What are bits in the context of channel capacity units? 'bits' are used with 2 different meanings.  One can use 'bits' to mean the binary digits i.e. 1's and 0's.  Bits are also the units of information in a event of discrete source.  I think when channel capacity is measured in bits/sec, we use the second meaning of bits.  Not how many 1's and 0's we can send down the channel but how much information we can send per second through that channel.  Is my interpretation right?
in Information Theory, the amount of information in a message is proportional to the logarithm of the probability of occurrence of the message:

$$ I(m) = -C \log\left( P(m) \right) $$

the only difference between different bases of logarithms is a scaling constant.  if $ C = \frac{1}{\log(2)} $, that is

$$ \begin{align}
I(m) &amp; = -\frac{1}{\log(2)} \log\left( P(m) \right) \\
     &amp;= - \log_2\left( P(m) \right) \\
 \end{align} $$

then we say that the $I(m)$ is in units of bits.  the reason why is if the message $m$ had only two possibilities and both had equal likelihood, then $P(m) = \frac12 $ and $I(m) = 1$.  there are two messages, two possibilities of equal likelihood, like heads and tails of a coin.  and you need only one bit, 0 or 1, to represent the two possibilities.