$6.(15$ points$)$ A $2-$way set associative cache can store $2$ KB of data and uses an LRU replacement strategy. Addresses are $16$ bits and are byte$-$addressable. The block size is $256$ bytes.

a$.(4$ points$)$ How many bits comprise the tag, set index, and block offset?

tag: bits

set index: bits

block offset: bits

b$.(11$ points$)$ Trace through the following sequence of addresses determining if there was a hit or a miss. The cache starts out empty.