Assuming no prefetchers and LRU as the replacing mechanism.
a) For direct-mapped cache, each memory entry can be only in one cache entry. The cache will map like this (default assuming uniform distribution):
Cache 0 --> can hold 0,4,8,12 of the main memory entries.
Cache 1 --> can hold 1,5,9,13 of the main memory entries.
Cache 2 --> can hold 2,6,10,14 of the main memory entries.
Cache 3 --> can hold 3,7,11,15 of the main memory entries.
After reset, the cache is empty.
Load from 0 will be missed and will be cached in cache entry 0.
Load from 1 will be missed and will be cached in cache entry 1.
Load from 2 will be missed and will be cached in cache entry 2.
Load from 8 will be missed and will be cached in cache entry 0 (replaced load 0).
Load from 9 will be missed and will be cached in cache entry 1 (replaced load 1).
load from 2 will be hit and will be taken from cache entry 2.
so we have 1 hit and and 5 misses, the hit rate is 1/(5+1) = 1/6 = 16%
b) For 2 ways associative, you will have for each entry in the memory 2 entries in the cache to go to. so set0 (entries 0,1 in the cache) will hold all the even main memory entries and set1 will hold all the odd entries, so if we span it we will have like this:
cache 0 (set 0) --> can hold 0,2,4,6,8,10,12,14 of the main memory entries.
cache 1 (set 0) --> can hold 0,2,4,6,8,10,12,14 of the main memory entries.
cache 2 (set 1) --> can hold 1,3,5,7,9,11,13,15 of the main memory entries.
cache 2 (set 0) --> can hold 1,3,5,7,9,11,13,15 of the main memory entries.
After reset the cache is empty.
Load from 0 will be missed and will be cached in cache entry 0.
Load from 1 will be missed and will be cached in cache entry 2.
Load from 2 will be missed and will be cached in cache entry 1.
Load from 8 will be missed and will be cached in cache entry 0 (replaced load 0 because we replace the Least Recently Used).
Load from 9 will be missed and will be cached in cache entry 3.
load from 2 will be hit and will be taken from cache entry 1.
in this case the hit rate is the same: 1/(5+1) = 1/6 = 16%