How Can You Easily Change Number Bases?

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Changing number bases can be simplified by using arithmetic in base 10, which allows for straightforward conversions to other bases. For example, to convert 116 to base 3, one can repeatedly divide by 3 and track the remainders. Similarly, converting 389 to base 7 involves dividing by 7 and noting the remainders. Mastery of arithmetic in various bases can facilitate easier conversions, but for those less familiar, using the definition of base notation is a reliable method. Understanding these techniques can significantly aid in base conversion tasks.
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Is there an easy way to change bases?
 
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yeah find a program to do it, or write your own... lol what bases are you talking about .. there are tricks for some.
 
i mean like any bases, what tricks are there, i like tricks. :smile:
 
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.
 
that really helps alot, thank you. :smile:
 
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