Question

This question investigates cache use in different types of cache. Consider a system of 8Kbytes of byte-addressable main memory partitioned into blocks of 32bytes each. The system has cache of size 512bytes. The main memory blocks are being accessed in the order shown in the tables (the numbers are in decimal). Assuming the cache is empty at the start.

Scenario 1: The system uses directly mapped cache.

How is the memory address to be interpreted?

Address field	Value	Reason
Word field length:
Block field length:
Tag field length:

Show whether each memory block access is a hit or a miss. Then compute the hit ratio.

Memory block	Address Tag field	Address Block field	Address Word field	Maps to cache block	Hit/Miss
1
5
21
7
5
1
17
7
17
5
Total

Answer 1

Address field	Value	Reason
Word field length:	5bits	Each block contains 32bytes, and we need Log(32)bit address to access.
Tag field length:	8bits	Memory size is 8kB, so width of address is 13bit. So tag = 13 - 5

Memory block	Address Tag field	Address Word field	Maps to cache block	Hit/Miss
1	00000001	00000	1	Miss
5	00000101	00000	2	Miss
21	00010100	00000	3	Miss
7	00000111	00000	4	Miss
5	00000101	00000	2	Hit
1	00000001	00000	1	Hit
17	00010001	00000	5	Miss
7	00000111	00000	4	Hit
17	00010001	00000	5	Hit
5	00000101	00000	2	Hit
Total				5/5

Therefore hit ratio is 0.5

NOTE that all Address Word field are marked zero, since only block information is given. We do not have information on which word is being accessed.

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