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Math Help - Converting Bases

  1. #1
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    Converting Bases

    1.) Convert (547)_10 to the _6 notation

    2.) Convert (6A3)_12 to the decimal notation.

    Note: _10 and _6 mean base 10 and base 6, respectively.
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  2. #2
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    Quote Originally Posted by fifthrapiers View Post
    1.) Convert (547)_10 to the _6 notation.
    Note 6^4 is too much.

    6^3=216 is the starting point.
    This divides the number 2 times remainder 115.

    Now 6^2=36 divides this number 3 times, remainder 7.

    Now 6^1=6 divides this number 1 times, remainder 1.

    Thus,
    (2311)_6 is the required number.
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    Quote Originally Posted by ThePerfectHacker View Post
    Note 6^4 is too much.

    6^3=216 is the starting point.
    This divides the number 2 times remainder 115.

    Now 6^2=36 divides this number 3 times, remainder 7.

    Now 6^1=6 divides this number 1 times, remainder 1.

    Thus,
    (2311)_6 is the required number.

    Where's the 2311 from, and I thought using this algorithm that you go until you have remainder 0

    EDIT: Oh, I see where it's from. Thanks.
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    I don't get what the A is. In my notes, I have this as an example:

    (28A)_12:

    12^2 = 1
    12^1 = 20
    units = 10

    I'm assuming when it goes over the base?
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    Hello, fifthrapiers!

    There is a "trick" to converting to another base . . .


    1) Convert 547 to base-6.

    1. Divide the number by 6, note the remainder. .547 6 = 91, rem. 1

    2. Divide the quotient by 6, note the remainder: .91 6 = 15, rem. 1

    3. Repeat step 2 until a 0 quotient is reached:. . . 15 6 = 2, rem. 3

    . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3 = 0, rem. 2


    Now read up the remainders.

    Answer: . 547 .= .2311_6



    2) Convert (6A3)_12 to base-10.

    (6A3)_12 .= .612 + 1012 + 31 .= .987

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    Quote Originally Posted by Soroban View Post
    [size=3]

    (6A3)_12 .= .612 + 1012 + 31 .= .987

    What exactly is the A? Mind explaining this a bit more?
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    Quote Originally Posted by fifthrapiers View Post
    What exactly is the A? Mind explaining this a bit more?
    When using a base higher than 10 we need symbols for numbers greater than 9 but less than 10. So the typical count goes:
    1 2 3 4 5 6 7 8 9 A B C D ... 10 11 12 13 14 15 16 17 18 19 1A 1B 1C 1D ... 20 etc.

    For base 12 we get:
    1 2 3 4 5 6 7 8 9 A B 10 11 12 13 14 15 16 17 18 19 1A 1B 20 etc.

    -Dan
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