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114)
2 a) \begin{align*}
3 y &= ( \bot \cdot \bar d + \top \cdot d) \cdot \bar c + (\bar a \cdot \bar d + (a \cdot b) \cdot d) \cdot c \\
4 &= d \cdot \bar c + (\bar a \cdot \bar d + (a \cdot b) \cdot d) \cdot c
5 \end{align*}
6 b) Abbildung \ref{fig:netz}
7 \begin{figure}[h]
8 \centering
9 \begin{circuitikz} \draw
10 (0,3) node (a) {$a$}
11 (0,2) node (b) {$b$}
12 (0,1) node (c) {$c$}
13 (0,0) node (d) {$d$}
14 (2,2.5) node [or port] (or1) {}
15 (a) -- (or1.in 1)
16 (b) -- (or1.in 2)
17 (4,2.5) node [not port] (not1) {}
18 (or1.out) -- (not1.in)
19 (6,1.75) node [and port] (and1) {}
20 (not1.out) -- (and1.in 1)
21 (c) -- (and1.in 2)
22 (2,0) node [not port] (not2) {}
23 (d) -- (not2.in)
24 (8,0.875) node [or port] (or2) {}
25 (and1.out) -- (or2.in 1)
26 (not2.out) -- (or2.in 2)
27 (10,0.875) node (y) {$y$}
28 (or2.out) -- (y);
29 \end{circuitikz}
30 \caption{Schaltnetz}
31 \label{fig:netz}
32 \end{figure}
33
3415)
35 a) $0 + 0 = 0$
36 b) $1 \cdot 1 = 1$
37 c) $| B^n | \cdot 2 = 2 \cdot 2^n = 2^{n+1}$
38 d) $(x_1 \cdot x_2 \cdot \bar x_3) + (x_3 \cdot x_4) + \bar x_2$ ist wahr für $(0, 0, 0, 0)$
39 e) $\lceil \log_2(n) \rceil$