A 2 GB (i.e., 2 middot 230 byte) memory system with 32-bit addresses is used wit

Question

A 2 GB (i.e., 2 middot 230 byte) memory system with 32-bit addresses is used with a 4-way set associative cache that contains a total of 65536 lines (each line is 512 bytes in size). How many different memory blocks could map to set 3 within this cache?) An SMP UMA system contains 64 processors and is to compute a running sum by adding all of the elements in a one million-element vector. Each processor takes one cycle to perform a single addition. How many cycles would it take just to do the required additions on this system?

Explanation / Answer

1.

Address mapping = block address / no of blocks in cache

Memory = 2*2^30 byte = 2^31*2^5/2*3 = 2^33

4 way set associative cache = 4*Lines*no of lines size

                                                = 4*65536*512

                                                = 2^27

No of blocks = 2^33/2^27 = 2^6 = 64

2.

Considering 1000~2^10 so 1 million records are equivalent to 2^20 records. No of processors= 64= 2^6

No of cycles = No of records/(No of processors*no of cycles per processor)

                   = 2^20/(2^6*1)

                   = 2^14

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