Assume the following information about a 2-level memory hierarchy system. Memory

ID: 3674591 • Letter: A

Question

Assume the following information about a 2-level memory hierarchy system.

Memory is byte addressable.

Memory capacity is 4 GB (G=2^30).

Cache capacity is 64 KB (K=2^10).

Block offset size is 8 bits.

Assuming that the CPU has generated the physical address X = (2293936063)10, answer the following questions.

1.If 2-way set associative is used, what is the size of each segment in bytes?

2.What is the block offset value?

3. If direct mapped is used, what is the index size?

4. If 2-way set associative is used, what is the index size?

1ans:

Given that Memory capacity= 4 GB i.e 2^2*2^30=2^ 2+30

= 2^32

32 address lines are needed for memory

Cache capacity= 64 KB i.e 2^6*2^10= 2^6+10

=2^16

16 address lines are needed for cache memory

So, that 16 segements with 64 kb cache memory is used to represent the memory capacity.

Size of each segment is 64kb.

2 ans:

Given that Block offset size is 8 bits.

So, that the value of Block offset is 2^8= 256bytes

3ans:

If direct mapping is used, the size of index is 256bytes because it uses a repetative memory locations for the same repeetative value.

4 ans:

if 2-way set associative is used, it is reduced to half i.e 128 bytes. Because it takes 2 bolcks for each set.

So, the index size is 128 bytes.

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