Unterschiede
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introduction_to_digital_systems:calc_decimal_example [2021/09/15 01:29] tfischer |
introduction_to_digital_systems:calc_decimal_example [2021/09/15 03:45] (aktuell) tfischer |
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Zeile 1: | Zeile 1: | ||
- | ~~REVEAL | + | ~~REVEAL ~~ |
- | | + | |
----> | ----> | ||
- | $I.\quad$ | + | Calculation example for decimal value |
<---- | <---- | ||
----> | ----> | ||
- | | value || 2 | 6 | 5 | 8 | , | 4 | 7 | | + | Idea: The numeral |
- | | index | + | |
- | | place value | $B^i$ | $10^3$ \\ $1000$ | $10^2$ \\ $100$ | $10^1$ \\ $10$ | $10^0$ \\ $1$ | | $10^-1$ \\ $0.1$ | $10^-2$ \\ $0.01$ | | + | |
- | | digit | $z_i$ | 2 | 6 | 5 | 8 | | 4 | 7 | + | |
- | | calculation | $z_i \cdot B^i$ | 2000 | 600 | 50 | 8 | | 0.4 | 0.07 | | + | |
- | | Result | + | |
- | <---- | + | |
- | ----> | ||
- | |aus (2+3)|$\color{blue}{I_p} = \color{blue}{I_m} = 0$ |$I_p$ und $I_m$ sind damit definiert| | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
<---- | <---- | ||
----> | ----> | ||
- | |aus (6)|$\color{blue}{I_o} = I_1 $ |$I_o$ ist damit bekannt, wenn $I_1$ bekannt ist| | + | so lets start |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
<---- | <---- | ||
----> | ----> | ||
- | |aus (7) und (3)|$I_1 - I_2 -\color{blue}{0} = 0 $ |$\quad$| | + | 1. Put space between the digits |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | <---- | + | |
- | ----> | + | \begin{align*} |
- | |$\quad$|$I_1 = I_2 = I_o$ |$\quad$| | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}: |
+ | \color{white}{\text{index}: | ||
+ | \color{white}{\text{place factor}: | ||
+ | \color{white}{} | ||
+ | \color{white}{\text{digits | ||
+ | \color{white}{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
<---- | <---- | ||
----> | ----> | ||
- | |$\quad$|$\color{blue}{I_1} = \color{blue}{I_2} = \color{blue}{I_o} | + | 2. Write down the index for each position. |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | <---- | + | |
- | ----> | + | \begin{align*} |
- | | $\quad$ |$\frac{U_1}{R_1}= \frac{U_2}{R_2} = \frac{U_A}{R_1 + R_2}$ | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}: |
+ | \color{blue }{\text{index}: | ||
+ | \color{white}{\text{place factor}: | ||
+ | \color{white}{} | ||
+ | \color{white}{\text{digits | ||
+ | \color{white}{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
<---- | <---- | ||
- | ----> | ||
- | | (10)|$U_2= U_A\cdot\frac{R_2}{R_1+R_2}$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | <---- | ||
----> | ----> | ||
- | $II.\quad$ | + | 3. calculate the place factor \\ $\quad$ |
+ | |||
+ | \begin{align*} | ||
+ | \begin{smallmatrix} | ||
+ | \color{black}{\text{numeral}: | ||
+ | \color{black}{\text{index}: | ||
+ | \color{blue }{\text{place factor}: | ||
+ | \color{white}{} | ||
+ | \color{white}{\text{digits | ||
+ | \color{white}{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
<---- | <---- | ||
- | ---->> | ||
- | |aus (0) |$\color{blue}{A_V}=\frac{U_A}{U_E}$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | << | ||
- | ---->> | + | ----> |
- | | $\quad$ |$A_V=\frac{U_A}{\color{blue}{U_E}}$ | + | 3. calculate the place factor |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | << | + | |
- | ---->> | + | \begin{align*} |
- | | $\quad$ |$A_V=\frac{U_A}{\color{blue}{U_2+U_D}}$ | $\quad$ | | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}: |
- | <<---- | + | \color{black}{\text{index}: |
+ | \color{blue }{\text{place factor}: | ||
+ | \color{blue }{} & | ||
+ | \color{white}{\text{digits | ||
+ | \color{white}{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
+ | <---- | ||
- | ---->> | ||
- | | $\quad$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | << | ||
- | ---->> | + | ----> |
- | | $\quad$ | + | 4. write down each digit of the numeral |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | << | + | |
- | ---->> | + | \begin{align*} |
- | | $\quad$ |$A_V=\frac{U_A}{U_A\cdot\frac{R_2}{R_1+R_2}+U_D}$ | $\quad$ | | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}: |
- | <<---- | + | \color{black}{\text{index}: |
+ | \color{black}{\text{place factor}: | ||
+ | \color{black}{} | ||
+ | \color{blue }{\text{digits | ||
+ | \color{white}{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
+ | <---- | ||
- | ---->> | ||
- | | $\quad$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | << | ||
- | ---->> | + | ----> |
- | | $\quad$ | + | 5. calculate the place value \\ $\quad$ |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | << | + | |
- | ---->> | + | \begin{align*} |
- | | $\quad$ |$A_V=\frac{U_A}{U_A\cdot\frac{R_2}{R_1+R_2}+\frac{U_A}{A_D}}$ | $\quad$ | | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}: |
- | <<---- | + | \color{black}{\text{index}: |
+ | \color{black}{\text{place factor}: | ||
+ | \color{black}{} | ||
+ | \color{black}{\text{digits | ||
+ | \color{blue }{\text{place value}: | ||
+ | \color{white}{\text{result}: | ||
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
+ | <---- | ||
- | ---->> | + | ----> |
- | | $\quad$ | + | 6.Add all place values |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | |
- | << | + | |
- | ---->> | + | \begin{align*} |
- | | $\quad$ |$A_V=\frac{1}{\frac{R_2}{R_1+R_2}+\frac{1}{A_D}}$ | $\quad$ | | + | \begin{smallmatrix} |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{numeral}:} & \color{black}{} & \color{black}{2} & \color{black}{6} & \color{black}{5} |
- | << | + | \color{black}{\text{index}: |
- | + | \color{black}{\text{place factor}: | |
- | ---->> | + | \color{black}{} & |
- | | $\quad$ |$A_V=\frac{1}{\frac{R_2}{R_1+R_2}+\color{blue}{\frac{1}{A_D}}}$ | mit $\frac{1}{A_D} \xrightarrow{A_D \rightarrow | + | \color{black}{\text{digits |
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | + | \color{black}{\text{place value}: |
- | <<---- | + | \color{blue }{\text{result}: |
+ | \end{smallmatrix} | ||
+ | \end{align*} | ||
+ | <---- | ||
- | ---->> | ||
- | | $\quad$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | << | ||
- | ---->> | ||
- | | $\quad$ | ||
- | |$\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$|$\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad\quad$| | ||
- | << |