From ce446da3763a50611565f9e4d671df9d55ad2969 Mon Sep 17 00:00:00 2001
From: Peter Gerwinski <peter.gerwinski@hs-bochum.de>
Date: Tue, 29 Mar 2022 08:41:17 +0200
Subject: [PATCH] Vorbereitung 29.3.2022

---
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 20220329/rtech-20220329.tex                   | 589 ++++++++++++++++++
 31 files changed, 887 insertions(+)
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 create mode 100644 20220329/rtech-20220329-fig9.tex
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diff --git a/20220329/rtech-20220329-fig1.tex b/20220329/rtech-20220329-fig1.tex
new file mode 100644
index 0000000..354733b
--- /dev/null
+++ b/20220329/rtech-20220329-fig1.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+      \psset{unit=0.6cm}
+      \psset{linewidth=0.03}
+      \begin{pspicture}(-3,-2)(3,2)
+        \logic[logicType=and](-0.75,-0.125){and1}
+        \psline[arrows=o-](-2,0|and12)(and12)
+        \uput[180](-2,0|and12){A}
+        \psline[arrows=o-](-2,0|and11)(and11)
+        \uput[180](-2,0|and11){B}
+        \psline[arrows=o-](2,0|and1Q)(and1Q)
+        \uput[0](2,0|and1Q){Q}
+      \end{pspicture}
+    
+\end{document}
diff --git a/20220329/rtech-20220329-fig10.pdf b/20220329/rtech-20220329-fig10.pdf
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diff --git a/20220329/rtech-20220329-fig12.tex b/20220329/rtech-20220329-fig12.tex
new file mode 100644
index 0000000..48c438f
--- /dev/null
+++ b/20220329/rtech-20220329-fig12.tex
@@ -0,0 +1,22 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-4,-4)(4,4)
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+      \psline[arrows=o-](-3,0|nand21)(nand21)
+      \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
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+      \uput[0](3,0|nand1Q){Q}
+      \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+      \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
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+      \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+    \end{pspicture}
+  
+\end{document}
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diff --git a/20220329/rtech-20220329-fig2.tex b/20220329/rtech-20220329-fig2.tex
new file mode 100644
index 0000000..354733b
--- /dev/null
+++ b/20220329/rtech-20220329-fig2.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+      \psset{unit=0.6cm}
+      \psset{linewidth=0.03}
+      \begin{pspicture}(-3,-2)(3,2)
+        \logic[logicType=and](-0.75,-0.125){and1}
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+        \uput[180](-2,0|and11){B}
+        \psline[arrows=o-](2,0|and1Q)(and1Q)
+        \uput[0](2,0|and1Q){Q}
+      \end{pspicture}
+    
+\end{document}
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diff --git a/20220329/rtech-20220329-fig3.tex b/20220329/rtech-20220329-fig3.tex
new file mode 100644
index 0000000..354733b
--- /dev/null
+++ b/20220329/rtech-20220329-fig3.tex
@@ -0,0 +1,17 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+      \psset{unit=0.6cm}
+      \psset{linewidth=0.03}
+      \begin{pspicture}(-3,-2)(3,2)
+        \logic[logicType=and](-0.75,-0.125){and1}
+        \psline[arrows=o-](-2,0|and12)(and12)
+        \uput[180](-2,0|and12){A}
+        \psline[arrows=o-](-2,0|and11)(and11)
+        \uput[180](-2,0|and11){B}
+        \psline[arrows=o-](2,0|and1Q)(and1Q)
+        \uput[0](2,0|and1Q){Q}
+      \end{pspicture}
+    
+\end{document}
diff --git a/20220329/rtech-20220329-fig4.pdf b/20220329/rtech-20220329-fig4.pdf
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diff --git a/20220329/rtech-20220329-fig4.tex b/20220329/rtech-20220329-fig4.tex
new file mode 100644
index 0000000..7670750
--- /dev/null
+++ b/20220329/rtech-20220329-fig4.tex
@@ -0,0 +1,55 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+    \newcommand{\invisible}{\tiny\color{white}}
+    \psset{logicLabelstyle=\invisible}
+    \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+    \psset{logicSymbolstyle=\logicSymbol}
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+    \psset{linewidth=0.03}
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+      \pnode(-1,1.5){A}
+      \uput[l](-2.5,0|A){$S$}
+      \pnode(1,1.5){B}
+      \ground[connectingdot=false](2,1.5)
+      \relais(A)(B){}
+      \pnode(2.5,2.5){A3}
+      \uput[l](2.0,0|A3){$R$}
+      \pnode(4.5,2.5){B3}
+      \ground[connectingdot=false](5.5,2.5)
+      \relais(A3)(B3){}
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+      \pnode(-3.0,-0.5){C1plus}
+      \uput[180](C1plus){\textbf{+}}
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+      \psline(B)(2,0|B)
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+  
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diff --git a/20220329/rtech-20220329-fig5.pdf b/20220329/rtech-20220329-fig5.pdf
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diff --git a/20220329/rtech-20220329-fig5.tex b/20220329/rtech-20220329-fig5.tex
new file mode 100644
index 0000000..7670750
--- /dev/null
+++ b/20220329/rtech-20220329-fig5.tex
@@ -0,0 +1,55 @@
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+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
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+    \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
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diff --git a/20220329/rtech-20220329-fig6.tex b/20220329/rtech-20220329-fig6.tex
new file mode 100644
index 0000000..48c438f
--- /dev/null
+++ b/20220329/rtech-20220329-fig6.tex
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index 0000000..9f924ad
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diff --git a/20220329/rtech-20220329-fig9.tex b/20220329/rtech-20220329-fig9.tex
new file mode 100644
index 0000000..9f924ad
--- /dev/null
+++ b/20220329/rtech-20220329-fig9.tex
@@ -0,0 +1,15 @@
+\documentclass{article}
+\input tmp.inputs
+\pagestyle{empty}
+\begin{document}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-4,-4)(4,4)
+      \pnode(0,0.5){A}
+      \pnode(0,-0.5){B}
+      \capacitor(A)(B){}
+      \psline[arrows=-o](A)(A|0,1)
+      \psline[arrows=-o](B)(B|0,-1)
+    \end{pspicture}
+  
+\end{document}
diff --git a/20220329/rtech-20220329.pdf b/20220329/rtech-20220329.pdf
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diff --git a/20220329/rtech-20220329.tex b/20220329/rtech-20220329.tex
new file mode 100644
index 0000000..5f72176
--- /dev/null
+++ b/20220329/rtech-20220329.tex
@@ -0,0 +1,589 @@
+% rtech-20220329.pdf - Lecture Slides on Computer Technology
+% Copyright (C) 2012, 2013, 2014, 2021, 2022  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: Vom Addierer zum Computer
+
+\documentclass[10pt,t]{beamer}
+
+\usepackage{pgslides}
+\usepackage{pdftricks}
+%\usepackage[obeyfamily=false,mathrm=mathsf,textrm=sffamily]{siunitx}
+%\usepackage{eurosym}
+
+\newrgbcolor{orange}{0.7 0.2 0.0}
+
+\newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+\newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+
+\begin{psinputs}
+  \usepackage[latin1]{inputenc}
+  \usepackage[german]{babel}
+  \usepackage[T1]{fontenc}
+  \usepackage{helvet}
+  \renewcommand*\familydefault{\sfdefault}
+  \usepackage{pstricks,pst-grad,pst-circ-pg}
+  \newcommand{\invisible}{\tiny\color{white}}
+  \psset{unit=1cm}
+  \psset{logicLabelstyle=\invisible}
+  \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+  \psset{logicSymbolstyle=\logicSymbol}
+  \newcommand{\Cin}{C\raisebox{-0.5ex}{\footnotesize in}}
+  \newcommand{\Cout}{C\raisebox{-0.5ex}{\footnotesize out}}
+\end{psinputs}
+
+\title{Rechnertechnik}
+\author{Prof.\ Dr.\ rer.\ nat.\ Peter Gerwinski}
+\date{29.\ März 2022}
+
+\begin{document}
+
+\maketitleframe
+
+\sectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \showsectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+      \begin{itemize}
+        \item[1.1] Was ist Rechnertechnik?
+        \item[1.2] Was ist ein Computer?
+      \end{itemize}
+    \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+      \begin{itemize}
+        \item[2.1] Logik-Schaltkreise
+        \item[2.2] Binärdarstellung von Zahlen
+        \item[2.3] Vom Logik-Schaltkreis zum Addierer
+        \color{medgreen}
+        \item[2.4] Negative Zahlen
+        \color{red}
+        \item[2.5] Vom Addierer zum Computer
+        \item[\dots]
+      \end{itemize}
+    \color{gray}
+    \item[\textbf{3}] \textbf{Architekturmerkmale von Prozessoren}
+    \item[\textbf{4}] \textbf{Der CPU-Stack}
+%    \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+%    \item[\textbf{6}] \textbf{Anwender-Software}
+%    \item[\textbf{7}] \textbf{Bus-Systeme}
+%    \item[\textbf{8}] \textbf{Pipelining}
+    \item[\textbf{\dots\hspace{-0.75em}}]
+%    \item[\textbf{9}] \textbf{Ausblick}
+  \end{itemize}
+
+\end{frame}
+
+\setcounter{section}{1}
+\section{Vom Schaltkreis zum Computer}
+\setcounter{subsection}{3}
+\subsection{Negative Zahlen}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Speicher ist begrenzt!\\
+  \textarrow\ feste Anzahl von Bits
+
+  \medskip
+
+  8-Bit-Zahlen ohne Vorzeichen: \lstinline{uint8_t}\\
+  \textarrow\ Zahlenwerte von \lstinline{0x00} bis \lstinline{0xff} = 0 bis 255\\
+  \pause
+  \textarrow\ 255 + 1 = 0
+
+  \pause
+  \medskip
+
+  8-Bit-Zahlen mit Vorzeichen: \lstinline{int8_t}\\
+  \lstinline{0xff} = 255 ist die "`natürliche"' Schreibweise für $-1$.\\
+  \pause
+  \textarrow\ Zweierkomplement
+
+  \pause
+  \medskip
+
+  Oberstes Bit = 1: negativ\\
+  Oberstes Bit = 0: positiv\\
+  \textarrow\ 127 + 1 = $-128$
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Speicher ist begrenzt!\\
+  \textarrow\ feste Anzahl von Bits
+
+  \medskip
+
+  16-Bit-Zahlen ohne Vorzeichen:
+  \lstinline{uint16_t}\hfill\lstinline{uint8_t}\\
+  \textarrow\ Zahlenwerte von \lstinline{0x0000} bis \lstinline{0xffff}
+  = 0 bis 65535\hfill 0 bis 255\\
+  \textarrow\ 65535 + 1 = 0\hfill 255 + 1 = 0
+
+  \medskip
+
+  16-Bit-Zahlen mit Vorzeichen:
+  \lstinline{int16_t}\hfill\lstinline{int8_t}\\
+  \lstinline{0xffff} = 66535 ist die "`natürliche"' Schreibweise für $-1$.\hfill
+  \lstinline{0xff} = 255 = $-1$\\
+  \textarrow\ Zweierkomplement
+
+  \medskip
+
+  Oberstes Bit = 1: negativ\\
+  Oberstes Bit = 0: positiv\\
+  \textarrow\ 32767 + 1 = $-32768$
+
+  \bigskip
+  Literatur: \url{http://xkcd.com/571/}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Frage: \emph{Für welche Zahl steht der Speicherinhalt\,
+  \raisebox{2pt}{%
+    \tabcolsep0.25em
+    \begin{tabular}{|c|c|}\hline
+      \rule{0pt}{11pt}a3 & 90 \\\hline
+    \end{tabular}}
+  (hexadezimal)?}
+  
+  \pause
+  \smallskip
+  Antwort: \emph{Das kommt darauf an.} ;--)
+
+  \pause
+  \medskip
+  Little-Endian:
+
+  \smallskip
+
+  \begin{tabular}{lrl}
+    als \lstinline,int8_t,: & $-93$ & (nur erstes Byte)\\
+    als \lstinline,uint8_t,: & $163$ & (nur erstes Byte)\\
+    als \lstinline,int16_t,: & $-28509$\\
+    als \lstinline,uint16_t,: & $37027$\\
+    \lstinline,int32_t, oder größer: & $37027$
+      & (zusätzliche Bytes mit Nullen aufgefüllt)
+  \end{tabular}
+
+  \pause
+  \medskip
+  Big-Endian:
+
+  \smallskip
+
+  \begin{tabular}{lrl}
+    als \lstinline,int8_t,:   & $-93$ & (nur erstes Byte)\\
+    als \lstinline,uint8_t,:  & $163$ & (nur erstes Byte)\\
+    als \lstinline,int16_t,:  & $-23664$\\
+    als \lstinline,uint16_t,: & $41872$\\ als \lstinline,int32_t,:  & $-1550843904$ & (zusätzliche Bytes\\
+    als \lstinline,uint32_t,: & $2744123392$  & mit Nullen aufgefüllt)\\
+    als \lstinline,int64_t,:  & $-6660823848880963584$\\
+    als \lstinline,uint64_t,: & $11785920224828588032$\\
+  \end{tabular}
+
+  \vspace*{-1cm}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsubsection
+
+  Aufbau einer Schaltung zum Bilden des Zweierkomplements:\\
+  {\color{red}Sie sind dran.}
+
+  \medskip
+
+  \textarrow\ Siehe: \file{../20220322/2er-komplement-$*$.png}
+
+\end{frame}
+
+\subsection{Vom Addierer zum Computer}
+
+\begin{frame}
+
+  \showsubsection
+
+  Wir können jetzt addieren und subtrahieren.\\
+  Wie bauen wir daraus einen Turing-vollständigen Computer?
+  \begin{itemize}
+    \pause
+    \item
+      Arithmetisch-logische Einheit (ALU)%\\
+%      (Skript: Seite 20)
+%    \pause
+    \item
+      Speicher
+%    \pause
+    \item
+      Takt
+  \end{itemize}
+
+\end{frame}
+
+\iffalse
+
+\begin{frame}
+
+  \showsubsection
+
+  Zeit ins Spiel bringen:
+  \begin{itemize}
+    \item sich 1 Bit merken: Flipflop
+    \item zeitlicher Ablauf: Taktgeber
+    \item voranschreiten: Zähler (aus Flipflops)
+  \end{itemize}
+
+  \pause
+  \bigskip
+
+  Programmieren:
+  \begin{itemize}
+    \item ALU kann verschiedene Operationen durchführen
+    \item Maschinensprache codiert, welche Operation ausgeführt werden soll
+    \item Das Laden von Registern ermöglicht auch Sprünge \textarrow\ Schleifen
+  \end{itemize}
+
+\end{frame}
+
+\fi
+
+\setcounter{subsection}{4}
+\subsection{Vom Addierer zum Computer}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  1-Bit-Multiplizierer
+  \visible<3->{= Und-Verknüpfung}
+
+  \medskip
+
+  \begin{tabular}{|c|c||c|}\hline
+    A & B & Q \\\hline\hline
+    0 & 0 & \visible<2->{0} \\\hline
+    0 & 1 & \visible<2->{0} \\\hline
+    1 & 0 & \visible<2->{0} \\\hline
+    1 & 1 & \visible<2->{1} \\\hline
+  \end{tabular}\quad\pause[3]
+  \begin{minipage}{2.5cm}
+    \vspace*{0.5cm}
+    \begin{pdfpic}
+      \psset{unit=0.6cm}
+      \psset{linewidth=0.03}
+      \begin{pspicture}(-3,-2)(3,2)
+        \logic[logicType=and](-0.75,-0.125){and1}
+        \psline[arrows=o-](-2,0|and12)(and12)
+        \uput[180](-2,0|and12){A}
+        \psline[arrows=o-](-2,0|and11)(and11)
+        \uput[180](-2,0|and11){B}
+        \psline[arrows=o-](2,0|and1Q)(and1Q)
+        \uput[0](2,0|and1Q){Q}
+      \end{pspicture}
+    \end{pdfpic}
+  \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsubsection
+
+  1-Bit-Multiplizierer = Und-Verknüpfung
+
+  \smallskip
+
+  n-Bit-Multiplizierer\pause: "`schriftlich"' multiplizieren
+
+  \bigskip
+  \pause
+
+  Beispiel: $13 \cdot 5$
+
+  \smallskip
+
+  \begin{tabular}{r}
+    $1101 \cdot 101$\\[-1.5\smallskipamount]
+    \rule{2cm}{1pt}\\
+    $1101\phantom{00}$\\
+    $0\phantom{0}$\\
+    $1101$\\[-1.5\smallskipamount]
+    \rule{2cm}{1pt}\\
+    $1000001$
+  \end{tabular}%
+  \begin{picture}(0,0)
+    \put(-0.95,-0.63){\mbox{\scriptsize 1}}
+    \put(-1.15,-0.63){\mbox{\scriptsize 1}}
+    \put(-1.35,-0.63){\mbox{\scriptsize 1}}
+    \put(-1.55,-0.63){\mbox{\scriptsize 1}}
+  \end{picture}\pause
+  \hspace*{2cm}%
+  \begin{minipage}{5cm}
+    Multiplizier-Schaltkreis\\
+    für zwei 2-Bit-Zahlen:\\[\smallskipamount]
+    \color{red}Sie sind dran.
+  \end{minipage}
+
+\end{frame}
+
+\begin{frame}
+
+  \showsubsection
+
+  Schaltkreis, der wahlweise eine von mehreren Verknüpfungen
+  durchführt:
+
+  \smallskip
+
+  \newterm{arithmetisch-logische Einheit\/} --
+  \newterm{arithmetic logic unit (ALU)}
+
+  \bigskip
+  
+  \begin{center}
+    \vspace*{-2.5cm}
+    \includegraphics{alu2.pdf}
+    \vspace*{-23cm}
+  \end{center}
+
+  \bigskip
+
+  Siehe z.\,B.: \url{https://en.wikipedia.org/wiki/File:74181aluschematic.png}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \begin{visibleenv}<2->
+    \showsubsection
+
+    Information speichern
+  \end{visibleenv}
+
+  \begin{pdfpic}
+    \newcommand{\invisible}{\tiny\color{white}}
+    \psset{logicLabelstyle=\invisible}
+    \newcommand{\logicSymbol}{\small\boldmath\bf\rule{0pt}{0.5cm}}
+    \psset{logicSymbolstyle=\logicSymbol}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-3,-2)(3,2)
+      \pnode(-1,1.5){A}
+      \uput[l](-2.5,0|A){$S$}
+      \pnode(1,1.5){B}
+      \ground[connectingdot=false](2,1.5)
+      \relais(A)(B){}
+      \pnode(2.5,2.5){A3}
+      \uput[l](2.0,0|A3){$R$}
+      \pnode(4.5,2.5){B3}
+      \ground[connectingdot=false](5.5,2.5)
+      \relais(A3)(B3){}
+      \pnode(-0.5,0){C0}
+      \psline[arrows=-*](C0)(-1.5,0)(-1.5,1.5)
+      \pnode(0.5,0.3){D0}
+      \pnode(0.5,-0.3){E0}
+      \pnode(3,-0.3){C3}
+      \pnode(4,0){D3}
+      \pnode(4,-0.6){E3}
+      \psline[arrows=*-,linewidth=2\pslinewidth](C3)(D3)
+      \pnode(7,0.7){D3plus}
+      \uput[180](D3plus){\textbf{+}}
+      \psline(E0)(C3)
+      \psline[arrows=->,arrowsize=0.3](D3)(D3plus|D3)(D3plus)
+      \psline[arrows=*-,linewidth=2\pslinewidth](C0)(D0)
+      \pnode(-0.5,-1.5){C1}
+      \pnode(0.5,-1.2){D1}
+      \pnode(0.5,-1.8){E1}
+      \uput[r](2.5,0|E1){$Q$}
+      \pnode(-3.0,-0.5){C1plus}
+      \uput[180](C1plus){\textbf{+}}
+      \psline[arrows=->,arrowsize=0.3](C1)(C1plus|C1)(C1plus)
+      \psline[arrows=*-,linewidth=2\pslinewidth](C1)(D1)
+      \psline[linestyle=dashed](0,-1.25)(0,1.0)
+      \psline[linestyle=dashed](3.5,-0.15)(3.5,2.0)
+      \psline[arrows=o-](-2.5,0|A)(A)
+      \psline[arrows=o-](2.0,0|A3)(A3)
+      \psline(B)(2,0|B)
+      \psline(B3)(5.5|B3)
+      \psline[arrows=o-](1.5,0|D0)(D0)
+      \psline[arrows=o-](1.5,0|D1)(D1)
+      \psline[arrows=o-](2.5,0|E1)(E1)
+      \psline[arrows=o-](5.0,0|E3)(E3)
+    \end{pspicture}
+  \end{pdfpic}
+
+  \pause
+
+  \newterm{Selbsthalteschaltung}
+
+  1-Bit-\newterm{Speicherzelle}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Information speichern
+
+  \begin{pdfpic}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-4,-4)(4,4)
+      \logic[logicType=nand](-0.75,2){nand1}
+      \logic[logicType=nand](-0.75,-2){nand2}
+      \psline[arrows=o-](-3,0|nand12)(nand12)
+      \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+      \psline[arrows=o-](-3,0|nand21)(nand21)
+      \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+      \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+      \uput[0](3,0|nand1Q){Q}
+      \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+      \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+      \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+      \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+    \end{pspicture}
+  \end{pdfpic}
+
+  \newterm{Bistabile Kippstufe} -- \newterm{Bistabiler Multivibrator} -- \newterm{Flip-Flop}
+
+  1-Bit-Speicherzelle
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Information speichern
+
+  \vspace*{-0.5cm}
+
+  \begin{pdfpic}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-4,-4)(4,4)
+      \pnode(0,0.5){A}
+      \pnode(0,-0.5){B}
+      \capacitor(A)(B){}
+      \psline[arrows=-o](A)(A|0,1)
+      \psline[arrows=-o](B)(B|0,-1)
+    \end{pspicture}
+  \end{pdfpic}
+
+  \vspace*{-1.0cm}
+
+  \newterm{Kondensator}
+
+  \only<2->{\newterm{dynamische\/}} 1-Bit-Speicherzelle\\
+  \pause
+  \textarrow\ benötigt \newterm{Refresh}-Schaltung
+
+  \pause[3]
+  \medskip
+  Flip-Flop
+
+  \newterm{statische\/} 1-Bit-Speicherzelle
+
+  \begin{pdfpic}
+    \psset{unit=0.6cm}
+    \psset{linewidth=0.03}
+    \begin{pspicture}(-4,-4)(4,4)
+      \logic[logicType=nand](-0.75,2){nand1}
+      \logic[logicType=nand](-0.75,-2){nand2}
+      \psline[arrows=o-](-3,0|nand12)(nand12)
+      \uput[180](-3,0|nand12){$\overline{\mbox{S}}$}
+      \psline[arrows=o-](-3,0|nand21)(nand21)
+      \uput[180](-3,0|nand21){$\overline{\mbox{R}}$}
+      \psline[arrows=o-](3,0|nand1Q)(nand1Q)
+      \uput[0](3,0|nand1Q){Q}
+      \psline[arrows=o-](3,0|nand2Q)(nand2Q)
+      \uput[0](3,0|nand2Q){$\overline{\mbox{Q}}$}
+      \psline[arrows=*-](2,0|nand1Q)(2,1.75)(-2,0.75)(-2,0|nand22)(nand22)
+      \psline[arrows=*-](2,0|nand2Q)(2,0.75)(-2,1.75)(-2,0|nand11)(nand11)
+    \end{pspicture}
+  \end{pdfpic}
+
+\end{frame}
+
+\begin{frame}[fragile]
+
+  \showsubsection
+
+  Computer
+  \begin{itemize}
+    \item Rechenwerk (ALU)
+    \item Speicher\pause: Register, adressierbarer Hauptspeicher
+    \pause
+    \item Takt\pause: Befehle abarbeiten
+    \pause
+    \item Peripherie: Kommunikation mit der Außenwelt
+    \pause
+    \arrowitem in Maschinensprache programmierbar
+  \end{itemize}
+
+\end{frame}
+
+\sectionnonumber{\inserttitle}
+
+\begin{frame}
+
+  \showsectionnonumber
+
+  \begin{itemize}
+    \item[\textbf{1}] \textbf{Einführung}
+    \item[\textbf{2}] \textbf{Vom Schaltkreis zum Computer}
+      \begin{itemize}
+        \item[2.1] Logik-Schaltkreise
+        \item[2.2] Binärdarstellung von Zahlen
+        \item[2.3] Vom Logik-Schaltkreis zum Addierer
+        \item[2.4] Negative Zahlen
+        \color{orange}
+        \item[2.5] Vom Addierer zum Computer
+        \item[\dots]
+      \end{itemize}
+    \color{gray}
+    \item[\textbf{3}] \textbf{Architekturmerkmale von Prozessoren}
+    \item[\textbf{4}] \textbf{Der CPU-Stack}
+%    \item[\textbf{5}] \textbf{Hardwarenahe Programmierung}
+%    \item[\textbf{6}] \textbf{Anwender-Software}
+%    \item[\textbf{7}] \textbf{Bus-Systeme}
+%    \item[\textbf{8}] \textbf{Pipelining}
+    \item[\textbf{\dots\hspace{-0.75em}}]
+%    \item[\textbf{9}] \textbf{Ausblick}
+  \end{itemize}
+
+\end{frame}
+
+\end{document}
-- 
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