Horner-Schema/Beispiele

Im folgenden sind einige Beispiele für die Umrechnung von Zahlen mit dem Horner-Schema angegeben. Die Summanden auf der rechten Seite jeder Gleichung sind farblich hervorgehoben, ebenso die dazugehörigen Ziffern auf der linken Seite jeder Gleichung in derselben Farbe.

Binär → dezimal

$${\begin{aligned}{\textrm {1}}&=\color {blue}{1}\\{\color {blue}{\textrm {1}}}{\color {orange}{\textrm {0}}}&={\color {blue}{1}}\cdot 2+{\color {orange}{0}}={\color {green}{2}}\\{\color {green}{\textrm {10}}}{\color {red}{\textrm {1}}}&={\color {green}{2}}\cdot 2+{\color {red}{1}}={\color {purple}{5}}\\{\color {purple}{\textrm {101}}}{\color {royalblue}{\textrm {0}}}&={\color {purple}{\textrm {5}}}\cdot 2+{\color {royalblue}{0}}={\color {gray}{10}}\\{\color {gray}{\textrm {1010}}}{\color {orchid}{\textrm {1}}}&={\color {gray}{\textrm {10}}}\cdot 2+{\color {orchid}{1}}={\color {brown}{21}}\\{\color {brown}{\textrm {10101}}}{\color {seagreen}{\textrm {0}}}&={\color {brown}{\textrm {21}}}\cdot 2+{\color {seagreen}{0}}=42\end{aligned}}$$

Hexadezimal → dezimal

$${\begin{aligned}{\textrm {C}}&=\color {blue}{12}\\{\color {blue}{\textrm {C}}}{\color {orange}{\textrm {0}}}&={\color {blue}{12}}\cdot 16+{\color {orange}{0}}={\color {green}{192}}\\{\color {green}{\textrm {C0}}}{\color {red}{\textrm {F}}}&={\color {green}{192}}\cdot 16+{\color {red}{15}}={\color {purple}{3087}}\\{\color {purple}{\textrm {C0F}}}{\color {royalblue}{\textrm {F}}}&={\color {purple}{\textrm {3087}}}\cdot 16+{\color {royalblue}{15}}={\color {gray}{49407}}\\{\color {gray}{\textrm {C0FF}}}{\color {orchid}{\textrm {E}}}&={\color {gray}{\textrm {49407}}}\cdot 16+{\color {orchid}{14}}={\color {brown}{790526}}\\{\color {brown}{\textrm {C0FFE}}}{\color {seagreen}{\textrm {E}}}&={\color {brown}{\textrm {790526}}}\cdot 16+{\color {seagreen}{14}}=12648430\end{aligned}}$$