Editing, new content, and more graphics.

Author: jessehamner

chapters/calculator.tex

@@ -0,0 +1,10 @@
+\section{Building an Adding Machine}
+All of these little units, experiments, and instruction have been moving towards a goal -- to make a primitive electronic calculator. Here, we will be able to add two four-bit numbers using only full adders, toggle switches, and LED blocks, all wired together on a breadboard. At the end of this unit, you will be able to enter two numbers in binary using toggle switches, and read the result on an LED readout, also in binary. There's no reason you have to stop at 4 bits -- the 8-LED block means you could add two 7-bit numbers if you have seven full adders and more toggle switches, without \emph{overflowing} the capabilities of the setup. ``Overflow'' means that you have tried to put numbers into the system that cannot be represented by the computer because they are too large, or else the result is too large to display. 
+
+\subsection*{Wiring up the adders}
+
+Put two sets of toggle switches on a breadboard and, if desired, two 8-LED readouts (one for each set of toggles). Wire up power and ground to the switches and LEDs, and wire the switch outputs to the LED inputs, moving from right to left, because the rightmost digit is the smallest number value in our example, either 0 or 1.
+
+Run wires out from the switches, perhaps using one color for one bank of switches, and a different color for the second bank, to each input of each full adder, and wire up each ``carry-out'' to the next (leftward!) ``carry-in''. The left-most carry-out digit should run to another LED, perhaps not on the 8-LED output, to indicate an overflow. The overflow, a type of error, means the answer is not correctly displayed on the LED output bar.
+
+Run each adder ``sum" wire to each output LED input. In doing this you will have wired up each column of output, meaning you can read off the sum of the two numbers.

chapters/logiccircuits.tex

@@ -14,10 +14,10 @@ \subsection*{A Half Adder}
 
 &
 
-\begin{tabular}{ll | ll | c}
+\begin{tabular}{ll | cc | c}
 \multicolumn{5}{c}{\textbf{Truth Table}}\\
 \hline\\[\negsep]
-\textbf{A} & \textbf{B} & \textbf{S} & \textbf{C} & \textbf{Decimal}\\
+\textbf{A} & \textbf{B} & \textbf{Sum} & \textbf{Carry} & \textbf{Decimal}\\
 \hline
 0 & 0 & 0 & 0 & 0 \\
 1 & 0 & 1  & 0 & 1 \\
@@ -35,7 +35,7 @@ \subsection*{A Half Adder}
 \end{figure}
 
 
-\begin{figure}[h!]
+\begin{figure}[hb!]
 \begin{center}
 
 \input{./include/halfadder2.tex}
@@ -58,7 +58,17 @@ \subsection*{Full Adder}
 \end{figure}
 
 
-\newpage
+\begin{figure}[h!]
+\begin{center}
+\includegraphics[scale=0.19]{FullAdderboard.png}
+\caption{A full-adder circuit, implemented on a small circuit board, with individual integrated circuit gates instead of discrete transistors. You can see the circuits easily but the board is much simpler to work with, compared to the single-gate boards.}
+\end{center}
+\end{figure}
+
+
+
+
+\clearpage
 
 \subsection*{Equality}
 
@@ -139,3 +149,4 @@ \section*{Memory}
 \caption{A static ram cell. It uses six transistors per bit instead of one transistor and a capacitor for bit (as used in dynamic ram, the main memory for the computer), so it's expensive and bulky, but it's also faster. Usually SRAM is used very close to the CPU core, so it is available for immediate use by the core processing operations. To keep the diagram simple, no resistors are shown. If you look closely at the M1/M2 and M3/M4 transistors, you can see that they are acting like inverters (that is, each pair makes a NOT gate).} % from Wikipedia and http://www.iue.tuwien.ac.at/phd/entner/node34.html 
 \end{center}
 \end{figure}
+

chapters/logicgates.tex

@@ -283,9 +283,13 @@ \subsection*{The NOT Gate}
 \clearpage
 \newpage
 
-\subsection*{Complex Gates}
+\section{Complex Logic Gates}
 
-Combining gates is possible to produce more complex circuits that answer different questions. A ``NOT-AND", or ``NAND", gate just reverses the value obtained from an AND gate -- so it has the exact opposite truth table. Since a NAND gate just reverses the output of AND, you can put a NOT gate on the result (output) line of an AND gate and make a NAND gate, just like you were using Legos.
+Combining gates is possible to produce more complex circuits that answer different questions, like outputs that tell us if two inputs are ``NOT AND" or ``NOT OR" or ``Exclusively OR". Each of these gates allows new comparisons between two inputs, but each is composed of the fundamental three gates, seen above. There is even an "Exclusive NOT OR" gate, which is how computers determine if two numbers are equal to each other.
+
+\subsection*{The NAND Gate}
+
+A ``NOT-AND", or ``NAND", gate just reverses the value obtained from an AND gate -- so it has the exact opposite truth table. Since a NAND gate just reverses the output of AND, you can put a NOT gate on the result (output) line of an AND gate and make a NAND gate, just like you were using Legos.
 
 
 \medskip
@@ -345,7 +349,7 @@ \subsection*{Complex Gates}
 
 \begin{figure}[h!]
 \begin{center}
-\includegraphics[scale=0.25]{trimmednandgate.png}
+\includegraphics[scale=0.16]{trimmednandgate.png}
 \caption{A circuit board designed to make a NAND gate. Note that it uses four transistors.}
 \label{fig:nandgate}
 \end{center}
@@ -354,6 +358,8 @@ \subsection*{Complex Gates}
 \clearpage
 \newpage
 
+\subsection*{The NOR Gate}
+
 Not surprisingly, there is also a NOR gate, that has the reverse truth table to an OR gate. NOR gates are easy to implement, though as we have said elsewhere, more complicated NOR gates save power. 
 
 \medskip
@@ -421,7 +427,8 @@ \subsection*{Complex Gates}
 \clearpage
 \newpage
 
-There is also the ``eXclusive-OR", or ``XOR", gate. The XOR gate output (result) is 1 when \emph{the inputs are not the same}. It returns a 1 if, and \emph{only} if, both inputs are different. That is, it provides a one ``exclusively if'' there is a single ``one'' (sometimes called ``logic high", for ``voltage above zero") in the two inputs. XOR gates take a lot of transistors to implement. The most common version requires 12, though it is possible to make an XOR gate with 8 transistors.
+\subsection*{The Exclusive-OR Gate}
+There is also the ``eXclusive-OR", or ``XOR", gate. The XOR gate output (result) is 1 when \emph{the inputs are not the same}. It returns a 1 if, and \emph{only} if, both inputs are different. That is, it provides a one ``exclusively if'' there is a single ``one'' (sometimes called ``logic high", for ``voltage above zero") in the two inputs. XOR gates take a lot of transistors to implement. The most common version requires 12, though it is possible to make an XOR gate with 8 transistors. See Figure \ref{fig:xorgate}.
 
 \medskip
 \begin{center}
@@ -475,6 +482,24 @@ \subsection*{Complex Gates}
 
 \bigskip
 
+\begin{figure}[h!]
+\begin{center}
+\fbox{
+\includegraphics[scale=0.15]{xorgatebreadboard.jpg}
+}
+\caption{An XOR gate wired up on a breadboard with discrete transistors and resistors. This is the same schematic (and the same color-coded signal wires) seen in Figure \ref{fig:xorgate}. The red switch is signal A and the blue switch is signal B. On the LED line, 0 and 1 are A and B, and 2 and 3 (lit up) are NOT A and NOT B.}
+\label{fig:xorbreadboard}
+\end{center}
+\end{figure}
 
 
+\begin{figure}[h!]
+\begin{center}
+\input{include/xorgate.tex}
+\caption{An exclusive-or (XOR) gate, composed of 12 transistors and some supporting resistors. You don't need to understand how it works, but it's not that hard if you break it down into signals and AND gates.}
+\label{fig:xorgate}
+\end{center}
+\end{figure}
+
+\clearpage
 

computertheoryforkids.pdf

@@ -127,13 +127,19 @@
 %---------------------------
 
 
-% Finally -- how do computers add? 
+% How do computers add? 
 % How do they store results?
 %---------------------------
 \newpage
 \input{./chapters/logiccircuits.tex}
 %---------------------------
 
+% Finally -- Let's make a simple calculator!
+%---------------------------
+\newpage
+\input{./chapters/calculator.tex}
+%---------------------------
+
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \end{document}

computertheoryforkids.tex

@@ -4,45 +4,39 @@
 	(0,4.0) node[ocirc](in) {} % IN node
 	(0,4.0) node[left] {{\color{red}$IN$}} % IN label
 
-	(8.5,4) node[ocirc](out){} % OUT node
-	(8.75,4) node[right] {{\color{red}$OUT$}} % OUT label
-	(7,4) |- (out)
-	(7,4) node[circ](){}
+	(6.5,4) node[ocirc](out){} % OUT node
+	(6.75,4) node[right] {{\color{red}$OUT$}} % OUT label
+	(5,4) |- (out)
+	(5,4) node[circ](){}
 
 % Vdd:
-	(7,7.5) node[vcc](vin){}
-    (6.5,7.5) node[above] {$V_{in}$} % Vin
+	(5,6.0) node[vcc](vin){}
+    (4.5,6.0) node[above] {$V_{in}$} % Vin
 
 % GND
-    (7,0) node[ground](ground){}
+    (5,0) node[ground](ground){}
 %   (7.75,0.5) node[below] {{\color{red}$GND$}} % GND
 
 % P-type FET
-	(7,5) node[pmos, emptycircle, xscale=1](Q1){}
-	(7.5,5.0) node[above]{$Q_1$}
+	(5,5) node[pmos, emptycircle, xscale=1](Q1){}
+	(5.5,5.0) node[above]{$Q_1$}
 
 % N-type FET
-	(7,3) node[nmos, rotate=0](Q2){}
-	(7.5,2.5) node[above]{$Q_2$}
+	(5,3) node[nmos, rotate=0](Q2){}
+	(5.5,2.5) node[above]{$Q_2$}
 
 % Resistors:
-	(5,3) to [R, l^=$R_1$](5,0)
+	(3,3) to [R, l^=$R_1$](3,0)
 	(Q2.S) to [R, -*, l^=$R_2$](ground) 
 	(in) to [R, -*, l^=$R_3$](3,4)
-	(3,3) to [R, l^=$R_4$](3,0)
-
 
 % nets:
 	(vin) |- (Q1.S)
-	(5,3) |- (Q2.G)
 	(3,3) |- (3,5)
-	(5,3) node[circ](){}
-	(5,0) node[circ](){}
 	(3,3) node[circ](){}	
 	(Q1.D) |- (Q2.D)
-	(5,0) |- (ground)
-	(3,3) |- (5,3)
+	(3,0) |- (ground)
+	(3,3) |- (Q2.G)
 	(3,5) |- (Q1.G)
-	(3,0) |- (5,0)
 ;
 \end{circuitikz}

images/FullAdderboard.png

@@ -4,12 +4,11 @@
 \hline\\[\negsep]
 JP1  &  Input/Output & Pin header    & 1X02 header     & Standard 2-pin 0.1" header \\[\sep]
 JP2  &  $V_{in}$ \& $GND$ & Pin header & 1X02 header     & Standard 2-pin 0.1" header \\[\sep]
-Q1   &  BS250       &  BS250         & TO-92-3     & P-type MOSFET transistor \\[\sep]
+Q1   &  ZVP3306A    & ZVP3306A       & TO-92-3     & P-type MOSFET transistor \\[\sep]
 Q2   &  2N7000      & 2N7000         & TO-92-3     & N-type MOSFET transistor \\[\sep]
 R1   &  100K        & Small resistor & 0204/5    & Pull-\emph{down} resistor \\[\sep]
 R2   &  10K (10,000$\Omega$)         & Small resistor & 0204/5    & Current-limiting resistor \\[\sep]
 R3   &  100R (100$\Omega$) & $\frac{1}{4}$-watt resistor & 0207/7 & Current-limiting resistor \\[\sep]
-R4   &  100K       & Small resistor & 0204/5    & Pull-\emph{down} resistor \\[\sep]
 
 \hline\\
 \end{tabular}