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introduction_to_digital_systems:calc_decimal_example [2021/09/15 03:28] – tfischerintroduction_to_digital_systems:calc_decimal_example [2021/09/15 03:45] (current) – tfischer
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 ----> ---->
-3. calculate the place factor \\ (= ..., thousands, hundreds, tens, ones, tenths, ...)+3. calculate the place factor \\ $\quad$
  
 \begin{align*} \begin{align*}
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 ----> ---->
-3. calculate the place factor \\ $\quad$+3. calculate the place factor \\ (= ..., thousands, hundreds, tens, ones, tenths, ...)
  
 \begin{align*} \begin{align*}
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 \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*}
 <---- <----
- 
-----> 
-\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 
-<---- 
- 
- 
-----> 
-\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 
-<---- 
-