Design a ternary Huffman code, using $0,1,$ and $2$ as letters, for a source with output

alphabet probabilities given by $\{0\mathrm{.}05,0\mathrm{.}1,0\mathrm{.}15,0\mathrm{.}17,0\mathrm{.}18,0\mathrm{.}22,0\mathrm{.}13\}.$ What is the

resulting average code word length? Compare the average code word length with

the entropy of the source. $($In what base would you compute the logarithms in the

expression for the entropy for a meaningful comparison?$)$