Problem $1$: Cache Organization $(153=45)$

Assume a memory subsystem with a cache of $16$ blocks and a main memory of $256$ blocks, where each

block includes $8$ bytes.

a$)$ In direct mapping, how many bits are needed for the tag filed, the index field, and the offset field?

b$)$ In fully associative mapping, how many bits are needed for the tag filed, the index field, and the offset

field?

c$)$ In $2-$way set associative mapping, how many bits are needed for the tag filed, the index field, and the

offset field?