Suppose you have a 4-letter alphabet {A, B, C, D} and you wish to devise a binary code (with no spaces) for this alphabet such that no two words would be encoded the same. For example, if A = 1 and B = 11, then AA and B would be encoded the same. It takes one second to transmit each character of the binary code (so, 101 would take 3 seconds and 110101 would take 6 seconds). (a) If each letter occurs with the same frequency, determine the most efficient code for the alphabet and explain why it is the most efficient. (b) Now suppose letter A occurs about 40% of the time, B and C both occur about 25% of the time each, and C occurs about 10% of the time. Determine the most efficient code and explain why it is the most efficient.

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