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1 | 14) | ||
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 | |||
34 | 15) | ||
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) $\lceil \log_2(n) \rceil$ | ||