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\title[Breadboard]{Breadboard logic}
\author{Tobias Eckert, Simon Pirkelmann}
\institute{\includegraphics[scale=0.5]{images/iR.pdf}}
\date{January 13th, 2020}


\AfterPreamble{\hypersetup{
  urlcolor=blue,
}}

\begin{document}

\begin{frame}
  \titlepage
\end{frame}

% Uncomment these lines for an automatically generated outline.
\begin{frame}{Outline}
  \tableofcontents
\end{frame}



\section{Boolean logic and basic gates}
\begin{frame}{Basic logic operation}
\begin{itemize}
	\item Two states \textbf{TRUE} and \textbf{FALSE}
	(also written as \textbf{1} and \textbf{0})
	\item Boolean logic describes logical operations
	
	\begin{minipage}{0.5\textwidth}
	\item \textbf{NOT}
	\begin{tabular}{c|c}
		A & Y\\
		\hline
		0 & 1 \\
		1 & 0
	\end{tabular}
	\item \textbf{AND}
		\begin{tabular}{cc|c}
			A & B & Y\\
			\hline
			0 & 0 & 0 \\
			1 & 0 & 0 \\
			0 & 1 & 0 \\
			1 & 1 & 1 \\
		\end{tabular}
	\item \textbf{OR}
		\begin{tabular}{cc|c}
			A & B & Y\\
			\hline
			0 & 0 & 0 \\
			1 & 0 & 1 \\
			0 & 1 & 1 \\
			1 & 1 & 1 \\
		\end{tabular}
		\end{minipage}%
		\begin{minipage}{0.5\textwidth}
	\item \textbf{XOR}
	\begin{tabular}{cc|c}
		A & B & Y\\
		\hline
		0 & 0 & 0 \\
		1 & 0 & 1 \\
		0 & 1 & 1 \\
		1 & 1 & 0 \\
	\end{tabular}
	\item \textbf{NAND}
		\begin{tabular}{cc|c}
			A & B & Y\\
			\hline
			0 & 0 & 1 \\
			1 & 0 & 1 \\
			0 & 1 & 1 \\
			1 & 1 & 0 \\
		\end{tabular}
		\end{minipage}
	\item In electronics boolean states are represented by different voltage levels, e.g.~\textbf{FALSE} = 0 V, \textbf{TRUE} = 5 V
\end{itemize}
\end{frame}

\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) {};
			\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[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) -- (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}
		}
		\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}{AND gate}
	\begin{overlayarea}{\textwidth}{\textheight}
		\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}{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, -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 ($(TL)!0.3!(BL)$) 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) to[empty led, name=OUT] (Y) 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}};
		\node[left] at (OUT.south) {\textbf{Y}};
	\end{circuitikz}
}
	\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}{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}
\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{Binary addition}
\begin{frame}{Binary addition}
	\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}
\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}
\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-> nibble \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}

\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 S-R latch}
\begin{itemize}
	\item S-R latch should only change state when certain conditions are met (e.g. on clock pulse)
	$\rightarrow$ gated S-R latch
\end{itemize}
\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}
\begin{itemize}
\item output \textbf{Q} can only change when \textbf{EN} is HIGH
\end{itemize}
\end{frame}

\begin{frame}{(Transparent) D latch}
\begin{itemize}
	\item Problem of "forbidden" state \textbf{R} = \textbf{S} = 1 for S-R latch\\
	$\rightarrow$ D latch prevents this from happening
\end{itemize}
\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}\\
Symbol:\\
\hspace{3cm}
	\begin{circuitikz}[scale=0.15]
		\ctikzset{chips/scale=0.75}
		\draw (0,0) node[dipchip, num pins=4, hide numbers, no topmark, external pins width=0, align=left] (DLATCH) {{\tiny D latch}};
		\draw (DLATCH.bpin 1) ++ (-2,0) node (D) {};
		\draw (DLATCH.bpin 2) ++ (-2,0) node (EN) {};
		\draw (DLATCH.bpin 4) ++ (2,0) node (Q) {};
		\draw (DLATCH.bpin 3) ++ (2,0) node (Qbar) {};
		
		\draw (D) to[short, o-] (DLATCH.bpin 1);
		\draw (EN) to[short, o-] (DLATCH.bpin 2);
		\draw (Q) to[short, o-] (DLATCH.bpin 4);
		\draw (Qbar) to[short, o-] (DLATCH.bpin 3);
		
		\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}

\begin{frame}{D flip-flop}
	\begin{itemize}
		\item Only want the state \textbf{Q} to change at specific point in time
		\item Implemented using two latches in master-slave configuration:
	\end{itemize}
	\begin{circuitikz}[scale=0.2]
		\ctikzset{chips/scale=1.0}
		
		% master
		\draw (0,0) node[dipchip, num pins=4, hide numbers, no topmark, external pins width=0, align=left] (DLATCH1) {{\tiny D latch}};
		\draw (DLATCH1.bpin 1) ++ (-4,0) node (D1) {};
		\draw (DLATCH1.bpin 2) ++ (-4,-6) node (EN1) {};
		\draw (EN1) ++ (3,0) node (P1) {};
		\draw (DLATCH1.bpin 4) ++ (2,0) node (Q1) {};
		\draw (DLATCH1.bpin 3) ++ (2,0) node (Qbar1) {};
		
		\draw (D1) to[short, o-] (DLATCH1.bpin 1);
		\draw (EN1) to[short, o-] (P1) |- (DLATCH1.bpin 2);
		\draw (Q1) to[short, -] (DLATCH1.bpin 4);
		
		\node[left] at (D1) {\textbf{D}};
		\node[left] at (EN1) {\textbf{CLK}};
		\node[left] at (DLATCH1.bpin 4) {\textbf{{\tiny Q1}}};	
		\node[left] at (DLATCH1.bpin 3) { $\overline{\mbox{\textbf{{\tiny Q1}}}}$};
		
		% slave
		\draw (20,0) node[dipchip, num pins=4, hide numbers, no topmark, external pins width=0, align=left] (DLATCH2) {{\tiny D latch}};
		\draw (DLATCH2.bpin 1) ++ (-2,0) node (D2) {};
		\draw (DLATCH2.bpin 2) ++ (-2,0) node (EN2) {};
		\draw (DLATCH2.bpin 4) ++ (4,0) node (Q2) {};
		\draw (DLATCH2.bpin 3) ++ (4,0) node (Qbar2) {};
		
		\draw (D2) to[short, -] (DLATCH2.bpin 1);
		\draw (EN2) to[short, -] (DLATCH2.bpin 2);
		\draw (Q2) to[short, o-] (DLATCH2.bpin 4);
		\draw (Qbar2) to[short, o-] (DLATCH2.bpin 3);
		
		\draw (Q1.center) -- (D2.center);
		
		\node[right] at (DLATCH2.bpin 1) {\textbf{{\tiny D2}}};
		\node[right] at (DLATCH2.bpin 2) {$\overline{\mbox{\textbf{{\tiny CLK}}}}$};
		\node[right] at (Q2) {\textbf{Q}};	
		\node[right] at (Qbar2) { $\overline{\mbox{\textbf{Q}}}$};
		
		% inverter
		\draw (P1) ++ (5,0) node[not port, scale=0.75] (NOT) {};
		\draw (P1) to[short,*-] (NOT.in);
		\draw (EN2.center) |- (NOT.out);
		
		\node[above] at (DLATCH1.n) {master};	
		\node[above] at (DLATCH2.n) {slave};	
		
		\draw (DLATCH1.nw) ++ (-2, 2.5) node (A) {};
		\draw (DLATCH2.ne) ++ (2, 2.5) node (B) {};
		\draw (DLATCH2.se) ++ (2, -7) node (C) {};
		\draw (DLATCH1.sw) ++ (-2, -7) node (D) {};
		\draw[dashed] (A.center) -- (B.center) -- (C.center) -- (D.center) -- (A.center);
	\end{circuitikz}
	\begin{itemize}
		\item \textbf{Q} changes only on falling edge of the \textbf{CLK} signal
	\end{itemize}	
\end{frame}

%\begin{frame}{Building a N-bit shift register}
%	content...
%\end{frame}

\end{document}
