91Ó°ÊÓ

Huffman encoding is done by following a path from the root to leaf of a full binary tree. Every left node of the tree is represented as 0 and every right node of the tree is represented as 1.

(a)

Let ${\mathrm{f}}_{\mathrm{a}}=50, {\mathrm{f}}_{\mathrm{b}}=20, {\mathrm{f}}_{\mathrm{c}}=30$. Prefix free encoding of these frequencies is:

The tree obtained is a full binary tree. Therefore, the frequencies $(50,20,30)$yield the codelocalid="1657259801818" $\left\{0,10,11\right\}.$

(b)

Prefix free encoding for the given code word is:

The tree obtained is not a full binary tree. Also, it violates an important property:

A codeword cannot be prefix of another codeword. Here, codeword of $\mathrm{a}\left(0\right)$ is the prefix of codeword of$\mathrm{c}\left(00\right)$ Therefore, the no frequencies can yield the code $\left\{0,1,00\right\}$.

(c)

Prefix free encoding for the given codeword is:

The tree obtained is not a full binary tree. Thus, no frequencies can yield such a code.

Hence, the codeword$\left\{0,10,11\right\}$ can only be yielded from the alphabets.