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uzy lol 2024-09-27 22:40:48 -07:00
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@ -3,6 +3,7 @@
\usepackage{fancyhdr} \usepackage{fancyhdr}
\usepackage{lastpage} \usepackage{lastpage}
\usepackage{hyperref} \usepackage{hyperref}
\usepackage{graphicx}
\pagestyle{fancy} \pagestyle{fancy}
\fancyhf{} \fancyhf{}
@ -15,17 +16,17 @@
\section{Truth Tables and Boolean Equations} \section{Truth Tables and Boolean Equations}
Derive a truth table and sum-of-products representation for a function: Derive a truth table and sum-of-products representation for a function:
\begin{itemize} \begin{itemize}
\item Inputs: consist of 3 values – A, B, C – that may be either True or False \item Inputs: consist of 3 values – A, B, C – that may be either True or False
\item Output: a single value – X – that is True when two and only two adjacent inputs are true \item Output: a single value – X – that is True when two and only two adjacent inputs are true
\end{itemize} \end{itemize}
Full instructions can be viewed in the \href{https://docs.google.com/document/d/1XpSKpgN0JamxbZtsq-ZivZxFwIlkMH-9futUYkL0g2E/edit}{problem set 1 document}. Full instructions can be viewed in the \href{https://docs.google.com/document/d/1XpSKpgN0JamxbZtsq-ZivZxFwIlkMH-9futUYkL0g2E/edit}{problem set 1 document}.
\subsection{Truth Table} \subsection{Truth Table}
\begin{center} \begin{center}
\begin{tabular}{|c|c|c|c|} \begin{tabular}{|c|c|c|c|}
\hline \hline
A & B & C & X \\ A & B & C & X \\
\hline \hline
@ -38,13 +39,78 @@ Full instructions can be viewed in the \href{https://docs.google.com/document/d/
1 & 1 & 0 & 1 \\ 1 & 1 & 0 & 1 \\
1 & 1 & 1 & 0 \\ 1 & 1 & 1 & 0 \\
\hline \hline
\end{tabular} \end{tabular}
\end{center} \end{center}
\subsection{Sum-of-Products Representation} \subsection{Sum-of-Products Representation}
\[ \[
X = (!A \&\& B \&\& C) || (A \&\& B \&\& !C) X = (!A \&\& B \&\& C) || (A \&\& B \&\& !C)
\]
\newpage
\section{Truth Tables and Boolean Equations 2}
Derive a truth table and sum-of-products representation for the function describing the operation of the 4-channel multiplexor shown in P\&H Fig B.5.10 (below).
Full instructions can be found \href{https://docs.google.com/document/d/1e3DLurnuYyMFrjvi_6Wir7A7KS7h3gS3DyRhnOQJYMw/edit}{here}.
\begin{center}
\includegraphics[scale=0.25]{resources/Set2.png}
\end{center}
\subsection{Truth Table}
\begin{center}
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Ainvert & Binvert & Less & S0 & S1 & S2 & S3 & Result \\
\hline
F & F & F & F & F & F & F & F \\
F & F & F & F & F & F & T & T \\
F & F & F & F & F & T & F & F \\
F & F & F & F & F & T & T & T \\
F & F & F & F & T & F & F & F \\
F & F & F & F & T & F & T & T \\
F & F & F & F & T & T & F & F \\
F & F & F & F & T & T & T & T \\
F & F & F & T & F & F & F & F \\
F & F & F & T & F & F & T & T \\
F & F & F & T & F & T & F & F \\
F & F & F & T & F & T & T & T \\
F & F & F & T & T & F & F & F \\
F & F & F & T & T & F & T & T \\
F & F & F & T & T & T & F & F \\
F & F & F & T & T & T & T & T \\
\hline
T & T & T & T & T & T & T & T \\
\hline
\end{tabular}
\end{center}
\subsection{Sum-of-Products Representation}
\[
\begin{aligned}
\text{Result} = & (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& !S1 \&\& !S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& !S1 \&\& S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& !S1 \&\& S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& S1 \&\& !S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& S1 \&\& !S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& S1 \&\& S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& !S0 \&\& S1 \&\& S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& !S1 \&\& !S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& !S1 \&\& !S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& !S1 \&\& S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& !S1 \&\& S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& S1 \&\& !S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& S1 \&\& !S2 \&\& S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& S1 \&\& S2 \&\& !S3) \\
& \,|| (!Ainvert \&\& !Binvert \&\& !Less \&\& S0 \&\& S1 \&\& S2 \&\& S3) \\
& \,|| \ldots \\
& \,|| (Ainvert \&\& Binvert \&\& Less \&\& S0 \&\& S1 \&\& S2 \&\& S3)
\end{aligned}
\] \]
\end{document} \end{document}

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