Consider the following messaging system. Messages are 8-letter long strings. They use an alphabet of 8 letters: {A,B,C,D,E,F,G,H}. Calculate the Entropy H (information measure in bits) of the following messages. Show your calculations:

S₁ = AAAAAAAA H(S₁) =

S₂ = AAAABBBB H(S₂) =

S₃ = AABBCCDD H(S₃) =

S₄ = ABCDEFGH H(S₄) =

Compare the entropy of a dice-roll for the fair dice (six-sided) and the fake dice.

Is the entropy of the fake dice greater than or less than the entropy of the fair dice?

Is the entropy of the fair dice greater or less than the maximum entropy of the 8-letter string of 8 letter alphabet?