Question

A Suppose you had a character set with n symbols. How many bits are needed if we are going to represent those symbols using a Tixed-length binary encoding? Enter a precise formula for this value, as a function of n (do not use "big-Oh notation). B Suppose you had a character set with 12 symbols. How many bits are needed if we are going to represent those symbols using a fixed-length binary encoding? Enter just a single number below

Answer 1

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Solution:

A. Given N symbols in the charset, we need to represent them with fixed length binary encoding.

Let the number of bits required = k

So we need 2^k >= N

Hence, k = Ceil(log₂N) = smallest integer greater than or equal to log₂N

Ceil stands for ceiling value

B. Given N=12

Using above formula k = Ceil(log₂12) = 4