From a8ca1428c2a00893e55ae300fe6c4e5868fe2f7d Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Thu, 5 Dec 2019 14:25:45 +0100
Subject: [PATCH] =?UTF-8?q?Musterl=C3=B6sung=2021.11.2019?=
MIME-Version: 1.0
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---
 20191121/hp-musterloesung-20191121.pdf | Bin 0 -> 101315 bytes
 20191121/hp-musterloesung-20191121.tex | 392 +++++++++++++++++++++++++
 README.md                              |   1 +
 3 files changed, 393 insertions(+)
 create mode 100644 20191121/hp-musterloesung-20191121.pdf
 create mode 100644 20191121/hp-musterloesung-20191121.tex

diff --git a/20191121/hp-musterloesung-20191121.pdf b/20191121/hp-musterloesung-20191121.pdf
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diff --git a/20191121/hp-musterloesung-20191121.tex b/20191121/hp-musterloesung-20191121.tex
new file mode 100644
index 0000000..555e154
--- /dev/null
+++ b/20191121/hp-musterloesung-20191121.tex
@@ -0,0 +1,392 @@
+% hp-musterloesung-20191121.pdf - Solutions to the Exercises on Low-Level Programming
+% Copyright (C) 2013, 2015, 2016, 2017, 2018, 2019  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 -- 21.\ November 2019}
+
+  \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}{20191121}{aufgabe-2.c}):
+
+    \begin{lstlisting}[gobble=6]
+      #include <avr/io.h>
+
+      int main (void)
+      {
+        DDRA = 0xff;
+        DDRB = 0xff;
+        DDRC = 0xff;
+        DDRD = 0xff;
+        PORTA = 0x1f;
+        PORTB = 0x10;
+        PORTD = 0x10;
+        PORTC = 0xfc;
+        while (1);
+        return 0;
+      }
+    \end{lstlisting}
+  \end{minipage}\hfill
+  \begin{minipage}[t]{3cm}
+    \strut\\[-\baselineskip]
+    \includegraphics[width=3cm]{leds.jpg}
+  \end{minipage}
+
+  \vspace*{-3cm}
+
+  \strut\hfill
+  \begin{minipage}{11.8cm}
+    \begin{itemize}
+      \item[(a)]
+        Was bewirkt dieses Programm? \points{4}
+      \item[(b)]
+        Wozu dienen die ersten vier Zeilen des Hauptprogramms? \points{2}
+      \item[(c)]
+        Was würde stattdessen die Zeile \lstinline{DDRA, DDRB, DDRC, DDRD = 0xff;} bewirken?
+        \points{2}
+      \item[(d)]
+        Schreiben Sie das Programm so um,
+        daß die durch das Programm dargestellte Figur spiegelverkehrt erscheint. \points{3}
+      \item[(e)]
+        Wozu dient das \lstinline{while (1)}? \points{2}
+      \item
+        Alle Antworten bitte mit Begründung.
+    \end{itemize}
+  \end{minipage}
+
+  \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 af2bd40..66695bf 100644
--- a/README.md
+++ b/README.md
@@ -47,6 +47,7 @@ Musterlösungen:
  * [31.10.2019: Strings, Programm analysieren, fehlerhaftes Primzahl-Programm](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191031/hp-musterloesung-20191031.pdf)
  * [07.11.2019: Arrays mit Zahlen, Datum-Bibliothek](https://gitlab.cvh-server.de/pgerwinski/hp/raw/master/20191107/hp-musterloesung-20191107.pdf)
  * [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)
 
 Tafelbilder:
 ------------
-- 
GitLab