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Math Help - powers of 2

  1. #1
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    powers of 2

    Every positive integer can be expressed in a unique way as the sum of powers of 2. Express 2008 as the sum of powers of 2.

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  2. #2
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    Possible solution

    I don't know if this is what you were looking for, but I got an answer:

    42^2 + 12^2 + 10^2 = 2008

    I started by squaring 45 and then moving back from there with 44, 43 and so on. I then subtracted this squared value from 2008. When I got to 42^2, which equals 1764, I subtracted it from 2008 and got 244.

    244 = 144 + 100
    244 = 12^2 + 10^2

    I then added these two squares to 42^2 and got 2008.
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  3. #3
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    Quote Originally Posted by nancymcwilliams View Post
    Every positive integer can be expressed in a unique way as the sum of powers of 2. Express 2008 as the sum of powers of 2.

    You are looking for a transcription of a decimal number into a dual number:

    2008=2^{10}+2^9+2^8+2^7+2^6+0\cdot 2^5+2^4+2^3+0\cdot 2^2+0\cdot 2^1+0\cdot 2^0

    Usually used writing:

    2008_{dec} = 11111011000_{bin}
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