\input{../../../../base/worksheet.tex} \noprintanswers \title{Arbeitsblatt Zahlensysteme} \header{Informatik}{}{13.11.2021} \footer{Stefan Rothe}{}{} \begin{document} \maketitle \begin{questions} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie die Dezimalzahlen ins Binärsystem um. Erkennen Sie ein Muster?} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $1$ & \answer{$1_2$} \\ \hline $3$ & \answer{$11_2$} \\ \hline $5$ & \answer{$101_2$} \\ \hline $7$ & \answer{$111_2$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $30$ & \answer{$1\,1110_2$} \\ \hline $31$ & \answer{$1\,1111_2$} \\ \hline $32$ & \answer{$10\,0000_2$} \\ \hline $33$ & \answer{$10\,0001_2$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $128$ & \answer{$1000\,0000_2$} \\ \hline $256$ & \answer{$1\,0000\,0000_2$} \\ \hline $512$ & \answer{$10\,0000\,0000_2$} \\ \hline $1024$ & \answer{$100\,0000\,0000_2$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % --------------------------------------------------------------------------- {\bf \question Rechnen Sie die Binärzahlen ins Dezimalsystem um. Erkennen Sie ein Muster?} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Binär} & \textbf{Dezimal} \\ \hline $1_2$ & \answer{$1$} \\ \hline $10_2$ & \answer{$2$} \\ \hline $100_2$ & \answer{$4$} \\ \hline $1000_2$ & \answer{$8$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Binär} & \textbf{Dezimal} \\ \hline $1001_2$ & \answer{$9$} \\ \hline $1\,0001_2$ & \answer{$17$} \\ \hline $10\,0001_2$ & \answer{$33$} \\ \hline $100\,0001_2$ & \answer{$65$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Binär} & \textbf{Dezimal} \\ \hline $10\,1010_2$ & \answer{$42$} \\ \hline $10\,1011_2$ & \answer{$43$} \\ \hline $10\,1100_2$ & \answer{$44$} \\ \hline $10\,1101_2$ & \answer{$45$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie die Dezimalzahlen ins Binärsystem um.} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $12$ & \answer{$1100_2$} \\ \hline $28$ & \answer{$1\,1100_2$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $38$ & \answer{$10\,0110_2$} \\ \hline $136$ & \answer{$1000\,1000_2$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Binär} \\ \hline $199$ & \answer{$1100\,0111_2$} \\ \hline $254$ & \answer{$1111\,1110_2$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie die Binärzahlen ins Dezimalsystem um.} \begin{figure}[H] \centering \begin{subfigure}{0.4\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Binär} & \textbf{Dezimal} \\ \hline $0010\,0001_2$ & \answer{$32+1=33$} \\ \hline $0001\,1010_2$ & \answer{$16+8+2=26$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.5\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Binär} & \textbf{Dezimal} \\ \hline $1110\,0101_2$ & \answer{$128+64+32+4+1=229$} \\ \hline $1101\,0110_2$ & \answer{$128+64+16+4+2=214$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Welches ist die grösste natürliche Zahl, welche mit den folgenden Anzahl Bit dargestellt werden kann?} \begin{figure}[H] \centering \begin{subfigure}{0.45\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Anzahl Bit} & \textbf{grösste Zahl} \\ \hline $4$ & \answer{$2^4-1 = 15$} \\ \hline $8$ & \answer{$2^8-1 = 255$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.45\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Anzahl Bit} & \textbf{grösste Zahl} \\ \hline $16$ & \answer{$2^{16}-1 = 65\,535$} \\ \hline $32$ & \answer{$2^{32}-1 = 4\,294\,967\,295$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie die Dezimalzahlen ins Hexadezimalsystem um. Erkennen Sie ein Muster?} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Hexadezimal} \\ \hline $9$ & \answer{$9_{16}$} \\ \hline $10$ & \answer{$A_{16}$} \\ \hline $11$ & \answer{$B_{16}$} \\ \hline $12$ & \answer{$C_{16}$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Hexadezimal} \\ \hline $13$ & \answer{$D_{16}$} \\ \hline $14$ & \answer{$E_{16}$} \\ \hline $15$ & \answer{$F_{16}$} \\ \hline $16$ & \answer{$10_{16}$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Dezimal} & \textbf{Hexadezimal} \\ \hline $30$ & \answer{$1E_{16}$} \\ \hline $31$ & \answer{$1F_{16}$} \\ \hline $32$ & \answer{$20_{16}$} \\ \hline $33$ & \answer{$21_{16}$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie die Hexadezimalzahlen ins Dezimalsystem um. Erkennen Sie ein Muster?} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hexadezimal} & \textbf{Dezimal} \\ \hline $1A_{16}$ & \answer{$26$} \\ \hline $2A_{16}$ & \answer{$42$} \\ \hline $3A_{16}$ & \answer{$58$} \\ \hline $4A_{16}$ & \answer{$74$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hexadezimal} & \textbf{Dezimal} \\ \hline $FC_{16}$ & \answer{$252$} \\ \hline $FD_{16}$ & \answer{$253$} \\ \hline $FE_{16}$ & \answer{$254$} \\ \hline $FF_{16}$ & \answer{$255$} \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hexadezimal} & \textbf{Dezimal} \\ \hline $10_{16}$ & \answer{$16$} \\ \hline $20_{16}$ & \answer{$32$} \\ \hline $30_{16}$ & \answer{$48$} \\ \hline $40_{16}$ & \answer{$64$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} % -------------------------------------------------------------------------- {\bf \question Rechnen Sie Zahlen zwischen Hexadezimal- und Binärsystem um.} \begin{figure}[H] \centering \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hex.} & \textbf{Binär} \\ \hline $7_{16}$ & \answer{$0111_2$} \\ \hline \answer{$9_{16}$} & $1001_2$ \\ \hline $C_{16}$ & \answer{$1100_2$} \\ \hline \answer{$F_{16}$} & $1111_2$ \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hex.} & \textbf{Binär} \\ \hline $\answer{BA_{16}}$ & $1011\,1010_2$ \\ \hline $\answer{92_{16}}$ & $1001\,0010_2$ \\ \hline $\answer{CC_{16}}$ & $1100\,1100_2$ \\ \hline $\answer{66_{16}}$ & $0110\,0110_2$ \\ \hline \end{tabularx} \end{subfigure} \begin{subfigure}{0.3\textwidth} \begin{tabularx}{\textwidth}{|r|R|} \hline \textbf{Hex.} & \textbf{Binär} \\ \hline $DA_{16}$ & \answer{$1101\,1010_2$} \\ \hline $BA_{16}$ & \answer{$1011\,1010_2$} \\ \hline $81_{16}$ & \answer{$1000\,0001_2$} \\ \hline $92_{16}$ & \answer{$1001\,0010_2$} \\ \hline \end{tabularx} \end{subfigure} \end{figure} \end{questions} \end{document}