Given the two files DNA$\_$SEQ, and PROT$\_$SEQ compress them using $($i$)$ Binary coding,

$($ii$)$ Huffman coding.

For binary coding if you have n unique letters, then you can use the binary representation for

each letter. For example, if the text has $8$ unique letters, then you can code the letters using three

$($log$2)$ bits as$,000,001,010,011,100,101,110,111.$ For Huffman coding use the method discussed

in the slides. As usual, for either method you can use or adapt codes available online.

$($i$)$ Compare the memory required to store $($a$)$ the DNA$\_$SEQ using Binary and

Huffman coding $($b$)$ PROT$\_$SEQ using Binary and Huffman coding. $(10)$

$($ii$)$ Discuss why the DNA$\_$SEQ did not show as significant savings as the PROT$\_$SEQ $(10)$

$($iii$)$ Develop an algorithm by which you can modify how you store the DNA$\_$SEQ so that you

obtain better saving than the binary method. This has to be a lossless compression, similar to

Huffman coding. You only have to describe the algorithm in

detail $($no code needed$)$ and explain why it will improve the storage. $(20)$