Unterschiede

Hier werden die Unterschiede zwischen zwei Versionen angezeigt.

--- introduction_to_digital_systems:calc_logic_example [2021/09/17 00:05] – tfischer
+++ introduction_to_digital_systems:calc_logic_example [2021/09/17 00:08] (aktuell) – tfischer
@@ Zeile 1: / Zeile 1: @@
 ~~REVEAL ~~
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
----->>
-example for a simplification with the rule for boolean algebra \\ \\
-\begin{align*}
-\begin{array}{ll}
-\overline{a \lor (b \land (\bar{a} \lor c) \land 1) \lor a}        &         \\
-\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
-\end{array}
-\end{align*}
-<<----
 ---->>
@@ Zeile 363: / Zeile 182: @@
 \begin{align*}
 \begin{array}{ll}
-/(a \quad \, + \quad\enspace b ) \qquad\qquad\quad        &      \color{white}{\overline{ab}}                 \\
+/(a \quad \, + \quad\enspace b ) \qquad\qquad\quad\;        &      \color{white}{\overline{ab}}                 \\
+\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
+\end{array}
+\end{align*}
+<<----
+---->>
+. $\color{blue}{\text{DeMorgan}}$ \\ \\ \\
+\begin{align*}
+\begin{array}{ll}
+\color{blue}{/(a \quad \, + \quad\enspace b )} \qquad\qquad\quad\;        &      \color{white}{\overline{ab}}                 \\
+\quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
+\end{array}
+\end{align*}
+<<----
+---->>
+. $\color{blue}{\text{DeMorgan}}$ \\ \\ \\
+\begin{align*}
+\begin{array}{ll}
+\;/a \quad \, \cdot \quad\enspace /b \qquad\qquad\quad\;        &      \color{white}{\overline{ab}}                 \\
 \quad\quad\quad\quad\quad\quad          & \quad\quad\quad\quad\quad\quad                  \\
 \end{array}
 \end{align*}
 <<----