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\title{Foundations of Information Systems}
\author{Winter Semester 2024--25, Exercise 2}
\date{For discussion on Wednesday, October 29, 2025}
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\begin{enumerate}

\item Perform the following conversion to different number systems:
\begin{enumerate}
\item $(\mathrm{DC})_{16} = (\ldots)_{2} = (\ldots)_{10}$
\item $(110101)_{2} = (\ldots)_{10} = (\ldots)_{16}$
\item $(1000)_{10} = (\ldots)_{2} = (\ldots)_{16}$
\end{enumerate}

\item Convert the following decimal numbers into binary.  Note that
the resulting binary representation may not terminate and become periodic.
\begin{enumerate}
\item $(9.5)_{10}$
\item $(\frac{44}7)_{10}$
\end{enumerate}

\item Convert from binary to decimal.
\begin{enumerate}
\item $(1101.0111)_2$
\item $(0.0\overline{1001})_2$
\end{enumerate}

\item Convert from decimal to hexadecimal (a) or back (b).
\begin{enumerate}
\item $(39.75)_{10}$
\item $(F.42)_{16}$
\end{enumerate}

\item Find the $8$-bit two's complement of $(67)_{10}$.

\item Which integer is represented by the bit pattern $10111010$
interpreted as $8$-bit two's complement representation?

\item Show that the two's complement of the two's complement of a bit
pattern returns the original bit pattern.


\end{enumerate}
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