)--(9.026,0.962)--(9.034,0.962)--(9.041,0.961)--(9.049,0.959)--(9.057,0.959)% + --(9.065,0.958)--(9.073,0.956)--(9.080,0.956)--(9.088,0.955)--(9.096,0.953)--(9.104,0.953)% + --(9.112,0.951)--(9.120,0.950)--(9.127,0.950)--(9.135,0.948)--(9.143,0.947)--(9.151,0.947)% + --(9.159,0.945)--(9.166,0.944)--(9.174,0.944)--(9.182,0.942)--(9.190,0.941)--(9.198,0.941)% + --(9.205,0.939)--(9.213,0.939)--(9.221,0.937)--(9.229,0.936)--(9.237,0.936)--(9.244,0.934)% + --(9.252,0.933)--(9.260,0.933)--(9.268,0.931)--(9.276,0.931)--(9.284,0.930)--(9.291,0.928)% + --(9.299,0.928)--(9.307,0.927)--(9.315,0.927)--(9.323,0.925)--(9.330,0.923)--(9.338,0.923)% + --(9.346,0.922)--(9.354,0.922)--(9.362,0.920)--(9.369,0.919)--(9.377,0.919)--(9.385,0.917)% + --(9.393,0.917)--(9.401,0.916)--(9.409,0.914)--(9.416,0.914)--(9.424,0.913)--(9.432,0.913)% + --(9.440,0.911)--(9.448,0.911)--(9.455,0.910)--(9.463,0.908)--(9.471,0.908)--(9.479,0.906)% + --(9.487,0.906)--(9.494,0.905)--(9.502,0.905)--(9.510,0.903)--(9.518,0.902)--(9.526,0.902)% + --(9.533,0.900)--(9.541,0.900)--(9.549,0.899)--(9.557,0.899)--(9.565,0.897)--(9.573,0.897)% + --(9.580,0.896)--(9.588,0.894)--(9.596,0.894)--(9.604,0.892)--(9.612,0.892)--(9.619,0.891)% + --(9.627,0.891)--(9.635,0.889)--(9.643,0.889)--(9.651,0.888)--(9.658,0.888)--(9.666,0.886)% + --(9.674,0.886)--(9.682,0.885)--(9.690,0.885)--(9.698,0.883)--(9.705,0.882)--(9.713,0.882)% + --(9.721,0.880)--(9.729,0.880)--(9.737,0.878)--(9.744,0.878)--(9.752,0.877)--(9.760,0.877)% + --(9.768,0.875)--(9.776,0.875)--(9.783,0.874)--(9.791,0.874)--(9.799,0.872)--(9.807,0.872)% + --(9.815,0.871)--(9.822,0.871)--(9.830,0.869)--(9.838,0.869)--(9.846,0.868)--(9.854,0.868)% + 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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) -- GitLab