# bits and bytes help!

• Oct 27th 2010, 07:50 PM
amma0913
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.
• Oct 27th 2010, 10:23 PM
CaptainBlack
Quote:

Originally Posted by amma0913
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