This is a question about memory organization which I have had very difficulty to understand,
Assume we have an N-way set associative cache with the capacity 4096bytes. The
set field size of the address is 7 bits and the tag field 21 bits. If we assume that
the cache is used together with a 32-bit processor, what is then the block size (in
bytes), how many valid bits does the cache contain, and what is the associativity of
the cache?
So, we have the following information about the processor and the cache -
Cache Size = 4096 B
Address bits = 32
Index bits = 7
Tag bits = 21
From the above information you can quickly calculate the number of bits required for the offset field -
Offset bits = Address bits - Tag bits - Index bits
Offset bits = 32 - 21 - 7 = 4
Offset bits = 4
Using the offset bits, you can find the block size, 2**offset bits
Block Size = 16 bytes
Next thing is the associativity of the cache We know that the index bits = 7. This means we have 128 blocks. Each block is 16 bytes wide.
Therefore, the number of ways in the cache would be -
Number of ways = Cache Size / (number of blocks * block Size)
Number of ways = 2 Hence the associativity is 2.
Regarding the number of valid bits. Each block requires a valid bit. Hence the number of valid bits would be -
Valid bits = 128*2
Valid bits = 256
Here are some equation that is good to know in order to solve question of these type.
Parameter to know
C = cache capacity
b = block size
B = number of blocks
N = degree of associativity
S = number of set
tag_bits
set_bits (also called index)
byte_offset
v = valid bits
Equations to know
B = C/b
S = B/N
b = 2^(byte_offset)
S = 2^(set_bits)
Memory Address
|___tag________|____set___|___byte offset_|
Now to the question
known:
C = 4096 bytes
set_bits = 7
tag_bits = 21
32 bits address field
Asked:
b?
N?
v?
Simply subtract the tag_bits and set_bits from the 32 bit field this gives you the byte_offset.
byte_offset = 32-21-7 = 4 bits
b = 2^4 = 16 bytes
S = 2^7 = 128 set
B = C/b = 4096/16 = 256
N = B/S = 256/128 = 2
v = B = 256 valid bits
