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14)
a) \begin{align*}
y &= ( \bot \cdot \bar d + \top \cdot d) \cdot \bar c + (\bar a \cdot \bar d + (a \cdot b) \cdot d) \cdot c \\
&= d \cdot \bar c + (\bar a \cdot \bar d + (a \cdot b) \cdot d) \cdot c
\end{align*}
b) Abbildung \ref{fig:netz}
\begin{figure}[h]
\centering
\begin{circuitikz} \draw
(0,3) node (a) {$a$}
(0,2) node (b) {$b$}
(0,1) node (c) {$c$}
(0,0) node (d) {$d$}
(2,2.5) node [or port] (or1) {}
(a) -- (or1.in 1)
(b) -- (or1.in 2)
(4,2.5) node [not port] (not1) {}
(or1.out) -- (not1.in)
(6,1.75) node [and port] (and1) {}
(not1.out) -- (and1.in 1)
(c) -- (and1.in 2)
(2,0) node [not port] (not2) {}
(d) -- (not2.in)
(8,0.875) node [or port] (or2) {}
(and1.out) -- (or2.in 1)
(not2.out) -- (or2.in 2)
(10,0.875) node (y) {$y$}
(or2.out) -- (y);
\end{circuitikz}
\caption{Schaltnetz}
\label{fig:netz}
\end{figure}
15)
a) $0 + 0 = 0$
b) $1 \cdot 1 = 1$
c) $| B^n | \cdot 2 = 2 \cdot 2^n = 2^{n+1}$
d) $(x_1 \cdot x_2 \cdot \bar x_3) + (x_3 \cdot x_4) + \bar x_2$ ist wahr für $(0, 0, 0, 0)$
e) $\lceil \log_2(n) \rceil$
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