# Can all information be expressed as bits?

1. Feb 28, 2013

### Jim Kata

I heard Claude Shannon believed all information could be expressed as a string of bits. Is there a theorem supporting this claim, or is this just some kind of folklore belief?

2. Feb 28, 2013

### phinds

3. Feb 28, 2013

### DrZoidberg

A system that has n possible states has an information content of log(n).
If you use log to the base 2 the unit is bits. For example a byte in a computer can have 256 different states, therefore it represents log2256 = 8 bits of information.
For every physical system - atoms, molecules, even black holes - you have a certain number of possible states that that system could be in. You can always measure the amount of classical information in bits. Classical information is everything that you could measure. But there is also quantum information which is expressed in qubits.

4. Mar 1, 2013

### f95toli

Yes, there are theorems proving that all bandlimited analogue information can be perfectly encoded into a string of bits. This is called the Nyquist-Shannon theorem, there is a nice wiki about it

http://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

Btw, that the information have to be bandlimited is not really an issue: ANY real physical process is in practice bandlimited, simply because you can approximate it with arbitrary precission.

Last edited: Mar 1, 2013