Omnimaga
General Discussion => Other Discussions => Math and Science => Topic started by: apcalc on February 22, 2011, 05:25:15 pm
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I was wondering: does anyone here know an extremely rapid/simple way to change the base of a number (by hand, not through a program :P)? I have used methods I read about on the Internet, but none of them are very fast for me to do. I always come across new ways to do things like this by hand, but I can't seem to find one for changing bases. Does anyone know of a way to do this? Thanks! :)
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Oh, yes, that is rather easy/fun. All you do is use mod values and you don't even need to know what that means!
Basically you do X/A and you take the whole part and the remainder. A is your base. so if you do x=117 and A=10 you get 11 and 7. 7 is the last digit. So:
117→q
117/10: q=11 7=r
11/10 : q=1 1=r
1/10 : q=0 1=r
so your number is 117 in base 10 (go figure). Now for base 16:
117/16: q=7 5=r
7/16 : q=0 7=r
so in hex, 117 is 75h
Just remember that after 9 you start to use letters starting at A.
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The way I like doing it is:
start with any number (1337_10)
Divide by the base you're calculating into (in this case, hex):
1337|16==>83r9
83|16==>5r3
5|16==>r5
Until you no longer have anything except for a remainder. Then read the remainders backwards.
539...easy?