My Math Forum Computation in Other Bases

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 February 13th, 2007, 03:04 PM #1 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 Computation in Other Bases How do I compute in other bases? I want to learn how to add, subtract, divide and multiply in other bases. Can someone, who is not uptight about my questions, help me here? Samples: (1) Compute 24 given in base 5 + 14 also in base 5. (2) Compute 32 given in base 5 - 14 also in base 5. (3) Compute 44 given in base 5 times 22 also in base 5. (4) Cumpute 1442 given in base 5 by 4 also in base 5. Thanks
 February 13th, 2007, 10:04 PM #2 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 The methods are the same, but the basic numerical facts have to be learnt again as they look different. For example 4 + 4 = 13 in base 5. You just remember that as a base 5 fact, along with all the base 5 multiplication tables.
 February 14th, 2007, 02:57 AM #3 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 ok Can you show me how to do the questions in other bases as indicated?
 February 14th, 2007, 05:00 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,931 Thanks: 2207 I don't know what methods you use for decimal arithmetic, and remembering tables can't be shown. However, I've already stated enough for you to attempt the first and third problems (since 4 + 4 = 4 * 2), so please do so and show us your working.
 February 14th, 2007, 06:06 AM #5 Senior Member   Joined: Nov 2006 From: I'm a figment of my own imagination :? Posts: 848 Thanks: 0 Skipjack, you can't expect symmetry to memorise multiplication tables in every base. Symmetry, addition and subtraction in other bases work the same as in base 10, except that, instead of carrying a 10, you carry a 5 (or a number equal to whichever base you are working with). Also you may find it easiest, especially with multiplication and division, to convert everything to base ten, perform the operation, and convert back to the original base. The ability to convert between bases is probably a pre-requisite to evaluating any sort of function in any other base (keeping in mind that you should convert between bases through base 10).
 February 14th, 2007, 08:36 AM #6 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms It's not hard at all. Just add the appropriate figures, remembering that you subtract b and carry one whenever the amount is at least b.
February 14th, 2007, 08:12 PM   #7
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Quote:
 Originally Posted by roadnottaken Skipjack, you can't expect symmetry to memorise multiplication tables in every base.
Obviously not, but the smaller bases are really easy. Let's take base 5 as an example. All you have to remember are the following:
2 * 4 = 13, 3 * 4 = 22, 4 * 4 = 31, 2 * 3 = 11, 3 * 3 = 14,
as the rest are the same as in the decimal system.

 February 18th, 2007, 03:51 PM #8 Senior Member   Joined: Dec 2006 From: New Jersey Posts: 378 Thanks: 1 ok Thank you all, especially roadnottaken.

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