\item \self Find a symbolic binary encoding for
$X = \{ 0,1, \ldots, 31 \}$.
Use it to find characteristic functions for the following sets. If possible, simplify the formulas.

  \begin{enumerate}
    \item $B =\{x \in X \mid 24 \leq x < 32\}$
    \item 
      $C = \left\{ x \in X \middle| \enspace
      \begin{array}{lll}
      4 & \leq \enspace x & < 8 \\
      12  & \leq \enspace x & < 16  \\
      20 & \leq \enspace x & < 24
      \end{array}
      \right\}$
  \end{enumerate}
  
  Compute the characteristic functions of the following sets by symbolic operations, using your results from before and simplify your formulas.
  \begin{enumerate}
    \item $D = B \cup C$
    \item $E = B \cap C$
  \end{enumerate}