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- Thread starter smize
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- #2

tiny-tim

Science Advisor

Homework Helper

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i'm not sure what you're trying to do

there's a general rule that log

does that help?

- #3

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there's a general rule that log_{a}b = log_{x}b/log_{x}a

Yes; I know the general log rules. I am part of the Math Academic team at my school and we are having to convert, for example, 2012

- #4

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Yes; I know the general log rules. I am part of the Math Academic team at my school and we are having to convert, for example, 2012_{3}to Base 6. The issue at hand is we, at most, have 45 seconds to do the calculations and guarantee they are correct. We are wondering if there is a way to do this without have to convert it to Base 10 first. A.K.A. is there a direct way to convert between two non-decimal number systems?

Yes, there is a way to do this, but all depends on how fast you can calculate.

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_{n-1}=0b_n+r_n[/tex]

Then [itex]r_n...r_2r_1[/itex] is the number you want.

- #5

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Let [itex]a[/itex] be your number and let p be the base you want to convert it. Use the division algorithm to write

you didn't define the division algorithm...And using this, a will have to equal a non base-10 number to another non base-10 number of a different number system.

- #6

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- #7

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

- #8

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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

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- #10

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Correct. And that might be a bit difficult.

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

- #11

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Correct. And that might be a bit difficult.

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

it is either that or converting to base 10 then the other bases. In some cases the multiple choice answers we have to choose from are also of 2 different bases -.- And we'll only have 45 seconds to answer.

- #12

coolul007

Gold Member

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for base 9 to base 3, 87 base 9 is 22 21 base 3

The others are a bit tougher

- #13

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Thank you coolul007. It is a very interesting method.

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