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\title{Foundations of Information Systems}
\author{Winter Semester 2023--24, Exercise 4}
\date{For discussion on Wednesday, November 15, 2023}
\maketitle


\begin{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.

\item Convert the following single-precision floating bit
representation to decimal:
\begin{equation*}
  1 \, 10001010 \, 11000010000000000000000
\end{equation*}

\item Adapt the computation of propagation of floating point error to
the case of floating point division.  You should find that floating
point division has moderate growth of relative error for all numbers.

\item Does the associative law hold for floating point computations?

\end{enumerate}
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