Converting any Number Base to Another
Date: 05/11/2001 at 10:38:58 From: Trish Subject: Converting any number base to another Dear Dr. Math, This site has been extremely useful; however, I am still having problems with the concept of number systems and their conversion from one to another. How can you convert numbers from any base into any other base? Q1) Is there a particular technique for the conversion of any number base into any other base? In addition to the above I also require information on basic numeric calculations within a base 5 system. I have played around with this and think the technique is correct, except for division; however, I could really use some input. 34021 - 24113 ------- 4403 (base 5) 34021 + 24113 ------- 102134 (base 5) 3212 x 2 ------ 10424 (base 5) Q2) How do I apply basic calculation of addition, subtraction, multiplication, and division in base 5? I would really appreciate the least complex answer you could give. Hope to hear from you soon. Regards, Trish
Date: 05/11/2001 at 14:43:56 From: Doctor TWE Subject: Re: Converting any number base to another Hi Trish! Thanks for writing to Dr. Math. A good place to start learning about different bases is the Dr. Math Number Bases FAQ at: http://mathforum.org/dr.math/faq/faq.bases.html Some good archive entries to look at for how to convert to and from another base to decimal (base 10) are: Binary Conversion http://mathforum.org/dr.math/problems/stirling1.7.98.html Converting Binary to and From Decimal http://mathforum.org/dr.math/problems/shroff.6.16.99.html Converting Bases http://mathforum.org/dr.math/problems/reinhardt12.21.97.html Mensa: Numbering for an Alternate World http://mathforum.org/dr.math/problems/mensanum.html In order to convert directly from one base to another, you have to be able to do arithmetic either in the base you are going to, or the base you are going from. Thus if you want to convert, for example, a value in base 12 to base 5 directly, you'd have to be comfortable either with addition and multiplication in base 5, or with subtraction and division in base 12. Since most people aren't that comfortable with alternate base arithmetic, I'd recommend doing this in two steps: first convert from base 12 to base 10 (our familiar decimal system), then convert from base 10 to base 5. For example, if I wanted to convert 3A7 (base 12) to base 5, I would first convert to decimal: 144 12 1 --- -- - 3 A 7 = 3 * 144 = 432 ^ + 10 * 12 = 120 A=10 + 7 * 1 = 7 --- 559 (base 10) Then I'd convert 559 to base 5: 5 ) 559 ----- 5 ) 111 r 4 ----- 5 ) 22 r 1 ---- 5 ) 4 r 2 --- 0 r 4 = 4214 (base 5) As for doing arithmetic in other bases, check out: Adding in Base 9 and Base 5 http://mathforum.org/dr.math/problems/costa10.21.97.html Binary Subtraction http://mathforum.org/dr.math/problems/houston.7.25.96.html Binary Operations http://mathforum.org/dr.math/problems/matt4.7.97.html Operations in Nondecimal Bases http://mathforum.org/dr.math/problems/paley.10.16.99.html Multiplying and Dividing Computer Style http://mathforum.org/dr.math/problems/hodsdon9.8.98.html Long Division in Binary http://mathforum.org/dr.math/problems/ames1.5.16.00.html Fraction/Decimal Conversion to Other Bases http://mathforum.org/dr.math/problems/trinidad8.12.98.html If you are still confused or have any further questions, write back. I hope this helps. - Doctor TWE, The Math Forum http://mathforum.org/dr.math/
Date: 06/06/2001 at 11:27:27 From: Trish Subject: Full Marks on Assignment, Thanks Thank you so very much for all your help with my questions relating to base conversion. With the information Dr. Math provided and the book _A Survey of Mathematics_, by Vivian Shaw Groza (Holt, Rinehart & Winston, New York, 1968), I managed to complete the assignment and obtain full marks. Thanks again, Trish
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