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Math Help - bits and bytes help!

  1. #1
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    bits and bytes help!

    You design a machine that can scan the location of every atom in Andrew’s body and build an exact replica, atom by atom. Let’s ignore for a minute why you might want to do that. You wish to specify the location of each atom to within 1.0 × 10^–11 m.

    In the machine, Andrew stands inside a box with dimensions 2.0 m × 0.5 m × 0.5 m. How many bits of information would be required to specify the location of a single atom in this box using (x, y, z) coordinates, to within 1.0 × 10^–11 m?

    Any ideas on how to solve this?! Any hints would be helpful.
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  2. #2
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    Quote Originally Posted by amma0913 View Post
    You design a machine that can scan the location of every atom in Andrew’s body and build an exact replica, atom by atom. Let’s ignore for a minute why you might want to do that. You wish to specify the location of each atom to within 1.0 × 10^–11 m.

    In the machine, Andrew stands inside a box with dimensions 2.0 m × 0.5 m × 0.5 m. How many bits of information would be required to specify the location of a single atom in this box using (x, y, z) coordinates, to within 1.0 × 10^–11 m?

    Any ideas on how to solve this?! Any hints would be helpful.
    Lets look at how many bits are required to specify the x-position to 1 \times 10^{-11}

    The lsb set will represent a distance of 1 \times 10^{-11}.

    In a word of length $$ n all bits set will represent 2^{n}-1 times the value corresponding to the lsb only set. So:

    2=(2^{n}-1)1 \times 10^{-11}

    or:

    n=\lceil \lg(2.10^{11}+1) \rceil = 38

    etc...

    CB
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