$1-$B$.$ Two codes for a discrete source of five independent symbols are:

$\backslash$table$[[$Letter$,$Probability,Code A$,$Code B$],[S_1,0\mathrm{.}4,00,0],[S_2,0\mathrm{.}25,01,01],[S_3,0\mathrm{.}15,101,011],[S_4,0\mathrm{.}12,110,0111],[S_5,0\mathrm{.}08,1111,01111]]$

a$)$ Determine whether each code is a prefix$-$condition code.

b$)$ Determine which one is a uniquely decodable. And which one is an instantaneous code.

c$)$ Determine the entropy of both codes. What is the code efficiency of each code?

d$)$ Explain how to improve the code efficiency.

e$)$ Find the binary Huffman code of this source. Find its code efficiency.