%--*- 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/Murdocca.bib} \addbibresource{bibliography/Walker.bib} \addbibresource{bibliography/Fairchild.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} \usepackage{multirow} \include{commands} \newcommand{\RCSid}[1]{\fontsize{7pt}{7pt}\selectfont $#1$ \today} %%BEGIN LANGUAGE lt \title{Generatoriai ir trigeriai} %%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{OnesComplementColor}{Magentish} \colorlet{TwosComplementColor}{Bluish} \colorlet{TwoToNthColor}{Orangish} \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{Papildomojo kodo gavimas} \begin{center} papildomasis kodas: \textcolor{TwosComplementColor}{$ 2^N - b $} \only<1>{\color{white}} \vfill \vfill \begin{tabular}{lllllll} \multirow{2}{*}{$-$} & 1 & 0 & 0 & 0 & 0 \\ & & $b_3$ & $b_2$ & $b_1$ & $b_0$ \\ \cline{1-6} & & \only<2->{\color{TwosComplementColor}} $c_3$ & \only<2->{\color{TwosComplementColor}} $c_2$ & \only<2->{\color{TwosComplementColor}} $c_1$ & \only<2->{\color{TwosComplementColor}} $c_0$ & \scriptsize \only<2->{\color{TwosComplementColor}} $\leftarrow$ papildomasis kòdas \end{tabular} \vfill \vfill \only<1-2>{\color{white}} $ \only<3->{\textcolor{TwosComplementColor}{2^N - b}} = (2^N-1) - b + 1 $ \only<1-3>{\color{white}} \vfill $ 1\,0000_2 = 1111_2 + 1 $ \vfill \vfill \only<1-4>{\color{white}} \begin{tabular}{lllllll} \multirow{2}{*}{$-$} & 0 & 1 & 1 & 1 & 1 & \footnotesize $\leftarrow (2^N-1)$ \\ & & $b_3$ & $b_2$ & $b_1$ & $b_0$ \\ \cline{1-6} \\ \multirow{2}{*}{$+$} & & \only<5->{\color{OnesComplementColor}} $\overline{b_3}$ & \only<5->{\color{OnesComplementColor}} $\overline{b_2}$ & \only<5->{\color{OnesComplementColor}} $\overline{b_1}$ & \only<5->{\color{OnesComplementColor}} $\overline{b_0}$ & \scriptsize \only<5->{\color{OnesComplementColor}} $\leftarrow$ atvirkštinis kòdas \\ & & & & & 1 \\ \cline{1-6} & & \only<5->{\color{TwosComplementColor}} $c_3$ & \only<5->{\color{TwosComplementColor}} $c_2$ & \only<5->{\color{TwosComplementColor}} $c_1$ & \only<5->{\color{TwosComplementColor}} $c_0$ & \scriptsize \only<5->{\color{TwosComplementColor}} $\leftarrow$ papildomasis kòdas \\ \end{tabular} \only<1-5>{\color{white}} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Papildinio iki 2 pavyzdys} \begin{center} $ 10_2 - 11_2 = \text{???} $ \vfill Raskime dviejų papildinį skaičiui $11_2$: \vfill \begin{tabular}{lllllll} \multirow{2}{*}{$-$} & 0 & 1 & 1 & 1 & 1 & \footnotesize $\leftarrow (2^N-1)$ \\ & & 0 & 0 & 1 & 1 \\ \cline{1-6} \\ & & \color{OnesComplementColor} $\overline{\mathrm{0}}$ & \color{OnesComplementColor} $\overline{\mathrm{0}}$ & \color{OnesComplementColor} $\overline{\mathrm{1}}$ & \color{OnesComplementColor} $\overline{\mathrm{1}}$ & \\ \multirow{2}{*}{$+$} & & \color{OnesComplementColor} 1 & \color{OnesComplementColor} 1 & \color{OnesComplementColor} 0 & \color{OnesComplementColor} 0 & \scriptsize \color{OnesComplementColor} $\leftarrow$ atvirkštinis kodas \\ & & & & & 1 \\ \cline{1-6} & & \color{TwosComplementColor} 1 & \color{TwosComplementColor} 1 & \color{TwosComplementColor} 0 & \color{TwosComplementColor} 1 & \scriptsize \color{TwosComplementColor} $\leftarrow$ papildomasis kodas \\ \end{tabular} \vfill $ 10_2 - 11_2 = 0010_2 + 1101_2 = 1111_2 = -1_2 $ \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Dviejų papildinio pavertimas į dešimtinę sistemą} \begin{center} \begin{tabular}{cc||cc} Dec. & 2's Compl. & Dec. & 2's Compl. \\ \hline 7 & 0111 & -1 & \only<2>{\bf}1\only<2>{\rm}111 \\ 6 & 0110 & -2 & \only<2>{\bf}1\only<2>{\rm}110 \\ 5 & 0101 & -3 & \only<2>{\bf}1\only<2>{\rm}101 \\ 4 & 0100 & -4 & \only<2>{\bf}1\only<2>{\rm}100 \\ 3 & 0011 & -5 & \only<2>{\bf}1\only<2>{\rm}011 \\ 2 & 0010 & -6 & \only<2>{\bf}1\only<2>{\rm}010 \\ 1 & 0001 & -7 & \only<2>{\bf}1\only<2>{\rm}001 \\ 0 & 0000 & \only<4>{\bf}-8 & \only<2,4>{\bf}1\only<2>{\rm}000 \\ \hline \end{tabular} \end{center} \only<2-3>{ Vyriausias neigiamo skaičiaus bitas (MSB) yra \textbf{1} } \only<3>{ %%BEGIN LANGUAGE lt Mažiausio atvaizduojamo neigiamo skaičiaus modulis yra \textit{didesnis} už didžiausio atvaizduojamo teigiamo. %%END LANGUAGE lt } \only<4->{ $$ \begin{aligned} 1011_2 = 1000_2 + 0011_2 &= -2^3 + 11_2 \\ &= \overset{\textcolor{TwoToNthColor}{-2^3}}{1}\; \overset{\textcolor{TwoToNthColor}{2^2}}{0}\; \overset{\textcolor{TwoToNthColor}{2^1}}{1}\; \overset{\textcolor{TwoToNthColor}{2^0}}{1} \\ &= -2^3 + 2^1 + 2^0 = -8_{10} + 2_{10} + 1_{10} \\ &= -5_{10} \\ \end{aligned} $$ } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Sudėties-atimties ALĮ} \begin{center} \small \only<1>{ $ 7_{10} + 3_{10} = 0111_2 + 0011_2 = 1010_2 = 10_{10} $ } \only<2>{ $ 7_{10} - 3_{10} = 0111_2 - 0011_2 = 0111_2 + 1101_2 = \textcolor{gray}{1}\;0100_2 = 4_{10} $ } \end{center} \begin{center} \scriptsize \begin{tikzpicture} \node(ALU) { \begin{minipage}{4cm} \only<1>{ \begin{center} \includegraphics[height=6cm]{drawings/adders/adder-subtractor-7+3.png} \end{center} } \only<2>{ \begin{center} \includegraphics[height=6cm]{drawings/adders/adder-subtractor-7-3.png} \end{center} } \end{minipage} }; \node (FA) at (2cm,2.5cm) { Pilni sumatoriai }; \draw [thick,->] (node cs:name=FA) -- (1cm,1.8cm); \node [text width=3cm,align = right] (AddSubCtrl) at (-3.3cm,2.8cm) { $\overline{\text{Sudėti}}/\text{Atimti}$ }; \node [ text width=3cm,align = right] (FirstLSB) at ( -3.4cm,1.85cm ) { Pirmo operando jauniausias bitas }; \node [text width=3cm,align = right] (SecondLSB) at ( -3.4cm,1.0cm ) { Antro operando jauniausias bitas }; \node [text width=3cm,align = right] (FirstMSB) at ( -3.4cm,-1.9cm ) { Pirmo operando vyriausias bitas }; \node [text width=3cm,align = right] (SecondMSB) at ( -3.4cm,-2.7cm ) { Antro operando vyriausias bitas }; \node (Out) at ( 2.5cm,0cm ) { \begin{minipage}{3cm} $$ \left. \begin{array}{l} \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \\ \end{array} \right\}\text{ Išvestis } $$ \end{minipage} }; \node [text width=3cm,align = left] (Cout) at (2.5cm,-3cm) { Išvesties perkėlimas }; \end{tikzpicture} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Kiti neigiamų skaičių atvaizdavimai} Ženklas/modulis: $$ 6_{10} = 0110_2 \text{;}\quad -6_{10} = 1110_2 $$ Papildinių aritmetika: $$ a + (-b) = a + \color{TwosComplementColor} \underbrace{ \color{OnesComplementColor} \underbrace{ ((2^N-1) - b) }_{ \text{one's complement} } \color{TwosComplementColor} + \: 1 }_{ \text{ \color{TwosComplementColor} 2's complement } } \color{black} - \;\textcolor{TwoToNthColor}{2^N} $$ Aritmetika su postūmiu $K$: $$ \begin{array}{r@{\:}c@{\;}l} K = & 2^{N-1} & \ \text{ \raisebox{0.15em}{ \footnotesize (kaip taisyklė, bet galimos ir kitos reikšmės) } } \\ b \leftrightarrow & K + b &= 2^{N-1} + b \\ -b \leftrightarrow & K + (-b) &= 2^{N-1} + (-b) \\ \end{array} $$ \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Kiti neigiamų skaičių atvaizdavimai} \scriptsize \begin{center} \begin{tabular}{|r|c|c|c|c|c|} \hline Skaičius & Be ženklo & Pap.\ iki 2 & Pap.\ iki 1 & $\pm$Modulis & Postūmis \footnote{$K = 4 = 2^{N-1}$, $N=3$} K \\ \hline 7 & 111 & - & - & - & - \\ 6 & 110 & - & - & - & - \\ 5 & 101 & - & - & - & - \\ 4 & 100 & - & - & - & - \\ 3 & 011 & 011 & 011 & 011 & 111 \\ 2 & 010 & 010 & 010 & 010 & 110 \\ 1 & 001 & 001 & 001 & 001 & 101 \\ 0 & 000 & 000 & 000 & 000 & 100 \\ -0 & - & - & 111 & 100 & - \\ -1 & - & 111 & 110 & 101 & 011 \\ -2 & - & 110 & 101 & 110 & 010 \\ -3 & - & 101 & 100 & 111 & 001 \\ -4 & - & 100 & - & - & 000 \\ \hline \end{tabular} \end{center} { \raggedleft \scriptsize See also:\\ \cite{Murdocca1999}, chapt.\ 2; \\ \cite{Walker1996}, ``Minus Zero'' \\ } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Generatoriai} \begin{center} \includegraphics[page=2,width=11cm,trim=4cm 22cm 4cm 3.7cm,clip]{bibliography/PDF/AN-118.pdf} \visible<2>{ \vspace{-\baselineskip} \parbox{8cm}{ \small ``It then becomes obvious that a “1” chases itself around the ring and the network oscillates.'' :) } } \vspace{0.5\baselineskip} %%\includegraphics[page=2,width=8cm,trim=11cm 18cm 4cm 6cm,clip]{bibliography/PDF/AN-118.pdf} \includegraphics[page=2,width=8cm,trim=11cm 18cm 4cm 7cm,clip]{bibliography/PDF/AN-118.pdf} \end{center} \flushright{\scriptsize\mycite{FairchildSemiconductor1974}} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Žiedinis generatorius} \begin{center} \includegraphics[page=2,width=8cm,trim=11cm 18cm 4cm 7cm,clip]{bibliography/PDF/AN-118.pdf} \end{center} \only<1>{ \begin{center} \includegraphics[width=6cm]{drawings/oscillators/ring-oscillator-error-state.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=6cm]{drawings/oscillators/interrupted-ring-oscillator-input0.png} \end{center} } \only<3>{ \begin{center} \includegraphics[width=6cm]{drawings/oscillators/interrupted-ring-oscillator-input1.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \newlength{\imagewdth} \setlength{\imagewdth}{9cm} \begin{frame} \frametitle{Taktinis generatorius} \only<1,8>{ \begin{center} \includegraphics[page=2,height=3cm,trim=11cm 18cm 4cm 7cm,clip]{bibliography/PDF/AN-118.pdf} \end{center} } \only<2,4,6>{ \begin{center} \includegraphics[height=3cm]{drawings/oscillators/interrupted-ring-oscillator-input1.png} \end{center} } \only<3,5,7>{ \begin{center} \includegraphics[height=3cm]{drawings/oscillators/interrupted-ring-oscillator-input0.png} \end{center} } \only<1>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-start.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse1.png} \end{center} } \only<3>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse1a.png} \end{center} } \only<4>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse2.png} \end{center} } \only<5>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse2a.png} \end{center} } \only<6>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse3.png} \end{center} } \only<7>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse3a.png} \end{center} } \only<8>{ \begin{center} \includegraphics[width=\imagewdth]{drawings/oscillators/oscillator+oscilloscope-pulse9a.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Lyginis inverterių skaičius} \only<1>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/stable-inverter-ring-out0.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/stable-inverter-ring-out1.png} \end{center} } \only<3>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/stable-inverter-ring-out0-inp-OK.png} \end{center} } \only<4>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/stable-inverter-ring-out0-inp-ERROR.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Lyginis inverterių skaičius} \framesubtitle{Būsenos nustatymas} \only<1,5>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-as-an-inverter-ring-hold0.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-as-an-inverter-ring-set1.png} \end{center} } \only<3>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-as-an-inverter-ring-hold1.png} \end{center} } \only<4>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-as-an-inverter-ring-set0.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{RS trigeris iš ARBA-NE ventilių} \only<1>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-as-a-NOR-ring-hold1.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=7cm]{drawings/triggers/RS-trigger-NOR-hold1.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{RS trigeris iš ARBA-NE arba IR-NE ventilių} \begin{center} \parbox[c]{4cm}{ \includegraphics[width=\linewidth]{drawings/triggers/RS-trigger-NOR-hold1.png} } \hspace{1em} \parbox[c]{4cm}{ \includegraphics[width=\linewidth]{drawings/triggers/RS-trigger-hold-1.png} } \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{RS trigeris} \begin{center} \begin{tabular}{c|c|c|c|c|l} \textbf{S} & \textbf{R} & $\mathrm{\mathbf{\overline{S}}}$ & $\mathrm{\mathbf{\overline{R}}}$ & \textbf{Q} \\ \hline 0 & 0 & 1 & 1 & Q & \visible<1,3,5>{$\leftarrow$} \\ 0 & 1 & 1 & 0 & 0 & \visible<2>{$\leftarrow$} \\ 1 & 0 & 0 & 1 & 1 & \visible<4>{$\leftarrow$} \\ 1 & 1 & 0 & 0 & X & \\ \end{tabular} \end{center} \begin{center} \renewcommand{\arraystretch}{1.1} \begin{tabular}{rcl} & \multirow{6}{*}{ \parbox[c]{3.8cm}{ \rule{0pt}{0.6\baselineskip} % Positioning images as described in % https://stackoverflow.com/questions/4683093/beamer-how-to-show-images-as-step-by-step-images: \includegraphics<1,5>[width=\linewidth]{drawings/triggers/RS-trigger-hold-1.png} \includegraphics<2>[width=\linewidth]{drawings/triggers/RS-trigger-set-0.png} \includegraphics<3>[width=\linewidth]{drawings/triggers/RS-trigger-hold-0.png} \includegraphics<4>[width=\linewidth]{drawings/triggers/RS-trigger-set-1.png} } } & \\ $\mathrm{\mathbf{\overline{S}}}$ & & $\mathrm{\mathbf{Q}}$ \\ \\ \\ \\ $\mathrm{\mathbf{\overline{R}}}$ & & $\mathrm{\mathbf{\overline{Q}}}$ \\ \end{tabular} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{RS trigerio įtampos epiūros} \begin{center} \includegraphics[width=9cm]{drawings/triggers/RS-trigger+oscilloscope-F1F2.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{RS trigerio įtampos epiūros} \begin{center} \includegraphics[width=11cm]{drawings/triggers/RS-trigger-skip-3rd+oscilloscope-14states.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Valdomas RS trigeris} \begin{center} \parbox[c]{6cm}{ \includegraphics[width=\linewidth]{drawings/triggers/RS-gated-trigger-hold-0.png} } \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{D trigeris (užsklanda)} \only<1>{ \begin{center} \includegraphics[width=6cm]{drawings/triggers/D-latch-hold-1.png} \end{center} } \only<2>{ \begin{center} \includegraphics[width=6cm]{drawings/triggers/D-latch-optimised-hold-1.png} \end{center} } \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{MS D trigeris (valdomas frontu)} \begin{center} \includegraphics<1>[height=3cm]{drawings/triggers/MS-D-flip-flop-hold-1.png} \includegraphics<2>[height=4cm]{drawings/triggers/D-MS-gated-flip-flop-from-JK-hold1.png} \end{center} \begin{center} \parbox{1.5cm}{ \includegraphics[width=\linewidth]{drawings/triggers/D-trigger-symbol-Logisim-ITA.png} } \hspace{1em} \parbox{2cm}{ \includegraphics[width=\linewidth]{drawings/triggers/D-trigger-symbol-Logisim-classic.png} } \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{MS D trigerio veikimas} \begin{center} \includegraphics[height=6cm]{drawings/triggers/D-flip-flop+oscilloscope.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{T trigeris} \begin{center} \includegraphics[height=4cm]{drawings/triggers/MS-T-flip-flop-hold-0.png} \end{center} \begin{center} \parbox{1.5cm}{ \includegraphics[width=\linewidth]{drawings/triggers/T-trigger-symbol-Logisim-ITA.png} } \hspace{1em} \parbox{2cm}{ \includegraphics[width=\linewidth]{drawings/triggers/T-trigger-symbol-Logisim-classic.png} } \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{T trigerio veikimas} \begin{center} \includegraphics[height=6cm]{drawings/triggers/T-flip-flop+oscilloscope.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Registrai} \begin{center} \includegraphics[height=4cm]{drawings/registers/data-register-4-bit-from-D-triggers-0101.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Skaitliukai} \begin{center} \includegraphics[height=3cm]{drawings/counters/counter-4-bit-from-T-triggers-1011.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Postūmio registrai} \begin{center} \includegraphics[height=2cm]{drawings/registers/shift-register-from-D-triggers.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Žiediniai postūmio registrai} \begin{center} \includegraphics[height=4cm]{drawings/registers/circular-shift-register-from-D-triggers.png} \vspace{\baselineskip} \includegraphics[height=2cm]{drawings/registers/logisim-evolution/circular-shift-register-from-D-triggers-chronogram-cut2.png} \end{center} \end{frame} %------------------------------------------------------------------------------ \begin{frame} \frametitle{Apibendrinimas} \begin{itemize} \item %%BEGIN LANGUAGE lt Neigiami sveiki skaičiai šiuolaikiniuose kompiuteriuose atvaizduojami papildomuoju kodu, bet įmanomi ir kiti atvaizdavimo metodai. %%END LANGUAGE lt \item %%BEGIN LANGUAGE lt Šiuolaikiniai kompiuteriai yra sinchroniniai – jie naudoja taktų generatorių visos grandinėms valdyti. %%END LANGUAGE lt \item %%BEGIN LANGUAGE lt Generatoriams ir atminties ląstelėms būtinas grįžtamasis ryšys. %%END LANGUAGE lt \item %%BEGIN LANGUAGE lt Iš pagrindinės RS trigerio schemos padaromos D- ir T- trigerių schemos, valdomos signalo lygiu arba frontu. %%END LANGUAGE lt \item %%BEGIN LANGUAGE lt Iš D- ir T-trigerių toliau konstruojami registrai ir skaitikliai – esminiai kompiuterių mazgai. %%END LANGUAGE lt \end{itemize} \end{frame} %------------------------------------------------------------------------------ \begin{frame}%%[allowframebreaks] \frametitle{Šaltiniai} \renewcommand{\bibfont}{\scriptsize} \printbibliography \end{frame} %------------------------------------------------------------------------------ \end{document} % 2020-10-05 09:17:02 EEST