File:Shannon entropy 5 coin illustration.svg

English: The elephant with 5 coins can send, ${\displaystyle 2^{5}=32,}$ different messages, which is associated with 5 bits of information (if the coins are "fair"). If three coins are given the the crow and two coins to the rat, the crow can send, ${\displaystyle 2^{3}=8,}$ different messages, while the rat can send only, ${\displaystyle 2^{2}=4,}$ different messages. Even though the rat and crow can independently send only ${\displaystyle 8+4=12}$ different messages, together, they possess the same number of bits of information, ${\displaystyle 2+3=5,}$ as the elephant had. This illustrates the additive nature of entropy.