%--*- latex -*----------------------------------------------------------------- %$Author: saulius $ %$Date: 2020-06-04 14:58:32 +0300 (Thu, 04 Jun 2020) $ %$Revision: 1524 $ %$URL: svn+ssh://saulius-grazulis.lt/home/saulius/svn-repositories/seminarai/2020-verifikacjos-seminarui/slides.tex $ %------------------------------------------------------------------------------ \documentclass[mathserif]{beamer} \usetheme{Warwick} \useoutertheme{infolines} \setbeamertemplate{headline}{} % removes the headline the infolines inserts %\setbeamertemplate{footline}[frame number] \renewcommand\familydefault{\rmdefault} % For XeLaTeX: % https://tex.stackexchange.com/questions/452151/how-do-i-render-the-word-v%C7%ABlundarkvi%C3%B0a-with-bookman-and-xelatex % "Use an OpenType clone of Bookman, for instance TeX Gyre Bonum": \usepackage{fontspec} \setmainfont{TeX Gyre Bonum} \usepackage[style=authoryear,maxnames=1,doi=true,url=true,backend=biber]{biblatex} %\addbibresource{bibliography/citations.bib} \addbibresource{bibliography/Intel.bib} \addbibresource{bibliography/AMD.bib} \addbibresource{bibliography/Jorgensen.bib} \newcommand{\mycite}{\parencite} \usepackage{colordvi} \usepackage{graphicx} \usepackage{tikz} \usetikzlibrary{snakes} \usepackage{verbatim} \usepackage{listings} \usepackage{chemfig} \usepackage{listings} % https://en.wikibooks.org/wiki/LaTeX/Algorithms % http://mirror.datacenter.by/pub/mirrors/CTAN/macros/latex/contrib/algorithmicx/algorithmicx.pdf \usepackage{algpseudocode} \usepackage{algorithm} \usepackage{amssymb} \include{commands} \newcommand{\RCSid}[1]{\fontsize{7pt}{7pt}\selectfont $#1$ \today} %%BEGIN LANGUAGE lt \title{Tarpinio kontrolinio aptarimas} %%END LANGUAGE lt \author{Saulius Gražulis} \date{Vilnius, 2020} % Define colors as in % https://venngage.com/blog/color-blind-friendly-palette/ ``Retro'' \definecolor{Bluish}{HTML}{63ACBE} \definecolor{Magentish}{HTML}{601A4A} \definecolor{Orangish}{HTML}{EE442F} \begin{document} \colorlet{IdentifierColor}{red!40!black} \colorlet{StringColor}{green!70!black} \colorlet{KwdColor}{Bluish} \colorlet{CommentColor}{Orangish} %------------------------------------------------------------------------------ \begin{frame} \titlepage \input{affiliation_lt} \begin{center} \mbox{} \hfill\hfill\hfill \includegraphics[height=1.5cm]{images/sp_VU_zenklas.eps} \hfill \includegraphics[height=1.5cm]{images/2019-05-02_Melynas_MIF-zenklas242x244.png} \hfill\hfill\hfill \mbox{} \end{center} \vfill %% \tiny %% \RCSid{ %% $Id: slides.tex 1524 2020-06-04 11:58:32Z saulius $ %% } \begin{flushright} \begin{minipage}[c]{0.67\textwidth} \tiny\raggedright %%BEGIN LANGUAGE lt Šį skaidrių rinkinį galima kopijuoti, kaip nurodyta Creative Commons %%END LANGUAGE lt \myhref{http://creativecommons.org/licenses/by-sa/4.0/}{Attribution-ShareAlike 4.0 International} licenzijoje \end{minipage} %% \begin{minipage}[c]{1.5cm} \myhref{http://creativecommons.org/licenses/by-sa/4.0/}{ \includegraphics[width=1.5cm]{images/CC-BY-SA.eps} } \end{minipage} \end{flushright} \end{frame} %============================================================================== \begin{frame} \frametitle{XOR ventilis} \begin{center} \parbox[c]{3cm}{ \includegraphics[width=\linewidth]{drawings/logic-gates/XOR-A0-B0.png} } \hspace{1em} \begin{tabular}{cc|c} \textbf{A} & \textbf{B} & \textbf{X} \\ \hline 0 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1 & 1 & 0 \\ \end{tabular} \end{center} Trys interpretacijos: \begin{enumerate} \item Vienas ir tik vienas įėjimas aktyvus \item Nelyginis įėjimų skaičius aktyvus \item Įėjimai nevienodi \end{enumerate} Visos trys interpretacijos sutampa dviejų įėjimų elementui... \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Daugelio įėjimų XOR ventilis} ... bet ne trims ir daugiau įėjimų ... \begin{center} \parbox[c]{3cm}{ \includegraphics[width=\linewidth]{drawings/logic-gates/3-input-XOR-all-1.png} } \footnotesize \begin{tabular}{ccc|c|c|c|} \hline \textbf{A} & \textbf{B} & \textbf{C} & \multicolumn{3}{c|}{ \textbf{X} } \\ \hline &&& Vienas iš 3 & Nelyginis įėjimų sk. & Neekvivalentumas \\ &&& XOR\footnote{\tiny Logisim} & $A \oplus B \oplus C$\footnote{\tiny Lustų gamintojai } & $A \not\equiv B \lor B \not\equiv C$ \\ \hline 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 1 & 1 & 1 & 1 \\ 0 & 1 & 0 & 1 & 1 & 1 \\ 0 & 1 & 1 & 0 & 0 & 1 \\ 1 & 0 & 0 & 1 & 1 & 1 \\ 1 & 0 & 1 & 0 & 0 & 1 \\ 1 & 1 & 0 & 0 & 0 & 1 \\ 1 & 1 & 1 & \bf 0 & \bf 1 & 0 \\ \hline \end{tabular} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Gamintojų interpretacija} $$ A \oplus B \oplus C $$ \begin{center} \includegraphics[page=2,width=9cm,trim=1cm 26cm 1cm 2cm,clip]{images/74LVC1G386-3-input-XOR/74LVC1G386.pdf} \includegraphics[page=2,width=11cm,trim=1cm 6cm 1cm 13cm,clip]{images/74LVC1G386-3-input-XOR/74LVC1G386.pdf} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Gamintojų interpretacija} $$ A \oplus B \oplus C $$ \begin{center} \includegraphics[page=3,width=9cm,trim=1cm 26cm 1cm 2cm,clip]{images/74LVC1G386-3-input-XOR/74LVC1G386.pdf} \includegraphics[page=3,width=11cm,trim=1cm 3cm 1cm 18.5cm,clip]{images/74LVC1G386-3-input-XOR/74LVC1G386.pdf} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Logisim interpretacija} \begin{center} \parbox[c]{3cm}{ \includegraphics[width=\linewidth]{drawings/logic-gates/3-input-XOR-all-1.png} } \parbox[c]{3cm}{ \includegraphics[width=\linewidth]{drawings/logic-gates/3-input-odd-parity-all-1.png} } \parbox[c]{3cm}{ \includegraphics[width=\linewidth]{drawings/logic-gates/3-input-XOR-as-M2-all-1.png} } \end{center} \begin{quote} But if there are more than two specified inputs, the XOR gate will emit 1 only when there is exactly one 1 input, whereas the Odd Parity gate will emit 1 if there are an odd number of 1 inputs. \end{quote} \rightline{\footnotesize\mywebref{http://www.cburch.com/logisim/docs/2.1.0/libs/gates/xor.html}} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Grėjaus kodai} \begin{center} \small \begin{tabular}{cccc} \hline \textbf{ Skaičius } & \textbf{ Grėjaus kodas } & \textbf{ Dvejetainis sk. } \\ \hline 0 & 0000 & 0000 \\ 1 & 0001 & 0001 \\ 2 & 0011 & 0010 \\ 3 & 0010 & 0011 \\ 4 & 0110 & 0100 \\ 5 & 0111 & 0101 \\ 6 & 0101 & 0110 \\ 7 & 0100 & 0111 \\ 8 & 1100 & 1000 \\ 9 & 1101 & 1001 \\ A & 1111 & 1010 \\ B & 1110 & 1011 \\ C & 1010 & 1100 \\ D & 1011 & 1101 \\ E & 1001 & 1110 \\ F & 1000 & 1111 \\ \hline \end{tabular} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Grėjaus kodo panaudojimas} \begin{center} \includegraphics[width=5cm]{images/Gray-code-encoder/Encoder_Disc_3-Bit.eps} \end{center} \rightline{\scriptsize\myhref{https://commons.wikimedia.org/w/index.php?curid=801435}{By jjbeard - Encoder\_disc.png, Public Domain}} \end{frame} %------------------------------------------------------------------------------ \lstset{ keywordstyle=\color{KwdColor}, commentstyle=\color{CommentColor}\ttfamily, identifierstyle=\color{IdentifierColor}, stringstyle=\color{StringColor}, basicstyle=\ttfamily } \begin{frame}[containsverbatim] \frametitle{Asemblerio programos dekodavimas} \begin{center} \begin{minipage}{0.2\textwidth} \lstset{language=[Motorola68k]Assembler,morekeywords={LDC,LD,ADDC,SUBC,JNEG,HALT,OUT}} \begin{lstlisting}[frame=trBL] LDC D1 ST A1 LDC D2 ST A2 LD A1 SUB A2 \end{lstlisting} \end{minipage} \hspace{1em} \begin{minipage}{0.2\textwidth} \lstset{language=[Motorola68k]Assembler,morekeywords={LDC,LD,ADDC,SUBC,JNEG,HALT,OUT}} \begin{lstlisting}[frame=trBL] LDC 12 ST 20 LDC 14 ST 21 LD 20 SUB 21 \end{lstlisting} \end{minipage} \end{center} \begin{minipage}{0.4\textwidth} \scriptsize \begin{itemize} \item $A \leftarrow 12$ \item $A \rightarrow [20] \text{; [20] is now 12}$ \item $A \leftarrow 14$ \item $A \rightarrow [21] \text{; [21] is now 14}$ \item $A \leftarrow [20] \text{; A is now 12} $ \item $A \leftarrow A - [21] \text{; A is now 12 - 14}$ \end{itemize} \end{minipage} \hspace{2em} \begin{minipage}{0.4\textwidth} Atsakymas: $ 12 - 14 = -2 = \mathrm{FFFE}_{16}$ \end{minipage} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Aktyvūs signalai komandos vykdymo metu} Instruction: LDC → opcode: \textbf{02}000B \begin{center} \includegraphics[width=12cm]{drawings/Harvard-CPU-Logisim/data-tract.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Skaičiavimo sistemos pagrindo pakeitimas} \begin{itemize} \item ketvertainė (pagrindu 4) → šešioliktainė $$4^2 = 16$$ \centerline{ \textcolor{gray}{0}1 21 33 10 22$_4$ → 19F4A$_{16}$ } \item dvejetainė → ketvertainė (pagrindu 4) \item trejetainė → devynetainė (pagrindu 9) \end{itemize} \end{frame} %------------------------------------------------------------------------------ %% \begin{frame}%%[allowframebreaks] %% %%LANGUAGE en \frametitle{References} %% %%LANGUAGE lt \frametitle{Šaltiniai} %% %%LANGUAGE ru \frametitle{Источники} %% %% \renewcommand{\bibfont}{\scriptsize} %% \printbibliography %% %% \end{frame} %------------------------------------------------------------------------------ \end{document} % 2020-11-15 19:30:22 EET