Problem 3. Networking in English Letters and bits Alice transfers information in

Question

Problem 3. Networking in English Letters and bits

Alice transfers information in English alphabets to Bob. There are 26 distinct alphabet letters; only alphabets are treated and capitalization is ignored. Part a uses the letters so that they are equally frequent while Parts d-f use the letters for English language.

b. Alice transforms each letter to bits and transfer the corresponding bits to Bob for each letter. Assuming that Alice cannot send a fraction of bits and she wants to be efficient (the less number of bits the better), how many bits are needed per letter?

Explanation / Answer

Since there are only 26 letters from a to z (since capitalization is ignored, we don't have to consider A-Z), the number of bits 'n' should be such that 2n-1 <= 26 <= 2n.

Clearly for n=5, 2n-1 = 16 and 2n = 32. Hence, the number of bits to represent each letter is 5.

Here are some examples of representation of the letters.

a -> 00000

b -> 00001

c -> 00010

d -> 00011

e -> 00100

f -> 00101

g -> 00110

................

z -> 11010

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