Final answer:
The hit rate of a direct-mapped cache with the given access pattern improves as the cache size increases, achieving 50% for a size 2 cache and 100% for sizes 4, 8, 16, and 32, since there are enough slots to accommodate all unique addresses after the initial load.
Step-by-step explanation:
The question asks about the hit rate for a direct-mapped cache given a specific access pattern. To determine the hit rate, we must look at how many times an accessed item is already in the cache (a hit) versus it having to be loaded from memory (a miss). In the access pattern 0, 4, 8, 0, 4, 8, the addresses accessed will map to different slots in the cache depending on its size.
- Size 2 cache: Each address will map to a separate cache line; however, because the cache can only hold 2 different addresses, and there are 3 unique addresses being accessed, we will have a hit for each repeat access after the first loop. This results in a hit rate of 50% or 3/6.
- Size 4 cache: The cache can hold all three unique addresses with one empty slot remaining, leading to a 100% hit rate after the initial load.
- Size 8 cache: This cache also leads to a 100% hit rate after the initial load since there are enough slots for all different addresses.
- Size 16 cache: Similarly, all addresses fit with even more empty slots, resulting in a 100% hit rate after the initial load.
- Size 32 cache: With plenty of room, all address accesses are hits after the initial load, maintaining a 100% hit rate.
To summarize, as the size of the direct-mapped cache increases, the hit rate improves due to the additional slots available for storing data, leading to fewer cache misses. However, beyond a certain point, increasing the cache size has no further benefit on the hit rate for a given access pattern.
Therefore the correct Option is a) of size 2.