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Thread: changing base of log without evaluating?

  1. #1
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    changing base of log without evaluating?

    Express 101101_2 in base 4

    okay im not sure what the question means but the answer was 231_4.
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  2. #2
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    Hello, requal!

    Express 101101_2 in base 4 without evaluating.

    Answer: 231_4

    The usual way is to convert the number to base-ten, then to base-four.

    But they expect us to convert to base-four directly.


    This can be done by breaking the number into two-digit groups: . 10\;11\;01

    \text{Then convert each each pair: }\:\underbrace{10_2}_{\downarrow}\:\underbrace{11_  2}_{\downarrow}\:\underbrace{01_2}_{\downarrow}
    . - . - . . . . . . . . . . . . . . . 2 \quad\;\;\: 3\quad\;\:\:1

    Therefore: . 101101_2 \;=\;231_4

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  3. #3
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    actually I think they want us to convert to base 10 than to base 4- can you show me how to do that because I kinda dont understand the above answer.
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  4. #4
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    Quote Originally Posted by requal View Post
    actually I think they want us to convert to base 10 than to base 4- can you show me how to do that because I kinda dont understand the above answer.
    101101_2 = 1 \times 2^0 + 0 \times 2^1 + 1 \times 2^2 + 1 \times 2^3 + 0 \times 2^4 + 1 \times 2^5 = \, ....
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