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Number base system

  1. Sep 15, 2009 #1
    1. The problem statement, all variables and given/known data

    This really isn't a calc question so forgive me.

    Determine which base(radix) is used in the following operation :

    a ) 1234 + 1234 + 1234 + 1234 = 11101
    b ) 19 * 18 = 297

    I know the answer to a but am not sure how to get it.
    What I see is the for a) the answer has to be greater than base 4, and for b) it has
    to be radix >=10.

    Is there some tricks that could help me figure out what base is in general a expression is on?
     
  2. jcsd
  3. Sep 15, 2009 #2

    Mark44

    Staff: Mentor

    For a, yes, the base has to be larger than 4, so use the fact that 4 + 4 + 4 + 4 = base + 1 or maybe 2* base + 1. Check the addition in a few bases (probably not an even base), starting with 5.

    For b, I agree that the base is probably larger than 10. Again try a few bases and see if you can find one for which 9 * 8 = base + 7. Since you're getting a unit's place of 7, it's probably not an even base.
     
  4. Sep 15, 2009 #3
    For A its 5, but I can't seem to figure out part B.

    This is what I got :

    let "r" be the base.

    (9*8)r = ?
    -----------

    r = x | result = y | (1|0)
    -----------------
    11 | 68 | 11 * 6 = 66, left over 2. False
    13 | 57 | 13 * 4 = 52, left over 5, False

    And it goes on.

    What I did was 9*8 = 72. In base 10. Then divide 72 by different bases to see if it matched up.

    wait is r = 13 correct?
     
    Last edited: Sep 15, 2009
  5. Sep 15, 2009 #4
    Yes, the radix is 13 in part (b). Can you show why?

    --Elucidus
     
  6. Sep 16, 2009 #5

    Mark44

    Staff: Mentor

    Keep in mind that the numbers in the product are in the same base as the answer, so what you have for b is 19r * 18r = 297r.

    What I did was to make an educated guess as to the base, and then convert all three numbers into their base-10 equivalents and check the multiplication in that more familiar base.
     
  7. Sep 16, 2009 #6
    I was thinking of doing that as well.

    Lets see :

    19r * 18r = 297r

    I know its not base 10, but from (base 10) 9*8 = 72
    Now I can use this to convert into other base and check accordingly.

    13*5 = 65;
    72 - 65 = 7

    So 7 is left over and even number of 13 is carried onto the next step. Ah, its just
    like you said, look for "base + 7".

    It would be nice if someone could offer alternative solution.
     
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