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o1KCI&&}qN?kUjZoNdEzirB9xh{bK_h3^_P4F*OP$B}Gq03TD(d-v9sr diff --git a/presentation.tex b/presentation.tex index ca01081..eae7d95 100644 --- a/presentation.tex +++ b/presentation.tex @@ -22,7 +22,7 @@ \usepackage{tcolorbox,listings} \usepackage{textpos} \usepackage{setspace} -\usepackage{circuitikz} +\usepackage{circuitikzgit} \usetikzlibrary{positioning} % Default fixed font does not support bold face @@ -154,7 +154,7 @@ showstringspaces=false % -\section{Boolean logic} +\section{Boolean logic and basic gates} \begin{frame}{Basic logic operation} \begin{itemize} \item Two states \textbf{TRUE} and \textbf{FALSE} @@ -212,56 +212,20 @@ showstringspaces=false % \end{itemize} \end{frame} -\begin{frame}{Basic gate functionality with push buttons} -\begin{minipage}{0.3\textwidth} -% AND gate - \ctikzset{bipoles/resistor/height=.2} -\textbf{AND gate}\\ -\begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - \draw (0,-3.5) node[pushbuttonshape,rotate=90](A) {\textbf{A}}; - \draw (0,-4.5) node[pushbuttonshape,rotate=90](B) {\textbf{B}}; - \draw (0,-1) node[](Y) {}; - \draw (0, -6) node[ground](GND) {}; - - \draw (VCC) to[R] (Y) to[empty led,name=OUT] (A.east) (A.west) -- (B.east) (B.west) -- (GND); - \node[left] at (OUT.south) {\textbf{Y}}; -\end{circuitikz} -\end{minipage}% -\begin{minipage}{0.3\textwidth} -\textbf{OR gate}\\ -\begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - - \draw (-1, -3) node (TL) {}; - \draw (1, -3) node (TR) {}; - \draw ($(TL)!0.5!(TR)$) node (INT1) {}; - \draw (-1, -5) node (BL) {}; - \draw (1, -5) node (BR) {}; - \draw ($(BL)!0.5!(BR)$) node (INT2) {}; - - \node (Y) at ($(VCC)!0.5!(INT1)$) {}; - - \draw (0, -6) node[ground](GND) {}; - - \draw ($(TL)!0.5!(BL)$) node[pushbuttonshape,rotate=90](A) {\textbf{A}}; - \draw ($(TR)!0.5!(BR)$) node[pushbuttonshape,rotate=90](B) {\textbf{B}}; - - \draw (VCC) to [R] (Y) to[empty led, name=OUT] (INT1.center); - \draw (INT1.center) -- (TL.center); - \draw (INT1.center) -- (TR.center); - \draw (TL.center) -- (A) -- (BL.center); - \draw (TR.center) -- (B) -- (BR.center); - \draw (BR.center) -- (INT2.center); - \draw (BL.center) -- (INT2.center); - \draw (INT2.center) -- (GND); - - \node[left] at (OUT.south) {\textbf{Y}}; -\end{circuitikz} -\end{minipage} -\begin{minipage}{0.3\textwidth} - \textbf{NOT gate\\ (inverter)}\\ - \begin{circuitikz} +\begin{frame}{Breadboard} + \vspace{1cm} + \begin{overlayarea}{\textwidth}{\textheight} + \begin{flushleft} +\includegraphics[scale=0.45]{images/Breadboard.jpg}\\ +\includegraphics<2>[scale=0.5]{images/Breadboard-Pinout.png} + \end{flushleft} + \end{overlayarea} +\end{frame} + +\begin{frame}{NOT gate (inverter)} + \begin{minipage}{0.6\textwidth} + \only<1>{ + \begin{circuitikz} \draw (0,0) node[vcc](VCC){5 V}; \draw (-1, -3) node (TL) {}; @@ -273,124 +237,209 @@ showstringspaces=false % \draw (0, -6) node[ground](GND) {}; - \draw ($(TL)!0.5!(BL)$) node[pushbuttonshape,rotate=90](A) {\textbf{A}}; + \draw ($(TL)!0.5!(BL)$) node[pushbuttonshape,rotate=90](P1) {}; + \draw ([xshift=-0.3cm]P1) node[] (A) {}; + \draw ($(TR)!0.5!(BR)$) node[emptylediodeshape, rotate=-90](B) {}; \draw (VCC) to[R] (INT1.center); \draw (INT1.center) -- (TL.center); \draw (INT1.center) -- (TR.center); - \draw (TL.center) -- (A) -- (BL.center); + \draw (TL.center) -- (P1) (P1) -- (BL.center); \draw (TR.center) -- (B) -- (BR.center); \draw (BR.center) -- (INT2.center); \draw (BL.center) -- (INT2.center); \draw (INT2.center) -- (GND); + \node[left] at (A) {\textbf{A}}; \node[left] at (B.south) {\textbf{Y}}; \end{circuitikz} -\end{minipage} + } + \only<2>{ + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + + \draw (-1, -3) node (TL) {}; + \draw (1, -3) node (TR) {}; + \draw ($(TL)!0.5!(TR)$) node (INT1) {}; + \draw (-1, -5) node (BL) {}; + \draw (1, -5) node (BR) {}; + \draw ($(BL)!0.5!(BR)$) node (INT2) {}; + + \draw (0, -6) node[ground](GND) {}; + + \draw ($(TL)!0.5!(BL)$) node[npn](P1) {}; + \draw ([xshift=-3cm]P1) node[] (A) {}; + + \draw ($(TR)!0.5!(BR)$) node[emptylediodeshape, rotate=-90](B) {}; + + \draw (VCC) to[R] (INT1.center); + \draw (INT1.center) -- (TL.center); + \draw (INT1.center) -- (TR.center); + \draw (TL.center) -- (P1.C) (P1.E) -- (BL.center); + \draw (TR.center) -- (B) -- (BR.center); + \draw (BR.center) -- (INT2.center); + \draw (BL.center) -- (INT2.center); + \draw (INT2.center) -- (GND); + + \draw (A) to[R,o-] (P1.B); + \node[left] at (A) {\textbf{A}}; + \node[left] at (B.south) {\textbf{Y}}; + \end{circuitikz} + } + \only<3->{ + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + + \draw (-1, -3) node (TL) {}; + \draw (1, -3) node (TR) {}; + \draw ($(TL)!0.5!(TR)$) node (INT1) {}; + \draw (-1, -5) node (BL) {}; + \draw (1, -5) node (BR) {}; + \draw ($(BL)!0.5!(BR)$) node (INT2) {}; + + \draw (0, -6) node[ground](GND) {}; + + \draw ($(INT1)!0.5!(INT2)$) node[npn](P1) {}; + \draw ([xshift=-3cm]P1) node[] (A) {}; + + \draw (VCC) to[R] (INT1.center); + \draw (INT1.center) to[short,-o] (TR.center); + \draw (INT1.center) -- (P1.C); + \draw (P1.E) -- (INT2.center); + \draw (INT2.center) -- (GND); + + \draw (A) to[R,o-] (P1.B); + \node[left] at (A) {\textbf{A}}; + \node[right] at (TR.center) {\textbf{Y}}; + \end{circuitikz} + } + \end{minipage}% + \begin{minipage}{0.4\textwidth} + \begin{tabular}{c|c} + A & Y\\ + \hline + 0 & 1 \\ + 1 & 0 + \end{tabular}\\[1cm] + \onslide<3>{ + {Symbol}:\\ + \begin{circuitikz} + \draw (0,0) node[not port] (NOT) {}; + \draw (NOT.in) ++ (-1,0) node (A) {}; + \draw (NOT.out) ++ (1,0) node (Y) {}; + \draw (NOT.in) to[short,-o] (A); + \draw (NOT.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[right] at (Y) {\textbf{Y}}; + + \end{circuitikz} + } + \end{minipage} \end{frame} -\begin{frame}{Breadboard} - \vspace{1cm} +\begin{frame}{AND gate} \begin{overlayarea}{\textwidth}{\textheight} - \begin{flushleft} -\includegraphics[scale=0.45]{images/Breadboard.jpg}\\ -\includegraphics<2>[scale=0.5]{images/Breadboard-Pinout.png} - \end{flushleft} + \begin{minipage}{0.6\textwidth} + \only<1>{ + \hspace{2.5cm} + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + \draw (0,-1) node[pushbuttonshape,rotate=90](A) {\textbf{A}}; + \draw (0,-2.5) node[pushbuttonshape,rotate=90](B) {\textbf{B}}; + \draw (0,-4.5) node[](Y) {}; + \draw (0, -6) node[ground](GND) {}; + + \draw (VCC) -- (A.east) (A.west) -- (B.east) (B.west) to[empty led,name=OUT] (Y) to[R] (GND); + \node[left] at (OUT.south) {\textbf{Y}}; + \end{circuitikz} + } + \only<2>{ + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + \draw (-3, -1) node (A) {}; + \draw (-3, -2.5) node (B) {}; + \draw (0,-1) node[npn](P1) {}; + \draw (0,-2.5) node[npn](P2) {}; + \draw (0, -6) node[ground](GND) {}; + + \draw (A) to[R,o-] (P1.B); + \draw (B) to[R,o-] (P2.B); + \draw (VCC) -- (P1.C) (P1.E) -- (P2.C) (P2.E) to[empty led, name=OUT] (0,-4.5) to[R] (GND); + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (OUT.nw) {\textbf{Y}}; + \end{circuitikz} + } + \only<3->{ + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + \draw (-3, -1) node (A) {}; + \draw (-3, -2.5) node (B) {}; + \draw (1, -4) node (Y) {}; + \draw (0,-1) node[npn](P1) {}; + \draw (0,-2.5) node[npn](P2) {}; + \draw (0, -6) node[ground](GND) {}; + + \draw (A) to[R,o-] (P1.B); + \draw (B) to[R,o-] (P2.B); + \draw (VCC) -- (P1.C) (P1.E) -- (P2.C) (P2.E) -- (0,-4.5) to[R] (GND); + \draw (0,-4) to[short,-o] (Y); + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + \end{circuitikz} + } + \end{minipage}% + \begin{minipage}{0.4\textwidth} + \begin{tabular}{cc|c} + A & B & Y\\ + \hline + 0 & 0 & 0 \\ + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + 1 & 1 & 1 \\ + \end{tabular}\\[1cm] + \onslide<4>{ + {Symbol}:\\ + \begin{circuitikz} + \draw (0,0) node[and port] (AND) {}; + \draw (AND.in 1) ++ (-1,0) node (A) {}; + \draw (AND.in 2) ++ (-1,0) node (B) {}; + \draw (AND.out) ++ (1,0) node (Y) {}; + \draw (AND.in 1) to[short,-o] (A); + \draw (AND.in 2) to[short,-o] (B); + \draw (AND.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + + \end{circuitikz} + } + \end{minipage} \end{overlayarea} \end{frame} -\begin{frame}{Basic gates with transistors} - \begin{overlayarea}{\textwidth}{\textheight} -\textbf{AND gate}\\ -\begin{minipage}{0.4\textwidth} -\only<1>{ + + +\begin{frame}{OR gate} +\begin{overlayarea}{\textwidth}{\textheight} +\begin{minipage}{0.6\textwidth} + \only<1>{ \begin{circuitikz} \draw (0,0) node[vcc](VCC){5 V}; - \draw (0,-3.5) node[pushbuttonshape,rotate=90](A) {\textbf{A}}; - \draw (0,-4.5) node[pushbuttonshape,rotate=90](B) {\textbf{B}}; - \draw (0,-1) node[](Y) {}; \draw (0, -6) node[ground](GND) {}; - - \draw (VCC) to[R] (Y) to[empty led,name=OUT] (A.east) (A.west) -- (B.east) (B.west) -- (GND); - \node[left] at (OUT.south) {\textbf{Y}}; - \end{circuitikz} -} -\only<2>{ - \begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - \draw (-3, -3) node (A) {}; - \draw (-3, -4.5) node (B) {}; - \draw (0,-3) node[npn](P1) {}; - \draw (0,-4.5) node[npn](P2) {}; - \draw (0, -5.5) node[ground](GND) {}; - - \draw (A) to[R,o-] (P1.B); - \draw (B) to[R,o-] (P2.B); - \draw (VCC) to[R] (0,-1.75) to[empty led, name=OUT] (P1.C) (P1.E) -- (P2.C) (P2.E) -- (GND); - \node[left] at (A) {\textbf{A}}; - \node[left] at (B) {\textbf{B}}; - \node[right] at (OUT.nw) {\textbf{Y}}; - \end{circuitikz} -} -\only<3->{ - \begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - \draw (-3, -3) node (A) {}; - \draw (-3, -4.5) node (B) {}; - \draw (2, -1.75) node (Y) {}; - \draw (0,-3) node[npn](P1) {}; - \draw (0,-4.5) node[npn](P2) {}; - \draw (0, -5.5) node[ground](GND) {}; - - \draw (A) to[R,o-] (P1.B); - \draw (B) to[R,o-] (P2.B); - \draw (VCC) to[R] (0,-1.75) -- (P1.C) (P1.E) -- (P2.C) (P2.E) -- (GND); - \draw (0,-1.75) to[short,-o] (Y); - \node[left] at (A) {\textbf{A}}; - \node[left] at (B) {\textbf{B}}; - \node[right] at (Y) {\textbf{Y}}; - \end{circuitikz} -} -\end{minipage}% -\begin{minipage}{0.4\textwidth} - \vspace{3cm} - \only<4>{ - {Symbol}: - \begin{circuitikz} - \draw (0,0) node[and port] (AND) {}; - \draw (AND.in 1) ++ (-1,0) node (A) {}; - \draw (AND.in 2) ++ (-1,0) node (B) {}; - \draw (AND.out) ++ (1,0) node (Y) {}; - \draw (AND.in 1) to[short,-o] (A); - \draw (AND.in 2) to[short,-o] (B); - \draw (AND.out) to[short,-o] (Y); - - \node[left] at (A) {\textbf{A}}; - \node[left] at (B) {\textbf{B}}; - \node[right] at (Y) {\textbf{Y}}; - - \end{circuitikz} -} -\end{minipage} -\end{overlayarea} -\end{frame} -\begin{frame}{Basic gates with transistors} -\begin{minipage}{0.5\textwidth} - \textbf{OR gate}\\ - \begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - - \draw (-1, -3) node (TL) {}; - \draw (1, -3) node (TR) {}; + + \draw (-1, -1.0) node (TL) {}; + \draw (1, -1.0) node (TR) {}; \draw ($(TL)!0.5!(TR)$) node (INT1) {}; - \draw (-1, -5.5) node (BL) {}; - \draw (1, -5.5) node (BR) {}; + \draw (-1, -3.5) node (BL) {}; + \draw (1, -3.5) node (BR) {}; \draw ($(BL)!0.5!(BR)$) node (INT2) {}; - \node (Y) at ($(VCC)!0.5!(INT1)$) {}; - - \draw (0, -6) node[ground](GND) {}; + \node (Y) at ($(INT2)!0.5!(GND)$) {}; \draw ($(TL)!0.3!(BL)$) node[npn](P1) {}; \draw ([xshift=-3cm]P1) node[] (A) {}; @@ -398,14 +447,14 @@ showstringspaces=false % \draw ($(TR)!0.7!(BR)$) node[npn](P2) {}; \draw ([xshift=-5cm]P2) node (B) {}; - \draw (VCC) to [R] (Y) to[empty led, name=OUT] (INT1.center); + \draw (VCC) -- (INT1.center); \draw (INT1.center) -- (TL.center); \draw (INT1.center) -- (TR.center); \draw (TL.center) -- (P1.C) (P1.E) -- (BL.center); \draw (TR.center) -- (P2.C) (P2.E) -- (BR.center); \draw (BR.center) -- (INT2.center); \draw (BL.center) -- (INT2.center); - \draw (INT2.center) -- (GND); + \draw (INT2.center) to[empty led, name=OUT] (Y) to [R] (GND); \draw (A) to[R,o-] (P1.B); \draw (B) to[R,o-] (P2.B); @@ -413,77 +462,580 @@ showstringspaces=false % \node[left] at (B) {\textbf{B}}; \node[left] at (OUT.south) {\textbf{Y}}; \end{circuitikz} -\end{minipage} +} + \only<2->{ + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + + \draw (0, -6) node[ground](GND) {}; + + \draw (-1, -1.0) node (TL) {}; + \draw (1, -1.0) node (TR) {}; + \draw ($(TL)!0.5!(TR)$) node (INT1) {}; + \draw (-1, -3.5) node (BL) {}; + \draw (1, -3.5) node (BR) {}; + \draw ($(BL)!0.5!(BR)$) node (INT2) {}; + \node (Y) at ($(INT2)!0.5!(GND)$) {}; + \draw (Y.north) ++ (1,0) node (OUT) {}; + + + \draw ($(TL)!0.3!(BL)$) node[npn](P1) {}; + \draw ([xshift=-3cm]P1) node[] (A) {}; + + \draw ($(TR)!0.7!(BR)$) node[npn](P2) {}; + \draw ([xshift=-5cm]P2) node (B) {}; + + \draw (VCC) -- (INT1.center); + \draw (INT1.center) -- (TL.center); + \draw (INT1.center) -- (TR.center); + \draw (TL.center) -- (P1.C) (P1.E) -- (BL.center); + \draw (TR.center) -- (P2.C) (P2.E) -- (BR.center); + \draw (BR.center) -- (INT2.center); + \draw (BL.center) -- (INT2.center); + \draw (INT2.center) -- (Y.center) to [R] (GND); + \draw (A) to[R,o-] (P1.B); + \draw (B) to[R,o-] (P2.B); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \draw (Y.north) to[short,-o] (OUT); + \node[right] at (OUT) {\textbf{Y}}; + \end{circuitikz} + } +\end{minipage}% +\begin{minipage}{0.4\textwidth} + \begin{tabular}{cc|c} + A & B & Y\\ + \hline + 0 & 0 & 0 \\ + 1 & 0 & 1 \\ + 0 & 1 & 1 \\ + 1 & 1 & 1 \\ + \end{tabular} \\[1cm] + \onslide<3>{{Symbol}:\\ + \begin{circuitikz} + \draw (0,0) node[or port] (OR) {}; + \draw (OR.in 1) ++ (-1,0) node (A) {}; + \draw (OR.in 2) ++ (-1,0) node (B) {}; + \draw (OR.out) ++ (1,0) node (Y) {}; + \draw (OR.in 1) to[short,-o] (A); + \draw (OR.in 2) to[short,-o] (B); + \draw (OR.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + + \end{circuitikz} + } +\end{minipage}% +\end{overlayarea} \end{frame} -\begin{frame} - -\begin{minipage}{0.5\textwidth} - \textbf{NOT gate\\ (inverter)}\\ - \begin{circuitikz} - \draw (0,0) node[vcc](VCC){5 V}; - - \draw (-1, -3) node (TL) {}; - \draw (1, -3) node (TR) {}; - \draw ($(TL)!0.5!(TR)$) node (INT1) {}; - \draw (-1, -5) node (BL) {}; - \draw (1, -5) node (BR) {}; - \draw ($(BL)!0.5!(BR)$) node (INT2) {}; - - \draw (0, -6) node[ground](GND) {}; - - \draw ($(TL)!0.5!(BL)$) node[npn](P1) {}; - \draw ([xshift=-3cm]P1) node[] (A) {}; - - \draw ($(TR)!0.5!(BR)$) node[emptylediodeshape, rotate=-90](B) {}; - - \draw (VCC) to[R] (INT1.center); - \draw (INT1.center) -- (TL.center); - \draw (INT1.center) -- (TR.center); - \draw (TL.center) -- (P1.C) (P1.E) -- (BL.center); - \draw (TR.center) -- (B) -- (BR.center); - \draw (BR.center) -- (INT2.center); - \draw (BL.center) -- (INT2.center); - \draw (INT2.center) -- (GND); - - \draw (A) to[R,o-] (P1.B); - \node[left] at (A) {\textbf{A}}; - \node[left] at (B.south) {\textbf{Y}}; - \end{circuitikz} -\end{minipage} +\begin{frame}{NAND gate} + \begin{overlayarea}{\textwidth}{\textheight} + \begin{minipage}{0.6\textwidth} + \begin{circuitikz} + \draw (0,0) node[vcc](VCC){5 V}; + \draw (-3, -3) node (A) {}; + \draw (-3, -4.5) node (B) {}; + \draw (2, -1.75) node (Y) {}; + \draw (0,-3) node[npn](P1) {}; + \draw (0,-4.5) node[npn](P2) {}; + \draw (0, -5.5) node[ground](GND) {}; + + \draw (A) to[R,o-] (P1.B); + \draw (B) to[R,o-] (P2.B); + \draw (VCC) to[R] (0,-1.75) -- (P1.C) (P1.E) -- (P2.C) (P2.E) -- (GND); + \draw (0,-1.75) to[short,-o] (Y); + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + \end{circuitikz} + \end{minipage}% + \begin{minipage}{0.4\textwidth} + \begin{tabular}{cc|c} + A & B & Y\\ + \hline + 0 & 0 & 1 \\ + 1 & 0 & 1 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + \end{tabular}\\[1cm] + {Symbol}: + \begin{circuitikz} + \draw (0,0) node[nand port] (AND) {}; + \draw (AND.in 1) ++ (-1,0) node (A) {}; + \draw (AND.in 2) ++ (-1,0) node (B) {}; + \draw (AND.out) ++ (1,0) node (Y) {}; + \draw (AND.in 1) to[short,-o] (A); + \draw (AND.in 2) to[short,-o] (B); + \draw (AND.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + + \end{circuitikz} + \end{minipage} + \end{overlayarea} \end{frame} \begin{frame}{Building some gates with other gates} - content... +\textbf{XOR gate}\\ +\begin{minipage}{0.6\textwidth} +\begin{circuitikz} +\draw (0,0) node[or port] (OR) {{\hspace*{-0.25cm}\tiny OR}}; +\draw (0,2) node[nand port] (NAND) {{\hspace*{-0.5cm}\tiny NAND}}; +\draw (2, 1) node[and port] (AND) {{\hspace*{-0.5cm}\tiny AND}}; +\draw (OR.in 1) ++ (-1,0) node (A) {}; +\draw (OR.in 2) ++ (-1,0) node (B) {}; +\draw (AND.out) ++ (0.5,0) node (Y) {}; + +\draw (A) to[short, o-] (OR.in 1); +\draw (B) to[short, o-] (OR.in 2); +\draw (OR.in 1) ++ (-0.5,0) to[short,*-] ([xshift=-0.5cm]NAND.in 1) -- (NAND.in 1); +\draw (OR.in 2) ++ (-0.3,0) to[short,*-] ([xshift=-0.3cm]NAND.in 2) -- (NAND.in 2); +\draw (NAND.out) |- (AND.in 1); +\draw (OR.out) |- (AND.in 2); +\draw (AND.out) to[short,-o] (Y); + +\node[left] at (A) {\textbf{A}}; +\node[left] at (B) {\textbf{B}}; +\node[right] at (Y) {\textbf{Y}}; +\end{circuitikz} +\onslide<2->{ +\\Alternatively using only \textbf{NAND} gates: +\begin{circuitikz} + \draw (0,0) node[nand port] (NAND1) {{\hspace*{-0.5cm}\tiny NAND}}; + \draw (2,1) node[nand port] (NAND2) {{\hspace*{-0.5cm}\tiny NAND}}; + \draw (2,-1) node[nand port] (NAND3) {{\hspace*{-0.5cm}\tiny NAND}}; + \draw (4,0) node[nand port] (NAND4) {{\hspace*{-0.5cm}\tiny NAND}}; + + \draw (NAND2.in 1) ++ (-2.5,0) node (A) {}; + \draw (NAND3.in 2) ++ (-2.5,0) node (B) {}; + \draw (NAND4.out) ++ (0.5,0) node (Y) {}; + + \draw (A) to[short, o-] (NAND2.in 1); + \draw (B) to[short, o-] (NAND3.in 2); + \draw (A) ++ (0.5,0) to[short,*-] (NAND1.in 1); + \draw (B) ++ (0.5,0) to[short,*-] (NAND1.in 2); + + \draw (NAND1.out) |- (NAND2.in 2); + \draw (NAND1.out) |- (NAND3.in 1); + \draw (NAND2.out) |- (NAND4.in 1); + \draw (NAND3.out) |- (NAND4.in 2); + + \draw (NAND4.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; +\end{circuitikz} +} +\end{minipage}% +\begin{minipage}{0.4\textwidth} + \begin{tabular}{cc|c} + A & B & Y\\ + \hline + 0 & 0 & 0 \\ + 1 & 0 & 1 \\ + 0 & 1 & 1 \\ + 1 & 1 & 0 \\ + \end{tabular}\\[3cm] + \onslide<3>{ + {Symbol}: + \begin{circuitikz} + \draw (0,0) node[xor port] (AND) {}; + \draw (AND.in 1) ++ (-1,0) node (A) {}; + \draw (AND.in 2) ++ (-1,0) node (B) {}; + \draw (AND.out) ++ (1,0) node (Y) {}; + \draw (AND.in 1) to[short,-o] (A); + \draw (AND.in 2) to[short,-o] (B); + \draw (AND.out) to[short,-o] (Y); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (Y) {\textbf{Y}}; + + \end{circuitikz} +} +\end{minipage} \end{frame} -\section{What can we do with logic gates} +\section{Binary addition} \begin{frame}{Binary addition} - Adding two bits\\ - can be implemented with one AND gate and one XOR gate + \begin{itemize} +\item Adding two 1-bit numbers:\\ + \begin{minipage}{0.25\textwidth} + \only<1-2>{ + \begin{tabular}{cc|cc} + A & B & Y &\\ + \hline + 0 & 0 & 0 &\\ + 1 & 0 & 1 &\\ + 0 & 1 & 1 &\\ + 1 & 1 & 10 & + \end{tabular} +} +\only<3->{ + \begin{tabular}{cc|cc} + A & B & C & S\\ + \hline + 0 & 0 & 0 & 0\\ + 1 & 0 & 0 & 1\\ + 0 & 1 & 0 & 1\\ + 1 & 1 & 1 & 0 + \end{tabular} + } +\end{minipage}% +\begin{minipage}{0.7\textwidth} + $\;$ + \onslide<2->{ + \\[1.5cm]$\leftarrow$ 2 bit output: \textbf{CARRY} and \textbf{SUM} + } +\end{minipage} +\item<4> Can be implemented with one AND gate and one XOR gate: +\begin{circuitikz} + \draw (0,0) node[xor port] (XOR) {{\hspace*{-0.0cm}\tiny XOR}}; + \draw (0, -1.5) node[and port] (AND) {{\hspace*{-0.5cm}\tiny AND}}; + \draw (XOR.in 1) ++ (-1,0) node (A) {}; + \draw (XOR.in 2) ++ (-1,0) node (B) {}; + \draw (XOR.out) ++ (0.5,0) node (SUM) {}; + \draw (AND.out) ++ (0.5,0) node (CARRY) {}; + + \draw (A) to[short, o-] (XOR.in 1); + \draw (B) to[short, o-] (XOR.in 2); + \draw (OR.in 1) ++ (-0.5,0) to[short,*-] ([xshift=-0.5cm]AND.in 1) -- (AND.in 1); + \draw (OR.in 2) ++ (-0.3,0) to[short,*-] ([xshift=-0.3cm]AND.in 2) -- (AND.in 2); + \draw (XOR.out) to[short,-o] (SUM); + \draw (AND.out) to[short,-o] (CARRY); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (SUM) {\textbf{SUM}}; + \node[right] at (CARRY) {\textbf{CARRY}}; + +\end{circuitikz} +\end{itemize} \end{frame} \begin{frame}{Full Adder} - content... +\begin{overlayarea}{\textwidth}{\textheight} +If we want to add N-bit numbers we have to account for the carry bit of lower-valued digits\\ +\begin{minipage}{0.35\textwidth} + {\small \begin{tabular}{ccc|cc} + \textbf{A} & \textbf{B} & \textbf{C}$_{in}$ & \textbf{C}$_{out}$ & \textbf{S} \\ + \hline + 0 & 0 & 0 & 0 & 0\\ + 1 & 0 & 0 & 0 & 1\\ + 0 & 1 & 0 & 0 & 1\\ + 0 & 0 & 1 & 0 & 1\\ + 1 & 1 & 0 & 1 & 0\\ + 1 & 0 & 1 & 1 & 0\\ + 0 & 1 & 1 & 1 & 0\\ + 1 & 1 & 1 & 1 & 1\\ + \end{tabular} + } +\end{minipage}% +\begin{minipage}{0.7\textwidth} + \only<2->{ + \begin{circuitikz}[scale=0.75] + \draw (0,0) node[xor port] (XOR1) + {{\hspace*{-0.0cm}\tiny XOR}}; + \draw (2.5,-1) node[xor port] (XOR2) {{\hspace*{-0.0cm}\tiny XOR}}; + \draw (4.75,-3.5) node[xor port] (XOR3) {{\hspace*{-0.0cm}\tiny XOR}}; + \draw (2.5, -2.75) node[and port] (AND1) {{\hspace*{-0.5cm}\tiny AND}}; + \draw (2.5, -4.5) node[and port] (AND2) {{\hspace*{-0.5cm}\tiny AND}}; + + \draw (XOR1.in 1) ++ (-0.75,0) node (A) {}; + \draw (XOR1.in 2) ++ (-0.75,0) node (B) {}; + \draw (XOR2.out) ++ (2.5,0) node (SUM) {}; + \draw (XOR2.in 2) ++ (-3.25,0) node (CARRYIN) {}; + \draw (XOR3.out) ++ (0.25,0) node (CARRYOUT) {}; + + \draw (A) to[short,o-] (XOR1.in 1); + \draw (B) to[short,o-] (XOR1.in 2); + \draw (CARRYIN) to[short, o-] (XOR2.in 2); + \draw (A) ++ (0.75,0) to[short,*-] ([xshift=-2.5cm]AND2.in 1) -- (AND2.in 1); + \draw (B) ++ (0.5,0) to[short,*-] ([xshift=-2.75cm]AND2.in 2) -- (AND2.in 2); + + \draw (XOR1.out) |- (XOR2.in 1); + \draw (XOR2.in 1) ++ (-0.25, 0) to[short,*-] ([xshift=-0.25cm]AND1.in 1) --(AND1.in 1); + \draw (XOR2.in 2) ++ (-0.75, 0) to[short,*-] ([xshift=-0.75cm]AND1.in 2) --(AND1.in 2); + + \draw (AND1.out) |- (XOR3.in 1); + \draw (AND2.out) |- (XOR3.in 2); + + \draw (XOR2.out) to[short,-o] (SUM); + \draw (XOR3.out) to[short,-o] (CARRYOUT); + + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[left] at (CARRYIN) {\textbf{C$_{IN}$}}; + \node[right] at (SUM) {\textbf{SUM}}; + \node[right] at (CARRYOUT) {\textbf{C$_{OUT}$}}; + \end{circuitikz} +} +\end{minipage} +\onslide<3>{ + {Symbol for full adder}: \\ + \hspace{4cm} + \begin{circuitikz}[scale=0.15] + \ctikzset{chips/scale=0.75} + \draw (0,0) node[dipchip, num pins=6, hide numbers, no topmark, external pins width=0, align=left, rotate=-90] (FULLADDER) {\rotatebox{90}{{\tiny 1 bit adder}}}; + \draw (FULLADDER.bpin 3) ++ (0,2) node (A) {}; + \draw (FULLADDER.bpin 1) ++ (0,2) node (B) {}; + \draw (FULLADDER.bpin 5) ++ (0,-2) node (SUM) {}; + \draw (FULLADDER.n) ++ (2,0) node (CARRYIN) {}; + \draw (FULLADDER.s) ++ (-2,0) node (CARRYOUT) {}; + + \draw (A) to[short, o-] (FULLADDER.bpin 3); + \draw (B) to[short, o-] (FULLADDER.bpin 1); + \draw (CARRYIN) to[short, o-] (FULLADDER.n); + + \draw (SUM) to[short, o-] (FULLADDER.bpin 5); + \draw (CARRYOUT) to[short, o-] (FULLADDER.s); + + \node[left] at (A) {\textbf{A}}; + \node[left] at (B) {\textbf{B}}; + \node[right] at (CARRYIN) {\textbf{C$_{IN}$}}; + \node[right] at (SUM) {\textbf{S}}; + \node[left] at (CARRYOUT) {\textbf{C$_{OUT}$}}; + \end{circuitikz} +} +\end{overlayarea} \end{frame} \begin{frame}{Building a N-bit adder} - Ripple carry adder +\begin{itemize} +\item Adding two N-bit binary numbers:\\ + \begin{tabular}{rccccc} + \textbf{A}: & & 1 & 0 & 1 & 1 \\ + \textbf{B}: & & 1 & 1 & 1 & 0 \\ + \textbf{CARRY}: & \onslide<9->{1} & \onslide<7->{1} & \onslide<5->{1} & \onslide<3->{0} & 0 \\ \hline + \textbf{SUM}: & \onslide<10->{1} & \onslide<8->{1} & \onslide<6->{0} & \onslide<4->{0} & \onslide<2->{1} + \end{tabular} + +\item<11-> 4 bit \textbf{ripple carry adder}:\\[0.2cm] + \begin{circuitikz}[scale=0.9] + + + \ctikzset{chips/scale=0.65} + % adder 0 + \draw (0,0) node[dipchip, num pins=6, hide numbers, no topmark, external pins width=0, align=left, rotate=-90] (FA0) {\rotatebox{90}{{\tiny 1 bit adder}}}; + \draw (FA0.bpin 3) ++ (0,1) node (A0) {}; + \draw (FA0.bpin 1) ++ (0,1) node (B0) {}; + \draw (FA0.bpin 5) ++ (0,-1) node (S0) {}; + + \draw (A0) to[short, o-] (FA0.bpin 3); + \draw (B0) to[short, o-] (FA0.bpin 1); + \draw (S0) to[short, o-] (FA0.bpin 5); + + \node[left] at (A0) {\textbf{A0}}; + \node[left] at (B0) {\textbf{B0}}; + \node[right] at (S0) {\textbf{S0}}; + \node[above right] at (FA0.n) {{\tiny \textbf{C}$_{IN}$}}; + \node[above left] at (FA0.s) {{\tiny \textbf{C}$_{OUT}$}}; + + % adder 1 + \draw (-3,0) node[dipchip, num pins=6, hide numbers, no topmark, external pins width=0, align=left, rotate=-90] (FA1) {\rotatebox{90}{{\tiny 1 bit adder}}}; + \draw (FA1.bpin 3) ++ (0,1) node (A1) {}; + \draw (FA1.bpin 1) ++ (0,1) node (B1) {}; + \draw (FA1.bpin 5) ++ (0,-1) node (S1) {}; + + \draw (A1) to[short, o-] (FA1.bpin 3); + \draw (B1) to[short, o-] (FA1.bpin 1); + \draw (S1) to[short, o-] (FA1.bpin 5); + + \node[left] at (A1) {\textbf{A1}}; + \node[left] at (B1) {\textbf{B1}}; + \node[right] at (S1) {\textbf{S1}}; + \node[above right] at (FA1.n) {{\tiny \textbf{C}$_{IN}$}}; + \node[above left] at (FA1.s) {{\tiny \textbf{C}$_{OUT}$}}; + + % adder 2 + \draw (-6,0) node[dipchip, num pins=6, hide numbers, no topmark, external pins width=0, align=left, rotate=-90] (FA2) {\rotatebox{90}{{\tiny 1 bit adder}}}; + \draw (FA2.bpin 3) ++ (0,1) node (A2) {}; + \draw (FA2.bpin 1) ++ (0,1) node (B2) {}; + \draw (FA2.bpin 5) ++ (0,-1) node (S2) {}; + + \draw (A2) to[short, o-] (FA2.bpin 3); + \draw (B2) to[short, o-] (FA2.bpin 1); + \draw (S2) to[short, o-] (FA2.bpin 5); + + \node[left] at (A2) {\textbf{A2}}; + \node[left] at (B2) {\textbf{B2}}; + \node[right] at (S2) {\textbf{S2}}; + \node[above right] at (FA2.n) {{\tiny \textbf{C}$_{IN}$}}; + \node[above left] at (FA2.s) {{\tiny \textbf{C}$_{OUT}$}}; + + % adder 3 + \draw (-9,0) node[dipchip, num pins=6, hide numbers, no topmark, external pins width=0, align=left, rotate=-90] (FA3) {\rotatebox{90}{{\tiny 1 bit adder}}}; + \draw (FA3.bpin 3) ++ (0,1) node (A3) {}; + \draw (FA3.bpin 1) ++ (0,1) node (B3) {}; + \draw (FA3.bpin 5) ++ (0,-1) node (S3) {}; + + \draw (A3) to[short, o-] (FA3.bpin 3); + \draw (B3) to[short, o-] (FA3.bpin 1); + \draw (S3) to[short, o-] (FA3.bpin 5); + + \node[left] at (A3) {\textbf{A3}}; + \node[left] at (B3) {\textbf{B3}}; + \node[right] at (S3) {\textbf{S3}}; + \node[above right] at (FA3.n) {{\tiny \textbf{C}$_{IN}$}}; + \node[above left] at (FA3.s) {{\tiny \textbf{C}$_{OUT}$}}; + + % connection between adders + \draw (FA0) ++ (1, -1) node[ground] (GND) {}; + \draw (GND) |- (FA0.n); + + \draw (FA0.s) -- (FA1.n); + \draw (FA1.s) -- (FA2.n); + \draw (FA2.s) -- (FA3.n); + + \draw (FA3.s) ++ (-0.5,0) to[short, o-] (FA3.s); + \end{circuitikz} +\item<12-> Note: propagation delay of full adders +\end{itemize} \end{frame} -\begin{frame}{Memory} - S-R-Latch +\section{Memory} + +\begin{frame}{S-R latch} +\begin{minipage}{0.5\textwidth} +\begin{circuitikz} + \draw (0,0) node[nor port] (NOR1) {{\hspace*{-0.0cm}\tiny NOR}}; + \draw (0,-3) node[nor port] (NOR2) {{\hspace*{-0.0cm}\tiny NOR}}; + + \draw (NOR1.in 1) ++ (-1, 0) node (R) {}; + \draw (NOR2.in 2) ++ (-1, 0) node (S) {}; + \draw (NOR1.out) ++ (1, 0) node (Q) {}; + \draw (NOR2.out) ++ (1, 0) node (Qbar) {}; + + \draw (NOR1.out) ++ (0.0, -0.5) node (P1) {}; + \draw (NOR2.in 1) ++ (-0.5, 0.5) node (P2) {}; + \draw (NOR1.out) |- (P1.center) -- (P2.center) |- (NOR2.in 1); + + \draw (NOR2.out) ++ (0.0, 0.5) node (P3) {}; + \draw (NOR1.in 2) ++ (-0.5, -0.5) node (P4) {}; + \draw (NOR2.out) |- (P3.center) -- (P4.center) |- (NOR1.in 2); + + \draw (R) to[short, o-] (NOR1.in 1); + \draw (S) to[short, o-] (NOR2.in 2); + \draw (Q) to[short, o-] (NOR1.out); + \draw (Qbar) to[short, o-] (NOR2.out); + + \node[left] at (R) {\textbf{R}}; + \node[left] at (S) {\textbf{S}}; + \node[right] at (Q) {\textbf{Q}}; + \node[right] at (Qbar) { $\overline{\mbox{\textbf{Q}}}$}; +\end{circuitikz} + \end{minipage}% +\begin{minipage}{0.25\textwidth} + \begin{tabular}{cc|ccl} + \textbf{S} & \textbf{R} & \textbf{Q} & $\overline{\mbox{\textbf{Q}}}$ &\\ + \hline + 0 & 0 & & &LATCHED \\ + 1 & 0 & 1 & 0 &\\ + 0 & 1 & 0 & 1 &\\ + 1 & 1 & & &UNDEFINED + \end{tabular} + \end{minipage}% +\begin{itemize} + \item Can be used to store 1 bit of information +\end{itemize} \end{frame} \begin{frame}{Gated latch} - content... +\begin{circuitikz} + \draw (0,0) node[nor port] (NOR1) {{\hspace*{-0.0cm}\tiny NOR}}; + \draw (0,-3) node[nor port] (NOR2) {{\hspace*{-0.0cm}\tiny NOR}}; + \draw (NOR1.in 1) ++ (-1, 0) node[and port] (AND1) {{\hspace*{-0.0cm}\tiny AND}}; + \draw (NOR2.in 2) ++ (-1, 0) node[and port] (AND2) {{\hspace*{-0.0cm}\tiny AND}}; + + \draw (AND1.in 1) ++ (-1, 0) node (R) {}; + \draw (AND2.in 2) ++ (-1, 0) node (S) {}; + \draw ($(R)!0.5!(S)$) node (EN) {}; + \draw (NOR1.out) ++ (1, 0) node (Q) {}; + \draw (NOR2.out) ++ (1, 0) node (Qbar) {}; + + \draw (NOR1.out) ++ (0.0, -0.5) node (P1) {}; + \draw (NOR2.in 1) ++ (-0.5, 0.5) node (P2) {}; + \draw (NOR1.out) |- (P1.center) -- (P2.center) |- (NOR2.in 1); + + \draw (NOR2.out) ++ (0.0, 0.5) node (P3) {}; + \draw (NOR1.in 2) ++ (-0.5, -0.5) node (P4) {}; + \draw (NOR2.out) |- (P3.center) -- (P4.center) |- (NOR1.in 2); + + \draw (EN) ++ (0.5, 0) node (P5) {}; + \draw (EN) to[short, o-*] (P5.center); + \draw (P5.center) |- (AND1.in 2); + \draw (P5.center) |- (AND2.in 1); + + \draw (R) to[short, o-] (AND1.in 1); + \draw (S) to[short, o-] (AND2.in 2); + \draw (Q) to[short, o-] (NOR1.out); + \draw (Qbar) to[short, o-] (NOR2.out); + + \draw (AND1.out) -- (NOR1.in 1); + \draw (AND2.out) -- (NOR2.in 2); + + \node[left] at (R) {\textbf{R}}; + \node[left] at (S) {\textbf{S}}; + \node[left] at (EN) {\textbf{EN}}; + \node[right] at (Q) {\textbf{Q}}; + \node[right] at (Qbar) { $\overline{\mbox{\textbf{Q}}}$}; +\end{circuitikz} \end{frame} \begin{frame}{D latch} - content... +\begin{circuitikz} + \draw (0,0) node[nor port] (NOR1) {{\hspace*{-0.0cm}\tiny NOR}}; + \draw (0,-3) node[nor port] (NOR2) {{\hspace*{-0.0cm}\tiny NOR}}; + \draw (NOR1.in 1) ++ (-1, 0) node[and port] (AND1) {{\hspace*{-0.0cm}\tiny AND}}; + \draw (NOR2.in 2) ++ (-1, 0) node[and port] (AND2) {{\hspace*{-0.0cm}\tiny AND}}; + \draw (AND1.in 1) ++ (-1, 0) node[not port] (NOT) {{\hspace*{-0.4cm}\tiny NOT}}; + + \draw (NOT.in) ++ (-1, 0) node (D) {}; + \draw (D) ++ (0, -2) node (EN) {}; + \draw (NOR1.out) ++ (1, 0) node (Q) {}; + \draw (NOR2.out) ++ (1, 0) node (Qbar) {}; + + \draw (NOR1.out) ++ (0.0, -0.5) node (P1) {}; + \draw (NOR2.in 1) ++ (-0.5, 0.5) node (P2) {}; + \draw (NOR1.out) |- (P1.center) -- (P2.center) |- (NOR2.in 1); + + \draw (NOR2.out) ++ (0.0, 0.5) node (P3) {}; + \draw (NOR1.in 2) ++ (-0.5, -0.5) node (P4) {}; + \draw (NOR2.out) |- (P3.center) -- (P4.center) |- (NOR1.in 2); + + \draw (NOT.out) -- (AND1.in 1); + + \draw (EN) ++ (2.5, 0) node (P5) {}; + \draw (EN) to[short, o-*] (P5.center); + \draw (P5.center) |- (AND1.in 2); + \draw (P5.center) |- (AND2.in 1); + + \draw (D) to[short, o-] (NOT.in); + \draw (D) ++ (0.5,0) node (P6) {}; + \draw (P6) to[short, *-] ([yshift=-1cm]P6); + \draw ([yshift=-1cm]P6) |- (AND2.in 2); + \draw (Q) to[short, o-] (NOR1.out); + \draw (Qbar) to[short, o-] (NOR2.out); + + \draw (AND1.out) -- (NOR1.in 1); + \draw (AND2.out) -- (NOR2.in 2); + + \node[left] at (D) {\textbf{D}}; + \node[left] at (EN) {\textbf{EN}}; + \node[right] at (Q) {\textbf{Q}}; + \node[right] at (Qbar) { $\overline{\mbox{\textbf{Q}}}$}; +\end{circuitikz} \end{frame} -\section{Latches and Flip-Flops} + \begin{frame}{Building a N-bit shift register} content...

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