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Converting between bases without base 10 midstep 
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#1
Jan2612, 05:29 PM

P: 78

I am currently trying to go between any two bases which are between and including base 2 to base 10. (i.e, base 10 to base 3, base 4 to base 6, etc...). Is there an equation or set of formulas for a onestep transition between the bases (or oneway method, rather than converting to base10 then to basex.



#2
Jan2612, 06:02 PM

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P: 26,148

hi smize!
i'm not sure what you're trying to do there's a general rule that log_{a}b = log_{x}b/log_{x}a … does that help? 


#3
Jan2612, 06:08 PM

P: 78




#4
Jan2612, 06:24 PM

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Converting between bases without base 10 midstep
Let [itex]a[/itex] be your number and let p be the base you want to convert it. Use the division algorithm to write [tex]a=b_1p+r_1[/tex] Use it again on [itex]b_1[/itex]: [tex]b_1=b_1p+r_2[/tex] Keep doing it until a [itex]b_n=0[/itex]. Then we have [tex]b_{n1}=0b_n+r_n[/tex] Then [itex]r_n...r_2r_1[/itex] is the number you want. 


#5
Jan2612, 06:32 PM

P: 78




#6
Jan2612, 06:52 PM

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#7
Jan2612, 06:57 PM

P: 78

Could you give an example of using that to convert between let's say, base 6 and base 4?



#8
Jan2612, 07:16 PM

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Let's pick 2201 base 4 and let's convert it base 6. So a=2201 and p=12 (remember to express p also in base 4).
2201= 12*103 + 11 122= 12*10 +2 10 = 12*0 +10 Thus 2201 in base 6 is 10 2 11. If we put 10=4 and 11=5, then we get 425. 


#9
Jan2612, 07:21 PM

P: 78

So the division algorithm does work for all bases, it is just a matter of familiarizing yourself with the multiplication tables of the other bases, correct?



#10
Jan2612, 07:22 PM

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P: 18,346

Maybe there are other methods, but I doubt it... 


#11
Jan2612, 07:27 PM

P: 78




#12
Feb412, 10:04 PM

P: 234

converting from power of 2 you just regroup the bits. base 2, 4, and 8 is easy same for base 3 and 9. 67 base 8 to base 2 110 111 then to base 4 11 01 11 or 313
for base 9 to base 3, 87 base 9 is 22 21 base 3 The others are a bit tougher 


#13
Feb712, 12:02 PM

P: 78

Thank you coolul007. It is a very interesting method.



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