Consider a system with a direct-mapped cache of size 64 (= 26) bytes, and a main

Question

Consider a system with a direct-mapped cache of size 64 (= 26) bytes, and a main memory of size of 1 KB (i.e.1024 or 210 bytes).

Each cache line contains 8 bytes. A program running on the system accesses the following bytes in the first ten steps:

1: 10 1010 0100

2: 10 1010 1000

3: 10 1010 0100

4: 01 0000 0000

5: 00 1010 0000

6: 00 1010 1100

7: 00 1010 0100

8: 01 0000 0000

9: 10 1010 0000

10: 01 0000 0000

Assuming that the initial values of the cache tags and the cache lines are completely arbitrary,

show which accesses will lead to a hit, and which will cause to a miss. Also, show how the cache

tags will change after each of the above steps. You should justify your answer.

Explanation / Answer

cache arrangement contains 8 rows and 8 coloumns. 8 coloumns correspond to the offset, and 8 rows are represented by 3 bits just after offset by 3rd 4th and 5th bit. Rest 4 are the tag bits, stored in the 4 bit tag of the cache line..

Last 4 bits (leftmost) are the tag of the cache line, and next 3 digits(out of 6, 3 are for offset) are the location of the cache line (not used in the tag),

1: 10 10"10 0"100 : miss-> cache line 100 contained arbitary data, now it contains tag 1010

2: 10 10"10 1"000 : miss-> cache line 101 contained arbitary data, now it contains tag 1010

3: 10 10"10 0"100 : hit-> cache line 100 contains the tag 1010, the required tag

4: 01 00"00 0"000 : miss-> cache line 000 contained arbitary data, now it contains tag 0100

5: 00 10"10 0"000 : miss-> cache line 100 contained 1010, now it contains tag 0010

6: 00 10"10 1"100 : miss-> cache line 101 contained 1010, now it contains tag 0010

7: 00 10"10 0"100 : hit-> cache line 100 contains the tag 0010, the required tag

8: 01 00"00 0"000 : hit-> cache line 000 contains the tag 0100, the required tag

9: 10 10"10 0"000 : miss-> cache line 100 contained 0010, now it contains tag 1010

10: 01 00"00 0"000: hit-> cache line 000 contains the tag 0100, the required tag

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