GATE | GATE-CS-2009 | Question 29

Consider a 4-way set associative cache (initially empty) with total 16 cache blocks. The main memory consists of 256 blocks and the request for memory blocks is in the following order:

0, 255, 1, 4, 3, 8, 133, 159, 216, 129, 63, 8, 48, 32, 73, 92, 155.

Which one of the following memory block will NOT be in cache if LRU replacement policy is used?
(A) 3
(B) 8
(C) 129
(D) 216


Answer: (D)

Explanation: 4 way set associative so 16 block will be divided in 4 sets of 4 blocks each.



We apply(Address mod  4) function to decide set.

Set 0 0 48 0 mod4=0 *
4 32 255 mod4=3 *
8 8 1 mod4=1 *
216 92 4 mod4=0 *
Set 1 1 1 3 mod4=3 *
133 133 8 mod4=0 *
129 129 133 mod4=1 *
73 73 159 mod4=3 *
Set 2 216 mod4=0 *
129 mod4=1 *
          63 mod4=3 *
8 mod4=0 *
Set 3 255 155 98 mod4=0 *
3 3 32 mod4=0 *
159 159 73 mod4=1 *
63 63 92 mod4=0 *
155 Mod4=3 *

All  * are misses S1 in the first stage ans S2 in the second.

In the second stage 216 is not present in the cache.

So (D) is correct option.

 

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