TI-86 Base Conversion ProgramDate: 03/19/2002 at 20:26:04 From: Amber Subject: Base conversion I need help writing a computer program for my TI-86 graphing calculator. I have finished writing a program that can convert any number in any base (one-ten) to base ten. Now I am writing a program to convert any number in base ten to a given base. Here is an example of what I am trying to do. Convert this number 131255 (base ten) = _________ (base 2) That is one example that this program might solve. I have tried to go about this a number of ways, and but I think that what is holding me back is that I don't know how to convert this problem by hand. Do you think you could lead me in the right direction? Thanks so much, Amber Date: 03/19/2002 at 20:46:52 From: Doctor Paul Subject: Re: Base conversion Find the largest power of 2 less than 131255: 2^17 = 131072 2^18 = 262144 Thus 131255 = 2^17 + ??? In fact, 131255 = 2^17 + 183 Now find the largest power of two less than 183 2^7 = 128 2^8 = 256 so 183 = 2^7 + ??? In fact, 183 = 2^7 + 55 Thus 131255 = 2^17 + 2^7 + 55 Now find the largest power of two less than 55... repeat until you obtain: 131255 = 2^17 + 2^7 + 2^5 + 2^4 + 2^2 + 2^1 + 2^0 Thus 131255 in base 2 is: 100000000010110111 To convert the base 10 number n to base p, find the highest power of p less than n and proceed as above. Be warned that you have to find multiples as well, as demonstrated below: convert 131255 to base 5: 5^7 = 78125 5^8 = 390625 How many times does 5^7 go into 131255? Just once (i.e., 2*5^7 > 131255). So we write: 131255 = 1*5^7 + 53130 5^6 = 15625 5^7 = 78125 but 5^6 goes into 53130 more than once. In fact it goes three times. Thus we write: 131255 = 1*5^7 + 3*5^6 + 6255 5^5 = 3125 5^6 = 15625 5^5 goes into 6255 twice so 131255 = 1*5^7 + 3*5^6 + 2*5^5 + 5 and we're done. So in base 5, 131255 = 13200010 The key to understanding this kind of conversion is to first understand what is meant by the base ten representation of a number such as 131255. It means: 1*10^5 + 3*10^4 + 1*10^3 + 2*10^2 + 5*10^1 + 5*10^0 The coefficients in front of the powers of 10 can be anything from 1 up to 9. In base p, you want to write the number as a sum of multiples of powers of p where the multiples can be anything from 1 up to p-1. Does this help? There's more in our archives about converting from base 10 to other bases. Take a look there if you're still confused. Please write back if you'd like to talk about this some more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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