Compare and contrast direct-mapped, set-associative and fully associative cache designs.

What will be an ideal response?

A direct-mapped cache maps values by some index found by taking the last several digits of an address.  With a direct-mapped cache there is a fixed number of slots, and a fixed number of address locations that can map to the given slot.  Even if an empty slot exists, it might not be used if the index does not map to that particular slot.
A fully associative cache is set up in such a way that any row in the cache can store the contents of any address.  Thus every location in the cache must be searched to determine if a particular value is in the cache
A set associative cache is a cache that is logically divided into N separate caches, and one of any of the N caches can store the value at the address that maps to that line.  In order to determine which cache holds the appropriate value, each cache must be inspected, and the proper address tag must be matched to determine which value is the one requested.