Misses and Associativity in Caches

Question: Finding the Number of Misses
Assume there are three small caches, each consisting of four one-word blocks: Find the number of misses for each cache organization given the following sequence of block addresses: 0, 8, 0, 6, and 8.

Answer:
The answers for the three caches are given as follows:

Direct-mapped cache
The table on the right shows to which cache block each block address maps. The following table shows the cache contents after each reference.
Block address Cache block
0 0 modulo 4 = 0
6 6 modulo 4 = 2
8 8 modulo 4 = 0

A blank entry means that the block is invalid, colored text in italic type shows a new entry added to the cache for the associated reference, and plain text shows an old entry in the cache:

Address of memory block accessed Hit or miss Contents of cache blocks after reference
0 1 2 3
0 miss Memory[0]      
8 miss Memory[8]      
0 miss Memory[0]      
6 miss Memory[0]   Memory[6]  
8 miss Memory[8]   Memory[6]  

The direct-mapped cache generates five misses for the five accesses.



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