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converting bases? (math, numbers)

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converting bases? (math, numbers)

Post  karooomph on Wed Jan 07, 2009 10:50 pm

How would I convert 16 base 10 (normal) into base 5?

Would be you able to show me a solid way to convert various bases all the time?

(until, now, I have been using some self-logic-some-trial method in my head) and I've decided I have to find a reliable standard way to do this.

Thanks!
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Re: converting bases? (math, numbers)

Post  bfrsoccer on Thu Jan 08, 2009 7:41 pm

Well, a number in a base, such 142 base 8, is basically just 1*82+4*81+2*80 in base 10 (digitn*basen+digitn-1*basen-1+...+digit0*base0, where base0 would just equal 1).

So, when converting from one base to another, we are solving the equation: digitn*basen+digitn-1*basen-1+...+digit0 = digit_2n*base_2n+digit_2n-1*base_2n-1+...+digit_20

This means when converting from some base to base 10 is easy because we can just plug in the appropriate digits, base, and powers into: digitn*basen+digitn-1*basen-1+...+digit0, and since we write numbers in a base-10 number system, this result is automatically in base 10 (so like in my example at the beginning, 142 base 8 = 1*82+4*81+2*80 = 98 base 10).

Converting from 10 to other bases is a bit trickier, since we're going from a number system we normally use and write in to one we don't. You can't just plug in the digits into digitn*basen+digitn-1*basen-1+...+digit0 as we did before...but, for example, to convert 98 base 10 to base 8, we would have the equation: digitn*basen+digitn-1*basen-1+...+digit0*base = 98.

To solve an equation like this, we'll "fill" up each digit, starting from the ones place. First, take the remainder of 98/8 - the operator that returns the remainder of the division is known as the modulus operator, or simply mod, so 98 mod 8 = 2 (just take the decimal part of the division of 98/8, which is .25, and multiply it by 8). So, so far, we have 2 in the ones place.

Next we do 98 mod 82, which equals 34, to see how much is in the eights place. Then, divide this result by 8, so 34/8=4.25. This means that 8 goes into 34 four whole times (the extra .25 is taken care of by the ones digit, 2, as 2/8=.25), so 4 is the the digit in the eights place, making our number so far: 42 base 8.

Finally, we do 98 mod 83, which actually equals 98 (this means we can stop the process of taking mods and dividing by 8power here because 98 mod 83 equalling 98 means that 83, which equals 512 base 10, is greater than 98). Then, we divide this result by 82 to see how many times 82 goes into it, or what the digit for the 82 place would be (like how you 403 divided by 102 equals 4.03, and 4 is the digit in the 102s place) - the result of this is 1.53125, so 1 is the digit in the 102s place, leaving us with the final answer of: 142 base 8 = 98 base 10.

So, now, in short, to convert 16 base 10 to base 5:
16 mod 5 = 1; digit in 1s place
(16 mod 52 = 16; now do 16/5 to find how many times it can fit in the 5s place, 16/5=3.2, so 3 is the digit in the 5s place; we also knows this is the last digit we need to worry about because 16 mod 52 = 16

31 is the final answer.
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Re: converting bases? (math, numbers)

Post  funion987 on Thu Jan 08, 2009 10:33 pm

Man. I'm glad I never have to go that far to answer a chemistry question. I don't know how you do it, bfr.... Nice use of sub and superscript.
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speechless

Post  karooomph on Fri Jan 09, 2009 11:26 pm

Shocked

to put in super and sub scripts, according to funion's info post you put these intriguing [sup] brackets. You did that at least 43 times in this detailed solution. That IS....dedication!
Pretty sure I won't have any more problems with bases from now on!!!

Thank you.

btw, gosh, I've been browsing through trying to answer any questions, but man, they're all like, "College Math, Riemann Theory, triflumetrapolimosiss! (you should get my point).
Tough.


But again, I will now always have this page for reference, thank you bfrsoccer!
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Re: converting bases? (math, numbers)

Post  funion987 on Sat Jan 10, 2009 2:24 pm

karooomph wrote:But again, I will now always have this page for reference, thank you bfrsoccer!
Unless I delete it....bwa ha ha ha. Twisted Evil
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Ahahaha!

Post  karooomph on Mon Jan 12, 2009 10:49 pm

I copied everything onto a word document, Ahahaha!

You can't stop me now... Evil or Very Mad
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Re: converting bases? (math, numbers)

Post  funion987 on Mon Jan 12, 2009 11:07 pm

Good thinking.
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Term Papers

Post  orten999 on Thu Apr 22, 2010 1:04 am

I am trying to convert base 10 to base 16 and I can’t seem to wrap myself around how to do this. I understand how you did the base 5, but the answers that I am coming up with aren’t matching the book so I am also confused!

Term Papers

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Re: converting bases? (math, numbers)

Post  mafiafran on Thu Aug 12, 2010 10:36 pm

Nice use of sub and superscript

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Re: converting bases? (math, numbers)

Post  LeeRain on Fri Sep 10, 2010 1:06 am

To solve an equation like this, we'll "fill" up each digit, starting from the ones place. First, take the remainder of 98/8 - the operator that returns the remainder of the division is known as the modulus operator, or simply mod, so 98 mod 8 = 2 (just take the decimal part of the division of 98/8, which is .25, and multiply it by Cool. So, so far, we have 2 in the ones place.




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