Consider a computer with the following characteristics: total of $8$ Mbytes of main memory; word size of $4$ byte; block size of $64$ bytes; and cache size of $512$ Kbytes.

a$.$ For the main memory addresses of $7$ AB$056,$ FFBBAC, and $2$F$3005,$ give the corresponding tag, cache line address, and word offsets for a direct$-$mapped cache.

b$.$ Give any two main memory addresses with different Aags that map to the same cache slot for a direct$-$mapped cache.

c$.$ For the main memory addresses of $7$ AB$056$ and FFBBAC, give the corresponding tag and offset values for a fully$-$associative cache.

d$.$ For the main memory addresses of $7$ AB$056$ and FFBBAC, give the corresponding tag, cache set, and offset values for a four$-$way setassociative cache.

$(8$ Marks$)$