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Homework Help: Easy way out :>

  1. Nov 29, 2004 #1
    Is there an easy way to change bases?
     
  2. jcsd
  3. Nov 29, 2004 #2
    yeah find a program to do it, or write your own... lol what bases are you talking about .. there are tricks for some.
     
  4. Nov 29, 2004 #3
    i mean like any bases, what tricks are there, i like tricks. :smile:
     
  5. Nov 30, 2004 #4

    HallsofIvy

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    Since you can easily do arithmetic in base 10, it is relatively easy to change from base 10 to any other base.

    Example: write 116 in base 3.

    3 divides into 116 38 times with remainder 2: 116= 3(38)+ 2
    3 divides into 38 12 times with remainder 2: 38= 3(12)+ 2 so
    116= 3(3(12)+ 2)+ 2
    3 divides into 12 4 times with remainder 0: 12= 3(4) so
    116= 3(3(3(4))+ 2)+ 2
    3 divides into 4 once with remainder 1:
    116= 3(3(3(3+ 1))+ 2)+ 2= 1*34+1*33+ 0*32+ 2*3+ 2 = 110223.

    That is, the last quotient, followed by the remainders.


    Similarly, to convert 389 to base 7: 7 divides into 389 55 times with remainder 4
    7 divides into 55 7 times with remainder 6
    7 divides into 7 1 time with remainder 0.
    Thus 389= 10647.

    IF you could easily do arithmetic in, say base 7, changing from base 7 to base 10 would be just as easy. Unfortunately I'm not that good in other bases so the simplest way of changing from base 7 to base 10 is just to use the definition of "base" notation.
    10647= 1*73+ 0*72+ 6*7+ 4= 1*343+ 0*49+ 6*7+ 4= 343+ 42+ 4= 38910.
     
  6. Nov 30, 2004 #5
    that really helps alot, thank you. :smile:
     
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