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session_4.tex
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\documentclass[11pt]{tudbeamer}
\usetheme{Luebeck}
\usepackage[utf8]{inputenc}
\usepackage{gensymb}
\usepackage{default}
\usepackage{ngerman}
\usepackage{float}
\usepackage{graphicx}
\usepackage{subcaption}
\usepackage{color}
% insert frame number
\expandafter\def\expandafter\insertshorttitle\expandafter{%
\insertshorttitle\hfill%
\insertframenumber\,/\,\inserttotalframenumber}
% Metadata
\title{Rechnerarchitektur 2016}
\subtitle{Session 4}
\author{Fredo Erxleben}
\begin{document}
\maketitle
\begin{frame}{Today}
Learn about:
\begin{itemize}
\item Boolean algebra
\item Boolean logic circuitry
\end{itemize}
\end{frame}
\section{Exercise 1}
\section{Exercise 2}
\section{Exercise 3}
\section{Exercise 4}
\begin{frame}[allowframebreaks]{Exercise 4.1}
A truth table with 2 variables has $2^2 = 4$ rows. \\
This results in $2^4 = 16$ possible result combinations.
\framebreak
\begin{tabular}{lcll}
$x_1$ & 0011 &&\\
$x_0$ & 0101 &&\\
\hline \\
& 0000 & $f_0 = 0$ & Constant 0 \\
& 0001 & $f_1 = x_1 x_0$ & Conjunction (AND) \\
& 0010 & $f_2 = x_1 \bar{x_0}$ & Inhibition \\
& 0011 & $f_3 = x_1$ & Identity \\
& 0100 & $f_4 = \bar{x_1} x_0$ & Inhibition \\
& 0101 & $f_5 = x_0$ & Identity \\
& 0110 & $f_6 = x_1 \oplus x_0$ & Antivalence (XOR) \\
& 0111 & $f_7 = x_1 + x_0$ & Disjunction (OR) \\
\end{tabular}
\framebreak
\begin{tabular}{lcll}
$x_1$ & 0011 &&\\
$x_0$ & 0101 &&\\
\hline \\
& 1000 & $f_8 = \bar{x_1 + x_0}$ & Antidisjunction (NOR) \\
& 1001 & $f_9 = \bar{x_1 \oplus x_0}$& Equivalence (XNOR) \\
& 1010 & $f_10 = \bar{x_0}$ & Negation (NOT) \\
& 1011 & $f_11 = x_1 + \bar{x_0}$ & Implication \\
& 1100 & $f_12 = \bar{x_1}$ & Negation (NOT) \\
& 1101 & $f_13 = \bar{x_1} + x_0$ & Implication \\
& 1110 & $f_14 = \bar{x_1 x_0}$ & Anticonjunction (NAND)\\
& 1111 & $f_15 = 1$ & Constant 1 \\
\end{tabular}
\end{frame}
\begin{frame}{Exercise 4.2}
\begin{itemize}
\item Law of commutation
\item Law of association
\item Law of distribution
\item Law of absorption
\item Neutral element
\item Complementary element
\item DeMorgan's Laws
\end{itemize}
\begin{block}{Principle of duality}
Negating each literal and switching of conjunction and disjunction yields the inverse of the original equation.
\end{block}
\end{frame}
\begin{frame}{Exercise 4.3 \dots 4.7}
$\rightarrow$ Blackboard
\end{frame}
\begin{frame}{Exercise 4.8}
Two possible approaches:\\
\begin{itemize}
\item Algebraic simulation of the circuit (yields truth table)
\item Symbolic calculation of the equation (yields logic formula)
\end{itemize}
Both solutions must yield the same result and can be transformed into one another.
\end{frame}
\section{Wrapping up}
\begin{frame}{Last slide (finally)}
(What do we say to the god of) Homework:
\begin{itemize}
\item Not today
\end{itemize}
\vspace{1em}
Next session we talk about
\begin{itemize}
\item More about logic circuit design
\end{itemize}
\vspace{1em}
\textbf{Also:} Question time!
\end{frame}
\end{document}