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\subsection{課題 1-1}
74HC08のANDゲートを使用した.
\subsubsection{動作}
\begin{figure}[tbh]
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\includegraphics[]{./assets/t-2/result/and-gate/state-00.jpg}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-gate/state-00.jpg}
\subcaption{$a = 0, \ b = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\includegraphics[]{./assets/t-2/result/and-gate/state-01.jpg}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-gate/state-01.jpg}
\subcaption{$a = 1, \ b = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\includegraphics[]{./assets/t-2/result/and-gate/state-11.jpg}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-gate/state-11.jpg}
\subcaption{$a = 1, \ b = 1$}
\end{minipage}
\caption{74HC08 AND Gate ($x = a \cdot b$)}
\caption{74HC08 AND Gate, Input A on Second from Right ($x = a \cdot b$)}
\label{fig:a1-1-res}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of $x = a \cdot b$}
\label{tab:a1-1-res-tt}
\begin{tabular}{ccc}
\hline
a & b & $x$ \\
\hline
0 & 0 & 0 \\
1 & 0 & 0 \\
0 & 1 & 0 \\
1 & 1 & 1 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 1-2}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-4/state-0000.jpg}
\subcaption{$a = 0, \ b = 0, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-4/state-0011.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-4/state-1111.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 1, \ d = 1$}
\end{minipage}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of $x = \overline{a \cdot b \cdot c \cdot d}$}
\label{tab:a1-2-res-tt}
\begin{tabular}{ccccc}
\hline
a & b & c & d & x \\
\hline
0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 1 \\
1 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \\
1 & 0 & 1 & 0 & 1 \\
0 & 1 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 & 1 \\
0 & 0 & 0 & 1 & 1 \\
1 & 0 & 0 & 1 & 1 \\
0 & 1 & 0 & 1 & 1 \\
1 & 1 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 & 1 \\
1 & 0 & 1 & 1 & 1 \\
0 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 0 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 1-3}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-4/state-0000.jpg}
\subcaption{$a = 0, \ b = 0, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-4/state-0010.jpg}
\subcaption{$a = 0, \ b = 1, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/and-4/state-1111.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 1, \ d = 1$}
\end{minipage}
\caption{
\parbox[t]{7.5cm}{4 Inputs AND Gate with Three 2 Inputs AND Gates, \\ Input A on Most Left ($x = (a \cdot b) \cdot (c \cdot d)$)}
}
\label{fig:a1-3-res}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of $x = (a \cdot b) \cdot (c \cdot d)$}
\label{tab:a1-3-res-tt}
\begin{tabular}{ccccc}
\hline
a & b & c & d & x \\
\hline
0 & 0 & 0 & 0 & 0 \\
1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 0 \\
1 & 1 & 0 & 0 & 0 \\
0 & 0 & 1 & 0 & 0 \\
1 & 0 & 1 & 0 & 0 \\
0 & 1 & 1 & 0 & 0 \\
1 & 1 & 1 & 0 & 0 \\
0 & 0 & 0 & 1 & 0 \\
1 & 0 & 0 & 1 & 0 \\
0 & 1 & 0 & 1 & 0 \\
1 & 1 & 0 & 1 & 0 \\
0 & 0 & 1 & 1 & 0 \\
1 & 0 & 1 & 1 & 0 \\
0 & 1 & 1 & 1 & 0 \\
1 & 1 & 1 & 1 & 1 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 1-4}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-from-ands/state-0000.jpg}
\subcaption{$a = 0, \ b = 0, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-from-ands/state-0101.jpg}
\subcaption{$a = 1, \ b = 0, \ c = 1, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/nand-from-ands/state-1111.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 1, \ d = 1$}
\end{minipage}
\caption{
\parbox[t]{8cm}{4 Inputs NAND Gate with Three 2 Inputs AND Gates and \\ a NOT Gate, Input A on Most Left ($x = \overline{(a \cdot b) \cdot (c \cdot d)}$)}
}
\label{fig:a1-4-res}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of $x = \overline{(a \cdot b) \cdot (c \cdot d)}$}
\label{tab:a1-2-res-tt}
\begin{tabular}{ccccc}
\hline
a & b & c & d & x \\
\hline
0 & 0 & 0 & 0 & 1 \\
1 & 0 & 0 & 0 & 1 \\
0 & 1 & 0 & 0 & 1 \\
1 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 1 \\
1 & 0 & 1 & 0 & 1 \\
0 & 1 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 & 1 \\
0 & 0 & 0 & 1 & 1 \\
1 & 0 & 0 & 1 & 1 \\
0 & 1 & 0 & 1 & 1 \\
1 & 1 & 0 & 1 & 1 \\
0 & 0 & 1 & 1 & 1 \\
1 & 0 & 1 & 1 & 1 \\
0 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 0 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 2-1}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/7seg-bcd/state-0.jpg}
\subcaption{$a = 0, \ b = 0, \ c = 0, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/7seg-bcd/state-7.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 1, \ d = 0$}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/7seg-bcd/invalid.jpg}
\subcaption{$a = 0, \ b = 1, \ c = 0, \ d = 1$}
\end{minipage}
\caption{7 Segment Driver (4 Bits BDC Input, LSB on Left)}
\label{fig:a2-1-res}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of 7 Segment Driver}
\label{tab:a2-1-res-tt}
\begin{tabular}{ccccccccccc}
\hline
a & b & c & d & A & B & C & D & E & F & G \\
\hline
0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\
1 & 0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & 1 & 1 & 0 & 1 & 1 & 0 & 1 \\
1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 \\
0 & 0 & 1 & 0 & 0 & 1 & 1 & 0 & 0 & 1 & 1 \\
1 & 0 & 1 & 0 & 1 & 0 & 1 & 1 & 0 & 1 & 1 \\
0 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\
0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 1 & 1 \\
1 & 0 & 0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 \\
0 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 0 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 2-2B}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-a.jpg}
\subcaption{$a = 0, \ b = 1, \ c = 0, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-b.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 0, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-c.jpg}
\subcaption{$a = 0, \ b = 0, \ c = 1, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-d.jpg}
\subcaption{$a = 1, \ b = 0, \ c = 1, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-e.jpg}
\subcaption{$a = 0, \ b = 1, \ c = 1, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/state-f.jpg}
\subcaption{$a = 1, \ b = 1, \ c = 1, \ d = 1$}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/7seg-hexa/invalid.jpg}
\subcaption{$a = 1, \ b = 0, \ c = 0, \ d = 1$}
\end{minipage}
\hspace{0.45\textwidth}
\caption{7 Segment Hexadecimal Decoder 10-15 Only (4 Bits BCD Input, LSB on Left)}
\label{fig:a2-2b-res}
\end{figure}
\subsubsection{観測された真理値表}
\begin{table}[H]
\centering
\caption{Observed Truth Table of 7 Segment Hexadecimal Decoder (* Indicates Don't Care Term)}
\label{tab:a2-2b-res-tt}
\begin{tabular}{ccccccccccc}
\hline
a & b & c & d & A & B & C & D & E & F & G \\
\hline
* & * & * & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
* & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 & 1 & 1 \\
1 & 1 & 0 & 1 & 0 & 0 & 1 & 1 & 1 & 1 & 1 \\
0 & 0 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 0 \\
1 & 0 & 1 & 1 & 0 & 1 & 1 & 1 & 1 & 0 & 1 \\
0 & 1 & 1 & 1 & 1 & 0 & 0 & 1 & 1 & 1 & 1 \\
1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 1 & 1 & 1 \\
\hline
\end{tabular}
\end{table}
\subsection{課題 3-1}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/rs-ff/initial.jpg}
\subcaption{Initial State}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/rs-ff/s-hold.jpg}
\subcaption{Set Hold}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/rs-ff/s-release.jpg}
\subcaption{Set Release}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=5cm]{./assets/t-2/result/rs-ff/r-hold.jpg}
\subcaption{Reset Hold}
\end{minipage}
\caption{
\parbox[t]{8cm}{RS Latch with OR Gates and NOT Gates (LEDs Represent Set, Reset, Inverted Output, Output from Left)}
}
\label{fig:a3-1-res}
\end{figure}
\subsubsection{観測された挙動}
\begin{table}[H]
\centering
\caption{Observed State Transition Table of RS Latch}
\label{tab:a3-1-res-st}
\begin{tabular}{ccccl}
\hline
$R$ & $S$ & $Q$ & $\overline{Q}$ & Action \\
\hline
0 & 0 & $Q$ & $\overline{Q}$ & Hold \\
0 & 1 & 1 & 0 & Set \\
1 & 0 & 0 & 1 & Reset \\
1 & 1 & X & X & Unstable Behaviour \\
\hline
\end{tabular}
\end{table}
\subsection{課題 3-2}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff/initial.jpg}
\subcaption{Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff/clk-1.jpg}
\subcaption{Clocked Once from Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff/clk-2.jpg}
\subcaption{Clocked Twice from Initial State}
\end{minipage}
\caption{D Flipflop Toggler}
\label{fig:a3-2-res}
\end{figure}
\subsubsection{観測された挙動}
\begin{table}[H]
\centering
\caption{Observed State Transition Table of D Flipflop Toggler}
\label{tab:a3-2-res-st}
\begin{tabular}{cccl}
\hline
$CK$ & $Q$ & $Q_{\text{next}}$ & Action \\
\hline
$\uparrow$ & 0 & 1 & Toggle \\
$\uparrow$ & 1 & 0 & Toggle \\
$\downarrow$ & * & Q & Hold \\
\hline
\end{tabular}
\end{table}
\subsection{課題 3-3}
\subsubsection{動作}
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit/initial.jpg}
\subcaption{Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit/clk-6.jpg}
\subcaption{Clocked Six Times from Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit/clk-15.jpg}
\subcaption{Clocked Fifteen Times from Initial State}
\end{minipage}
\caption{4 Bits D Flipflop Counter (LSB on Right)}
\label{fig:a3-3-res}
\end{figure}
\subsubsection{観測された挙動}
\begin{table}[H]
\centering
\caption{Observed State Transition Table of 4 Bits D Flipflop Counter}
\label{tab:a3-3-res-st}
\begin{tabular}{cccccccl}
\hline
$Q$ & CK & $Q_{\text{next}}$ & $D_A$ & $D_B$ & $D_C$ & $D_D$ & Action \\
\hline
0 & $\uparrow$ & 1 & 0 & 0 & 0 & 0 & Count \\
1 & $\uparrow$ & 2 & 1 & 1 & 1 & 1 & Count \\
2 & $\uparrow$ & 3 & 0 & 1 & 1 & 1 & Count \\
3 & $\uparrow$ & 4 & 1 & 0 & 1 & 1 & Count \\
4 & $\uparrow$ & 5 & 0 & 0 & 1 & 1 & Count \\
5 & $\uparrow$ & 6 & 1 & 1 & 0 & 1 & Count \\
6 & $\uparrow$ & 7 & 0 & 1 & 0 & 1 & Count \\
7 & $\uparrow$ & 8 & 1 & 0 & 0 & 1 & Count \\
8 & $\uparrow$ & 9 & 0 & 0 & 0 & 1 & Count \\
9 & $\uparrow$ & 10 & 1 & 1 & 1 & 0 & Count \\
10 & $\uparrow$ & 11 & 0 & 1 & 1 & 0 & Count \\
11 & $\uparrow$ & 12 & 1 & 0 & 1 & 0 & Count \\
12 & $\uparrow$ & 13 & 0 & 0 & 1 & 0 & Count \\
13 & $\uparrow$ & 14 & 1 & 1 & 0 & 0 & Count \\
14 & $\uparrow$ & 15 & 0 & 1 & 0 & 0 & Count \\
15 & $\uparrow$ & 0 & 1 & 0 & 0 & 0 & Count \\
* & $\downarrow$ & $Q$ & * & * & * & * & Hold \\
\hline
\end{tabular}
\end{table}
\subsection{課題 3-4}
? にはANDゲートを使用した.
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit-cond/initial.jpg}
\subcaption{Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit-cond/clk-3.jpg}
\subcaption{Clocked 3 Times from Initial State}
\end{minipage}
\begin{minipage}[h]{0.3\textwidth}
\centering
\includegraphics[width=4cm]{./assets/t-2/result/d-ff-4-bit-cond/halt.jpg}
\subcaption{Halt State}
\end{minipage}
\caption{4 Bits D Flipflop Counter with Halt Condition (LSB on Right)}
\label{fig:a3-4-res}
\end{figure}
\subsubsection{観測された挙動}
\begin{table}[H]
\centering
\caption{Observed State Transition Table of 4 Bits D Flipflop Counter with Halt Condition}
\label{tab:a3-4-res-st}
\begin{tabular}{cccccccl}
\hline
$Q$ & CK & $Q_{\text{next}}$ & $D_A$ & $D_B$ & $D_C$ & $D_D$ & Action \\
\hline
0 & $\uparrow$ & 1 & 0 & 0 & 0 & 0 & Count \\
1 & $\uparrow$ & 2 & 1 & 1 & 1 & 1 & Count \\
2 & $\uparrow$ & 3 & 0 & 1 & 1 & 1 & Count \\
3 & $\uparrow$ & 4 & 1 & 0 & 1 & 1 & Count \\
4 & $\uparrow$ & 5 & 0 & 0 & 1 & 1 & Count \\
5 & $\uparrow$ & 6 & 1 & 1 & 0 & 1 & Count \\
6 & $\uparrow$ & 7 & 0 & 1 & 0 & 1 & Count \\
7 & $\uparrow$ & 7 & 1 & 0 & 0 & 1 & Halt \\
* & $\downarrow$ & $Q$ & * & * & * & * & Hold \\
\hline
\end{tabular}
\end{table}
\subsection{応用課題 A}
\cref{tab:a3-3-res-st}での状態0から状態1になる時の応答波形は\cref{fig:aa-res}となった.
\begin{figure}[H]
\centering
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=6cm]{./assets/t-2/result/signal-timing/first-second-bit.jpg}
\subcaption{First and Second Bits}
\end{minipage}
\begin{minipage}[h]{0.45\textwidth}
\centering
\includegraphics[width=6cm]{./assets/t-2/result/signal-timing/third-fourth-bit.jpg}
\subcaption{Third and Forth Bits}
\end{minipage}
\caption{Response Signals of Counter Output when State Transitions from 0 to 1}
\label{fig:aa-res}
\end{figure}
各出力がTC74HC74のHレベルの入力電圧に達っするまでの時間を応答時間とし,
それぞれの応答時間の概算は\cref{tab:aa-res}となった.
\begin{table}[H]
\centering
\caption{Response Time of Each Bit}
\label{tab:aa-res}
\begin{tabular}{cr}
\hline
Bit & Response Time (ns) \\
\hline
0 & 30 \\
1 & 60 \\
2 & 80 \\
3 & 75 \\
\hline
\end{tabular}
\end{table}