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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