Massimiliano Sala edited bits1.tex  over 7 years ago

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%From the rules of the sum of bits, we can derive how to compute \emph{mul% tiples} of bits.\\   \begin{Exercise}\label{FirstSumMult}  Compute the following operations in $\F_b$: $\Fb$:  \begin{itemize}  \item $(1+1)+0$  \item $(1+1)+1 $  \item $(1+1)\cdot 1$  \item $(0+0)+1+(1+0)*1$ $(0+0)+1+(1+0)\cdot 1$  \end{itemize}  \end{Exercise} 

\begin{Exercise}\label{Opposto}  What is the opposite of   \begin{itemize}  \item $(1+0)*1$? $(1+0)\cdot 1$?  \item $(0+0)*0$? $(0+0)\cdot 0$?  \item $1+1+1+1+0+1+(1*1)$? $1+1+1+1+0+1+(1\cdot 1)$?  \end{itemize}  \end{Exercise}  It is time that we introduce more formalism. We can consider any set $G$ endowed with an operation $*$ such that for any $a,b$ in $G$ the operation outputs another element $a*b$ of $G$. 

\caption{Logic}\label{Logic}  \end{table}  We conclude this section with proposing a few exercises.  \begin{Exercise}\label{XorIsNice}  What can you observe by comparing tables \ref{SumProd} and \ref{Logic}?  \end{Exercise}