معمارية : مثال حول placement methods

Example on Placement problem
By : Noor Kadhum
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A) Using all placement techniques to determine the no. of bits in each field in the address depending on the following information:
Size of M.M= 64 KW.
Size of Cache= 2 KW.
Size of block = 16 W.
Size of set = 2 block.

Sol:
The first think you should take into account is the size of memories, they must be in word unit. In this question there is no problem .
Length of address = 16 bits.

-----------------------------------------------------------------------------------------Direct method
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1- Word field : from the block size:
Size of block = 16 W= 24 --> 4 bit for this field.
2-Block field (it is computed from the no. block):
No .of block= size of cache/ size of block
= 2kw / 16 w
= 211/24
= 27--> 7 bits in block field.
3- tag field= address length- sum of other fields
= 16-(block+word)
= 16 – (7+4)
= 5

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2)Full associative
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1- Word field : is constant in all methods = 4 bits
3- tag field= address length- sum of other fields
= 16-( word)
= 16 – (4)
= 12

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3) Set associative:
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1- Word field : is constant in all methods = 4 bits
2-set field (it is computed from the no. sets in cache):
No .of sets= no. of block in cache/ no. of block in set
= 27 / 2
= 26--> 6 bits in block field.
3- tag field= address length- sum of other fields
= 16-(set+word)
= 16 – (6+4)
= 6

B) Draw the address format with pointing the number of bits for each field using the all placement algorithms. Suppose that:
Size of M.M= 1 MB.
Size of Cache= 4 KB.
The block contains 2W.
There are 4 blocks in each set.

Sol:-
The first think you should take into account is the size of memories, they must be in word unit. In this question we need conversion for both memories:
Size of M.M= 1 MB= 220 B = 220 B / 2 B = 219 W
Size of cache= 4KB= 212 B = 212 B / 2 B = 211 W
Length of address = ------- bits. How?

-----------------------------------------------------------------------------------------Direct method
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1- Word field : from the block size:
Word field = ---------- bit for this field.
2-Block field (it is computed from the no. block):
No .of block = size of cache/ size of block
= ------ .so, there are --------- bits in block field.
3- tag field= address length- sum of other fields
= -----------------

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2- Full associative
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1- Word field : is constant in all methods = ------- bits
3- tag field= address length- sum of other fields
=----------------

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3- Set associative:
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1- Word field : is constant in all methods = --------- bits
2-set field (it is computed from the no. sets in cache):
No .of sets= no. of block in cache/ no. of block in set
= ---------.so, there are ------- bits in set field.
3- tag field= address length- sum of other fields
= ---------------