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Thread: Number Bases

  1. #1

    Number Bases

    59 in base b converts to 113 decimal. What does 16 become ? I understand binary theory. Is there a formula similar to a binomial expansion that can be used ? If you can do 1 problem, like binary theory , all are easyish , I hope. Thanks.

  2. #2
    Elite Member
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    Hello, stevieg!

    Very little of what you posted makes any sense . . .


    59 in base b converts to 113 decimal. .What does 16 become?
    . . I assume that is: 16, base b.

    I understand binary theory.
    . . Do you mean binary numbers?
    Is there a formula similar to a binomial expansion that can be used?
    . . Do you mean (a + b)n?
    If you can do 1 problem, like binary theory, all are easyish, I hope.
    Thanks.

    And there must be typo.

    [tex]59_b[/tex] cannot equal [tex]113_{10}[/tex] . . . unless we can have: [tex]b = 20\tfrac{4}{5}[/tex]

  3. #3
    Elite Member
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    "59 in base b" means 5b+ 9 in decimal so your problem is telling you that 5b+ 9= 113. Solving that for b, 5b= 113- 9= 104 so that b=20 and 4/5. A fractional base is peculiar (as Soroban notes) but is theoretically possible.

    But there turns out to be a very simple answer! Since 16 is less than that b, it would be written as 0b+ 16= 16, base b.
    Last edited by HallsofIvy; 05-05-2012 at 10:09 AM.

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