For instance, in the above example, a 16 bit channel could be said to have a channel capacity of 16 Sh, but when connected to a particular information source which only sends one of 8 possible messages, one would compute the entropy of its output as no more than 3 Sh. And if one already had been informed through a side channel that the message must be among one or the other set of 4 possible messages, then one could calculate the mutual information of the new message (having 8 possible states) as no more than 2 Sh. Although there are an infinite possibilities for a real number chosen between 0 and 1, so-called differential entropy can be used to quantify the information content of an analog signal, such as related to the enhancement of signal to noise ratio or confidence of a hypothesis test.