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Time intervals are a multi-base arithmatic problem.

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  • hjwoudenberg@aol.com
    Mathematical descriptions of the problem: Mixed radix _numeral systems_ (http://en.wikipedia.org/wiki/Numeral_system) are unique in that the numerical base
    Message 1 of 1 , Dec 8, 2004
      Mathematical descriptions of the problem:

      Mixed radix numeral systems are unique in that the numerical base may vary from position to position. Such numerical representation is advantageous when representing units that are equivalent to each other, but not by the same ratio. For example, 2 weeks, 5 days, 7 hours, 45 minutes, 15 seconds, and 500 milliseconds can be rendered in mixed-radix notation as:

      \begin{bmatrix} 2, 5, 7, 45, 15, 500 \\ \quad 7, 24, 60, 60; 1000 \end{bmatrix} \mbox{seconds}

      The digits are written above their base, and a semicolon is used to indicate the radix point.

      Mixed-radix numbers of the same base can be manipulated using a generalization of manual arithmetic algorithms. 


      Except, no-one describes how to generalize the mathematic algorithms. 


      I have made two functions that add or subtract multi-base numbers.  They work with other bases than the Gregorian date.  Binary based numbers can only approximate the decimal fraction . For example (one-tenth or one cent).  These functions give exact answers. 


      Tested with over 10 million dates they give a unique number for difference, substation and addition.



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