$($a$)$ DNA sequences have four possible bases: C G A T$.$ Below is an

example of a part of a DNA sequence is shown.

GATCCTCCAT ATACAACGGT ATCTCCACCT

CAGGTTTAGA TCTCAACAAC GGAACCATTG

$($i$)$ Consider an ASCII encoding of the example below $($ignoring

spaces between bases$),$ what is the number of bits used to store

the example in memory?

$($ii$)$ Give a better suited encoding considering that DNA sequences

only contain four possible bases.

$($iii$)$ What is the compression ratio obtained by using the encoding you

chose in $($ii$)$ instead of the ASCII encoding?

$($b$)($i$)$ Consider the following shorter example:

ATATCGCATC

Perform LZW compression on this short example using the

following initial dictionary:

$0,1,2,3$

$C,A,G,T$

Show the dictionary constructed during compression and the

compressed data.

$($ii$)$ Using the same dictionary, expand the following compressed

data:

$0,2,1,4,4,5,2$

Show the dictionary after uncompressing each code and the

uncompressed sequence.

$($iii$)$ What is the compression ratio obtained on these small examples

from the ASCII encoding and considering that $8-$bits integers are

used to encode the compressed string? Why is this result different

from the average ratio of $4$ obtained on typical human genome

$($which is a DNA sequence of about $3,000$ megabytes of

uncompressed data$)?$ solve all the questions