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Multiplying in Bases Greater Than 10

Date: 10/13/2002 at 07:17:58
From: Christal 
Subject: Multiplying using bases greater than 10

I need to know how to multiply and divide by bases greater than 10.  
I searched the archives and when it comes to multiplication and 
addition, all I see is problems worked out in bases smaller than 10.  
I'm really stuck on how to figure out double digit bases.  I would 
appreciate your help.


Date: 10/13/2002 at 23:23:20
From: Doctor Peterson
Subject: Re: Multiplying using bases greater than 10

Hi, Christal.

There is no difference between bases larger and smaller than ten, 
except that you need extra symbols. For example, in base 16 we use

    0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

as our digits. To multiply, you use the same methods you use in base 
ten, but just need a different multiplication table. Here is an 
example:

      2B
    * A4
    ----
      AC <-- 2B * 4
    1AE  <-- 2B * A
    ----
    1B8C <-- sum

To multiply B by 4, if you don't have a table you have to convert to 
decimal and back: B is 11, times 4 is 44, which is 2C in base 16; so I 
wrote the C and carried the 2. Then I multiplied 2 by 4, giving 8, 
and added to 2, giving A. 

The only thing here that you would not have needed to do in base 8, 
say, is converting the B to 11, which is just the meaning of the 
digit.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Number Sense/About Numbers

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