$[84$ points$]$ Given a single$-$level $2-$way set associative cache, which has $2$ cache sets in total, and each cache block size is $2$ bytes. Assume the address is $4-$bits wide.

a$)[3$ points$]$ How many bits of the address are used for the tag bits, set index bits, and byte offset bits, respectively?

b$)[41$ points$]$ Assume initially the cache is empty, i$.$e$.,$ all cache lines are invalid. Assume we use an LRU $($Least Recently Used$)$ cache replacement policy: when there is no empty cache block in the cache set, a cache block that is least recently used will be selected as the victim