 Formally, the amount of classical information we gain, on average, when we learn the value of a random variable (or, equivalently, the amount of uncertainty in the value of a random variable before we learn its value) is represented by a quantity called the Shannon entropy, measured in bits (Shannon and Weaver, 1949). A random variable is defined by a probability distribution over a set of values. In the case of a binary random variable, with equal probability for each of the two possibilities, the Shannon entropy is one bit, representing maximal uncertainty. For all other probabilities — intuitively, representing some information about which alternative is more likely — the Shannon entropy is less than one. For the case of maximal knowledge or zero uncertainty about the alternatives, where the probabilities are 0 and 1, the Shannon entropy is zero. (Note that the term ‘bit’ is used to refer to the basic unit of classical information in terms of Shannon entropy, and to an elementary two-state classical system considered as representing the possible outputs of an elementary classical information source.)