%--*- 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 $
%------------------------------------------------------------------------------

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% 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":
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\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}

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\usepackage{amssymb}
\usepackage{multirow}

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\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
