From 2dc847de3a6877407be4aef91820979fccb9f243 Mon Sep 17 00:00:00 2001 From: Peter Gerwinski <peter.gerwinski@hs-bochum.de> Date: Tue, 22 Jan 2019 23:40:15 +0100 Subject: [PATCH] =?UTF-8?q?Musterl=C3=B6sung=2026.11.2018?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 20181126/hp-musterloesung-20181126.pdf | Bin 0 -> 101748 bytes 20181126/hp-musterloesung-20181126.tex | 392 +++++++++++++++++++++++++ README.md | 2 + hp-slides-2018ws.pdf | Bin 3086762 -> 3086762 bytes 4 files changed, 394 insertions(+) create mode 100644 20181126/hp-musterloesung-20181126.pdf create mode 100644 20181126/hp-musterloesung-20181126.tex diff --git a/20181126/hp-musterloesung-20181126.pdf b/20181126/hp-musterloesung-20181126.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cb8689bb094c58140add898f1e7e2dabd1c95b2d GIT binary patch literal 101748 zcmY!laB<T$)HCH$y>R8|4K7m!1BLvgEG`=xeV^34^pXq(BU3XA1u)Qe%giZBEz)<( 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Solutions to the Exercises on Low-Level Programming / Applied Computer Sciences +% Copyright (C) 2013, 2015, 2016, 2017, 2018 Peter Gerwinski +% +% This document is free software: you can redistribute it and/or +% modify it either under the terms of the Creative Commons +% Attribution-ShareAlike 3.0 License, or under the terms of the +% GNU General Public License as published by the Free Software +% Foundation, either version 3 of the License, or (at your option) +% any later version. +% +% This document is distributed in the hope that it will be useful, +% but WITHOUT ANY WARRANTY; without even the implied warranty of +% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +% GNU General Public License for more details. +% +% You should have received a copy of the GNU General Public License +% along with this document. If not, see <http://www.gnu.org/licenses/>. +% +% You should have received a copy of the Creative Commons +% Attribution-ShareAlike 3.0 Unported License along with this +% document. If not, see <http://creativecommons.org/licenses/>. + +% README: Zahlensysteme, Mikrocontroller + +\documentclass[a4paper]{article} + +\usepackage{pgscript} +\usepackage{sfmath} + +\begin{document} + + \section*{Hardwarenahe Programmierung\\ + Musterlösung zu den Übungsaufgaben -- 26.\ November 2018} + + \exercise{Zahlensysteme} + + Wandeln Sie ohne Hilfsmittel + + \begin{minipage}[t]{0.3\textwidth} + \begin{itemize} + \item + nach Dezimal: + \begin{itemize} + \item[(a)] + 0010\,0000$_2$ + \item[(b)] + 42$_{16}$ + \item[(c)] + 17$_8$ + \end{itemize} + \end{itemize} + \end{minipage}\hfill + \begin{minipage}[t]{0.3\textwidth} + \begin{itemize} + \item + nach Hexadezimal: + \begin{itemize} + \item[(d)] + 0010\,0000$_2$ + \item[(e)] + 42$_{10}$ + \item[(f)] + 192.168.20.254$_{256}$ + \end{itemize} + \end{itemize} + \end{minipage}\hfill + \begin{minipage}[t]{0.3\textwidth} + \begin{itemize} + \item + nach Binär: + \begin{itemize} + \item[(g)] + 750$_8$ + \item[(h)] + 42$_{10}$ + \item[(i)] + AFFE$_{16}$ + \end{itemize} + \end{itemize} + \end{minipage} + + \medskip + + Berechnen Sie ohne Hilfsmittel: + \begin{itemize} + \item[(j)] + 750$_8$ \& 666$_8$ + \item[(k)] + A380$_{16}$ + B747$_{16}$ + \item[(l)] + AFFE$_{16} >> 1$ + \end{itemize} + + Die tiefgestellte Zahl steht für die Basis des Zahlensystems. + Jede Teilaufgabe zählt 1 Punkt. \addtocounter{points}{12} + + (In der Klausur sind Hilfsmittel zugelassen, + daher ist dies \emph{keine\/} typische Klausuraufgabe.) + + \solution + + Wandeln Sie ohne Hilfsmittel + + \begin{itemize} + \item + nach Dezimal: + \begin{itemize} + \item[(a)] + $0010\,0000_2 = 32_{10}$ + + Eine Eins mit fünf Nullen dahinter steht binär für $2^5 = 32$:\\ + mit $1$ anfangen und fünfmal verdoppeln. + \item[(b)] + $42_{16} = 4 \cdot 16 + 2 \cdot 1 = 64 + 2 = 66$ + \item[(c)] + $17_8 = 1 \cdot 8 + 7 \cdot 1 = 8 + 7 = 15$ + \end{itemize} + Umwandlung von und nach Dezimal ist immer rechenaufwendig. + Umwandlungen zwischen Binär, Oktal und Hexadezimal gehen ziffernweise + und sind daher wesentlich einfacher. + \item + nach Hexadezimal: + \begin{itemize} + \item[(d)] + $0010\,0000_2 = 20_{16}$ + + Umwandlung von Binär nach Hexadezimal geht ziffernweise:\\ + Vier Binärziffern werden zu einer Hex-Ziffer. + \item[(e)] + $\rm 42_{10} = 32_{10} + 10_{10} = 20_{16} + A_{16} = 2A_{16}$ + \item[(f)] + $\rm 192.168.20.254_{256} = C0\,A8\,14\,FE_{16}$ + + Umwandlung von der Basis 256 nach Hexadezimal geht ziffernweise:\\ + Eine 256er-Ziffer wird zu zwei Hex-Ziffern. + + Da die 256er-Ziffern dezimal angegeben sind, + müssen wir viermal Dezimal nach Hexadezimal umwandeln. + Hierfür bieten sich unterschiedliche Wege an. + + $\rm 192_{10} = 128_{10} + 64_{10} = 1100\,0000_{2} = C0_{16}$ + + $\rm 168_{10} = 10_{10} \cdot 16_{10} + 8_{10} = A_{16} \cdot 10_{16} + 8_{16} = A8_{16}$ + + $20_{10} = 16_{10} + 4_{10} = 10_{16} + 4_{16} = 14$ + + $\rm 254_{10} = 255_{10} - 1_{10} = FF_{16} - 1_{16} = FE_{16}$ + \end{itemize} + \item + nach Binär: + \begin{itemize} + \item[(g)] + $750_8 = 111\,101\,000_2$ + + Umwandlung von Oktal nach Binär geht ziffernweise:\\ + Eine Oktalziffer wird zu drei Binärziffern. + \item[(h)] + $\rm 42_{10} = 2A_{16}$ (siehe oben) $= 0010\,1010_{16}$ + + Umwandlung von Hexadezimal nach Binär geht ziffernweise:\\ + Eine Hex-Ziffer wird zu vier Binärziffern. + \item[(i)] + $\rm AFFE_{16} = 1010\,1111\,1111\,1110_2$ + + Umwandlung von Hexadezimal nach Binär geht ziffernweise:\\ + Eine Hex-Ziffer wird zu vier Binärziffern. + \end{itemize} + \end{itemize} + + \medskip + + Berechnen Sie ohne Hilfsmittel: + \begin{itemize} + \item[(j)] + $750_8\,\&\,666_8 + = 111\,101\,000_2\,\&\,110\,110\,110_2 + = 110\,100\,000_2 + = 640_8$ + + Binäre Und-Operationen lassen sich am leichtesten + in binärer Schreibweise durchführen. + Umwandlung zwischen Oktal und Binär geht ziffernweise: + Eine Oktalziffer wird zu drei Binärziffern und umgekehrt. + + Mit etwas Übung funktionieren diese Operationen + auch direkt mit Oktalzahlen im Kopf. + + \item[(k)] + $\rm\phantom{+}A380_{16}$\\ + $\rm+\kern2ptB747_{16}$\\[-\medskipamount] + \rule{1.4cm}{0.5pt}\\ + $\rm 15AC7_{16}$ + \begin{picture}(0,0) + \put(-1.4,0.35){\mbox{\scriptsize\bf 1}} + \end{picture} + + Mit Hexadezimalzahlen (und Binär- und Oktal- und sonstigen Zahlen) + kann man genau wie mit Dezimalzahlen schriftlich rechnen. + Man muß nur daran denken, daß der "`Zehner"'-Überlauf nicht bei + $10_{10}$ stattfindet, sondern erst bei $10_{16} = 16_{10}$ + (hier: $\rm 8_{16} + 4_{16} = C_{16}$ und + $\rm 3_{16} + 7_{16} = A_{16}$, aber + $\rm A_{16} + B_{16} = 10_{10} + 11_{10} + = 21_{10} = 16_{10} + 5_{10} = 10_{16} + 5_{16} = 15_{16}$). + + \item[(l)] + $\rm AFFE_{16} >> 1 + = 1010\,1111\,1111\,1110_2 >> 1 + = 0101\,0111\,1111\,1111_2 + = 57FF_{16}$ + + Bit-Verschiebungen lassen sich am leichtesten + in binärer Schreibweise durchführen. + Umwandlung zwischen Hexadezimal und Binär geht ziffernweise: + Eine Hex-Ziffer wird zu vier Binärziffern und umgekehrt. + + Mit etwas Übung funktionieren diese Operationen + auch direkt mit Hexadezimalzahlen im Kopf. + + \end{itemize} + + \exercise{Mikrocontroller} + + \begin{minipage}[t]{10cm} + An die vier Ports eines ATmega16-Mikrocontrollers sind Leuchtdioden angeschlossen: + \begin{itemize} + \item + von links nach rechts an die Ports A, B, C und D, + \item + von oben nach unten an die Bits Nr.\ 0 bis 7. + \end{itemize} + + Wir betrachten das folgende Programm (\gitfile{hp}{20181126}{aufgabe-2.c}): + + \begin{lstlisting}[gobble=6] + #include <avr/io.h> + + int main (void) + { + DDRA = 0xff; + DDRB = 0xff; + DDRC = 0xff; + DDRD = 0xff; + PORTA = 0x1f; + PORTB = 0x10; + PORTD = 0x10; + PORTC = 0xfc; + while (1); + return 0; + } + \end{lstlisting} + \end{minipage}\hfill + \begin{minipage}[t]{3cm} + \strut\\[-\baselineskip] + \includegraphics[width=3cm]{leds.jpg} + \end{minipage} + + \vspace*{-3cm} + + \strut\hfill + \begin{minipage}{11.8cm} + \begin{itemize} + \item[(a)] + Was bewirkt dieses Programm? \points{4} + \item[(b)] + Wozu dienen die ersten vier Zeilen des Hauptprogramms? \points{2} + \item[(c)] + Was würde stattdessen die Zeile \lstinline{DDRA, DDRB, DDRC, DDRD = 0xff;} bewirken? + \points{2} + \item[(d)] + Schreiben Sie das Programm so um, + daß die durch das Programm dargestellte Figur spiegelverkehrt erscheint. \points{3} + \item[(e)] + Wozu dient das \lstinline{while (1)}? \points{2} + \item + Alle Antworten bitte mit Begründung. + \end{itemize} + \end{minipage} + + \solution + + \begin{itemize} + \item[(a)] + \textbf{Was bewirkt dieses Programm?} + + \newcommand{\x}{$\bullet$} + \renewcommand{\o}{$\circ$} + + \begin{minipage}[t]{0.75\textwidth}\parskip\smallskipamount + Es läßt die LEDs in dem rechts abgebildeten Muster aufleuchten,\\ + das z.\,B.\ als die Ziffer 4 gelesen werden kann. + + (Das Zeichen \x\ steht für eine leuchtende, \o\ für eine nicht leuchtende LED.) + + Die erste Spalte (Port A) von unten nach oben gelesen (Bit 7 bis 0)\\ + entspricht der Binärdarstellung von \lstinline{0x1f}: 0001\,1111. + + Die dritte Spalte (Port C) von unten nach oben gelesen (Bit 7 bis 0)\\ + entspricht der Binärdarstellung von \lstinline{0xfc}: 1111\,1100. + + Die zweite und vierte Spalte (Port B und D) von unten nach oben gelesen\\ + (Bit 7 bis 0) entsprechen der Binärdarstellung von \lstinline{0x10}: 0001\,0000. + + Achtung: Die Zuweisung der Werte an die Ports erfolgt im Programm\\ + \emph{nicht\/} in der Reihenfolge A B C D, sondern in der Reihenfolge A B D C. + \end{minipage}\hfill + \begin{minipage}[t]{0.15\textwidth} + \vspace*{-0.5cm}% + \begin{tabular}{cccc} + \x & \o & \o & \o \\ + \x & \o & \o & \o \\ + \x & \o & \x & \o \\ + \x & \o & \x & \o \\ + \x & \x & \x & \x \\ + \o & \o & \x & \o \\ + \o & \o & \x & \o \\ + \o & \o & \x & \o \\ + \end{tabular} + \end{minipage} + + \item[(b)] + \textbf{Wozu dienen die ersten vier Zeilen des Hauptprogramms?} + + Mit diesen Zeilen werden alle jeweils 8 Bits aller 4 Ports + als Output-Ports konfiguriert. + + \item[(c)] + \textbf{Was würde stattdessen die Zeile \lstinline{DDRA, DDRB, DDRC, DDRD = 0xff;} bewirken?} + + Der Komma-Operator in C bewirkt, daß der erste Wert berechnet + und wieder verworfen wird und stattdessen der zweite Wert weiterverarbeitet wird. + Konkret hier hätte das zur Folge, + daß \lstinline{DDRA}, \lstinline{DDRB} und \lstinline{DDRC} + gelesen und die gelesenen Werte ignoriert werden; + anschließend wird \lstinline{DDRD} der Wert \lstinline{0xff} zugewiesen. + Damit würde also nur einer von vier Ports überhaupt konfiguriert. + + Da es sich bei den \lstinline{DDR}-Variablen + um \lstinline{volatile}-Variable handelt, + nimmt der Compiler an, daß der Lesezugriff schon irgendeinen Sinn hätte. + Der Fehler bliebe also unbemerkt. + + \item[(d)] + \textbf{Schreiben Sie das Programm so um, + daß die durch das Programm dargestellte Figur spiegelverkehrt erscheint.} + + Hierzu vertauschen wir die Zuweisungen + an \lstinline{PORTA} und \lstinline{PORTD} + sowie die Zuweisungen + an \lstinline{PORTB} und \lstinline{PORTC}: + + \begin{lstlisting}[gobble=8] + PORTD = 0x1f; + PORTC = 0x10; + PORTA = 0x10; + PORTB = 0xfc; + \end{lstlisting} + + Damit ergibt sich eine Spiegelung an der vertikalen Achse. + + Alternativ kann man auch an der horizontalen Achse spiegeln. + Dafür muß man die Bits in den Hexadezimalzahlen umdrehen: + + \begin{lstlisting}[gobble=8] + PORTA = 0xf8; + PORTB = 0x08; + PORTD = 0x08; + PORTC = 0x3f; + \end{lstlisting} + + Die Frage, welche der beiden Spiegelungen gewünscht ist, + wäre übrigens \emph{auch in der Klausur zulässig}. + + \item[(e)] + \textbf{Wozu dient das \lstinline{while (1)}?} + + Mit dem \lstinline{return}-Befehl am Ende des Hauptprogramms + gibt das Programm die Kontrolle an das Betriebssystem zurück. + + Dieses Programm jedoch läuft auf einem Mikrocontroller, + auf dem es kein Betriebssystem gibt. + Wenn das \lstinline{return} ausgeführt würde, + hätte es ein undefiniertes Verhalten zur Folge. + + Um dies zu verhindern, endet das Programm in einer Endlosschleife, + mit der wir den Mikrocontroller anweisen, + nach der Ausführung des Programms \emph{nichts mehr\/} zu tun + (im Gegensatz zu: \emph{irgendetwas Undefiniertes\/} zu tun). + + \end{itemize} + +\end{document} diff --git a/README.md b/README.md index c8b14be..cb26cc0 100644 --- a/README.md +++ b/README.md @@ -58,6 +58,8 @@ Musterlösungen: * [29.10.2018: Strings, Primzahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20181029/hp-musterloesung-20181029.pdf) * [05.11.2018: Ausgabe von Hexadezimalzahlen, Einfügen in Strings, Länge von Strings](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20181105/hp-musterloesung-20181105.pdf) * [12.11.2018: Text-Grafik-Bibliothek, Datum-Bibliothek, Kondensator](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20181112/hp-musterloesung-20181112.pdf) + * [19.11.2018: Arrays mit Zahlen, hüpfender Ball](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20181119/hp-musterloesung-20181119.pdf) + * [26.11.2018: Zahlensysteme, Mikrocontroller](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20181126/hp-musterloesung-20181126.pdf) Tafelbilder: ------------ diff --git a/hp-slides-2018ws.pdf b/hp-slides-2018ws.pdf index 45f835f657ea04347d9506ceeaec365c6d8fed71..c22b6bfd1d123bd1b79eb0cf05c629df624905d1 100644 GIT binary patch delta 204 zcmZ3rc@HB9H?%OeFtsqZu(YtYu(hzaaI|o?aJ6u^@U-x@@U`%_2($>c2(<{eh_r~d zh_#5fNVG_{NVQ0}$h63|$hF9~D6}ZHD77fJsI;iIsI{oKXtZdyXtij!=(Ol=(fj(C z-N?w;*wWBo`k%*o(lE|;xhHxxe9o?h&gL$bCeBXICI*IvCWgkYX67!=&gPa*<_4~2 S&dzoUHiVRHzxzq=tQr8`PCfDf delta 204 zcmZ3rc@HB9H?%OeFtsqZu(YtYu(hzaaI|o?aJ6u^@U-x@@U`%_2($>c2(<{eh_r~d zh_#5fNVG_{NVQ0}$h63|$hF9~D6}ZHD77fJsI;iIsI{oKXtZdyXtij!=(Ol=(fj(C z-O#|mz}VP$`k%*o(lE|;xhHxxe9oq(=7vs=PDbW#2IeLv7A6+Xh6XO?mL^87#->iL Su4Z-$HiVRHzxzq=tQr8sYdvrP -- GitLab