Q13a

A language uses an alphabet of six letters, $\left\{a, b, c, d, e, f\right\}$. The relative frequency of use of each letter of the alphabet in the language is as given below:

$$\begin{array}{|ll|ll|}\hline & \text{LETTER} & \text{RELATIVE FREQUENCY OF USE}\\\hline &\ a &\ 0.19 \\ &\ b &\ 0.05 \\ &\ c &\ 0.17 \\ &\ d &\ 0.08 \\&\ e &\ 0.40 \\ &\ f &\ 0.11 \\\hline \end{array}$$

Design a prefix binary code for the language which would minimize the average length of the encoded words of the language.