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introduction_to_digital_systems:calc_decimal_example [2021/09/15 03:27] tfischer |
introduction_to_digital_systems:calc_decimal_example [2021/09/15 03:45] (aktuell) tfischer |
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3. calculate the place factor \\ (= ..., thousands, hundreds, tens, ones, tenths, hundredths, ...) | 3. calculate the place factor \\ $\quad$ |
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\begin{align*} | \begin{align*} |
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3. calculate the place factor \\ $\quad$ | 3. calculate the place factor \\ (= ..., thousands, hundreds, tens, ones, tenths, ...) |
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\begin{align*} | \begin{align*} |
\color{black}{} & \color{black}{} & \color{black}{1000} & \color{black}{100 } & \color{black}{10 } & \color{black}{1 } & \color{black}{0.1 } & \color{black}{0.01 } \\ | \color{black}{} & \color{black}{} & \color{black}{1000} & \color{black}{100 } & \color{black}{10 } & \color{black}{1 } & \color{black}{0.1 } & \color{black}{0.01 } \\ |
\color{black}{\text{digits }:} & \color{black}{z_i} & \color{black}{2} & \color{black}{6} & \color{black}{5} & \color{black}{8 } & \color{black}{4} & \color{black}{7} \\ | \color{black}{\text{digits }:} & \color{black}{z_i} & \color{black}{2} & \color{black}{6} & \color{black}{5} & \color{black}{8 } & \color{black}{4} & \color{black}{7} \\ |
\color{black}{\text{place value}:} & \color{black}{z_i \cdot B^i} & \color{black}{2000} & \color{black}{600} & \color{black}{50} & \color{black}{8 } & \color{black}{0.4} & \color{black}{0.07} \\ | \color{black}{\text{place value}:} & \color{black}{z_i \cdot B^i} & \color{black}{2000} & \color{black}{600} & \color{black}{50} & \color{black}{8} & \color{black}{0.4} & \color{black}{0.07} \\ |
\color{blue }{\text{result}:} & \color{blue }{\sum_i{ z_i \cdot B^i }} & & & \color{blue }{2658.47} \\ | \color{blue }{\text{result}:} & \color{blue }{\sum_i{ z_i \cdot B^i }} & & & \color{blue }{2658.47} \\ |
\end{smallmatrix} | \end{smallmatrix} |
\end{align*} | \end{align*} |
<---- | <---- |
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\begin{align*} | |
\begin{smallmatrix} | |
\color{blue }{\text{numeral}:} & \color{blue }{} & \color{blue }{2} & \color{blue }{6} & \color{blue }{5} & \color{blue }{8.} & \color{blue }{4} & \color{blue }{7} \\ | |
\color{blue }{\text{index}:} & \color{blue }{i} & \color{blue }{3} & \color{blue }{2} & \color{blue }{1} & \color{blue }{0 } & \color{blue }{-1} & \color{blue }{-2} \\ | |
\color{blue }{\text{place factor}:} & \color{blue }{B^i} & \color{blue }{10^3} & \color{blue }{10^2} & \color{blue }{10^1} & \color{blue }{10^0} & \color{blue }{10^{-1}} & \color{blue }{10^{-2}} \\ | |
\color{blue }{} & \color{blue }{} & \color{blue }{1000} & \color{blue }{100 } & \color{blue }{10 } & \color{blue }{1 } & \color{blue }{0.1 } & \color{blue }{0.01 } \\ | |
\color{blue }{\text{digits }:} & \color{blue }{z_i} & \color{blue }{2} & \color{blue }{6} & \color{blue }{5} & \color{blue }{8 } & \color{blue }{4} & \color{blue }{7} \\ | |
\color{blue }{\text{place value}:} & \color{blue }{z_i \cdot B^i} & \color{blue }{2000} & \color{blue }{600} & \color{blue }{50} & \color{blue }{8 } & \color{blue }{0.4} & \color{blue }{0.07} \\ | |
\color{blue }{\text{result}:} & \color{blue }{\sum_i{ z_i \cdot B^i }} & & & \color{blue }{2658.47} \\ | |
\end{smallmatrix} | |
\end{align*} | |
First: But space between the digits to see the thousands, hundreds, tens, ones, tenths, hundredths | |
<---- | |
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\begin{align*} | |
\begin{smallmatrix} | |
\color{black}{\text{numeral}:} & \color{black}{} & \color{black}{2} & \color{black}{6} & \color{black}{5} & \color{black}{8.} & \color{black}{4} & \color{black}{7} \\ | |
\color{black}{\text{index}:} & \color{black}{i} & \color{black}{3} & \color{black}{2} & \color{black}{1} & \color{black}{0 } & \color{black}{-1} & \color{black}{-2} \\ | |
\color{black}{\text{place factor}:} & \color{black}{B^i} & \color{black}{10^3} & \color{black}{10^2} & \color{black}{10^1} & \color{black}{10^0} & \color{black}{10^{-1}} & \color{black}{10^{-2}} \\ | |
\color{black}{} & \color{black}{} & \color{black}{1000} & \color{black}{100 } & \color{black}{10 } & \color{black}{1 } & \color{black}{0.1 } & \color{black}{0.01 } \\ | |
\color{black}{\text{digits }:} & \color{black}{z_i} & \color{black}{2} & \color{black}{6} & \color{black}{5} & \color{black}{8 } & \color{black}{4} & \color{black}{7} \\ | |
\color{black}{\text{place value}:} & \color{black}{z_i \cdot B^i} & \color{black}{2000} & \color{black}{600} & \color{black}{50} & \color{black}{8 } & \color{black}{0.4} & \color{black}{0.07} \\ | |
\color{black}{\text{result}:} & \color{black}{\sum_i{ z_i \cdot B^i }} & & & \color{black}{2658.47} \\ | |
\end{smallmatrix} | |
\end{align*} | |
First: But space between the digits to see the thousands, hundreds, tens, ones, tenths, hundredths | |
<---- | |
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