a$.$ Determine the number of padding bits, total length and number of blocks used in HMAC for the hash functions SHA $512$ and MDS if the input message to be sent is M$=1011011100011110$ and the key $K=10111011.(5$ Marks$)$

b$.$ Evaluate the value of $Ch(c,f,g),$Maj$(a,b,c),$ of SHAS$12$ algorithm for the buffers $\text{'}$a$\text{'},\text{'}b\text{'},\text{'}c\text{'},\text{'}e\text{'},\text{'}f\text{'},$ and $\text{'}g\text{'}$ that contain the hexi$-$decimal values as follows: $1111777700001111,$ FFFF$222222221111,$ BBBB$999911112222,$ CCCC$222222220000,1111$DDDD$22221111,$ and $33331111$AAAAFFFF, respectively. $(5$ Marks$)$