From dc76e09714cb0392ec71d4fee18fdc1e01cab338 Mon Sep 17 00:00:00 2001
From: Gregor Kleen <gkleen@yggdrasil.li>
Date: Sun, 15 May 2016 21:41:32 +0200
Subject: carch 03

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 ss2016/carch/03/abgabe.md | 39 +++++++++++++++++++++++++++++++++++++++
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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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