1. Here is a series of address references given as word addresses: 3, 3, 11, 11,

Question

1. Here is a series of address references given as word addresses: 3, 3, 11, 11, 12, 15, 16, 12, 23, 1, 2, 3, 46, 47, 19, 11, 3, 22, 4, 27, 26, and 11.

-Assuming a direct mapped cache with 16 one-word blocks that is initially empty, please do the following: (1) label each reference in the list as a hit or a miss, (2) clearly show the final contents of the cache, and (3) show the total number of hits and misses.

-Repeat the above (1), (2), and (3) assuming now we use a direct mapped cache with 4 four-word blocks (i.e. each block contains 4 words and total we have four blocks so the total size of cache remains as16 words.)

Explanation / Answer

Cache size: 16 blocks
Block size: 1 word

So
offset: 0bit
index : 4bits
tag   : 4bits (considering 8bit addressing system)

address   tag   index   offset   hit/Miss
3   0000   0011       Miss
3   0000   0011       Hit
11   0000   1011       Miss
11   0000   1011       Hit
12   0000   1100       Miss
15   0000   1111       Miss
16   0001   0000       Miss
12   0000   1100       Hit
23   0001   0111       Miss
1   0000   0001       Miss
2   0000   0010       Miss
3   0000   0011       Hit
46   0010   1110       Miss
47   0010   1111       Miss
19   0001   0011       Miss
11   0000   1011       Hit
3   0000   0011       Miss
22   0001   0110       Miss
4   0000   0100       Miss
27   0001   1011       Miss
26   0001   1010       Miss
11   0000   1011       Miss

Misses: 17
Hits: 5

-----------------------------------------------------------------------------------------------------------------------------------------------------------

Cache size: 4 blocks
Block size: 4 words

So
offset: 2bits
index : 2bits
tag   : 4bits (considering 8bit addressing system)

address   tag   index   offset   hit/Miss
3   0000   00   11   Miss
3   0000   00   11   Hit
11   0000   10   11   Miss
11   0000   10   11   Hit
12   0000   11   00   Miss
15   0000   11   11   Miss
16   0001   00   00   Miss
12   0000   11   00   Hit
23   0001   01   11   Miss
1   0000   00   01   Hit
2   0000   00   10   Hit
3   0000   00   11   Hit
46   0010   11   10   Miss
47   0010   11   11   Hit
19   0001   00   11   Miss
11   0000   10   11   Hit
3   0000   00   11   Miss
22   0001   01   10   Hit
4   0000   01   00   Miss
27   0001   10   11   Miss
26   0001   10   10   Hit
11   0000   10   11   Miss

Miss: 12
Hit: 10

Here you go champ. I have kept things simple and and tried my best to explain to the point. If incase you are still facing problem with the answer, please feel free to comment below. I shall be glad to help you.

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