Conflict misses doubt.

Question

I read that if block size increases, then we have fewer blocks so number of conflict misses increases.

My doubt is how will the conflict misses increase ? If cache size is constant, then by increasing block size we have fewer blocks but SAME TAG bits . So the number of blocks that would be mapped to each line of cache would be same and hence number of conflict misses should remain same right?

Comments

By increasing block size the number of cache lines will decrease .

now we have less number of cache lines than before so conflict misses may increase.

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You just said the first 3 lines of the question. I am asking the reason.

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Take 2 caches one with 4 lines and the other one with 8 lines. Now if you map some blocks into both of the caches lets say by using direct mapping then the first cache you will use the function n mod 4 and in the second cache you will use n mod 8 to map the block.
Now take the example of blocks like
0,4,0,12,0,4
Now cache with 4 blocks will have 3 conflict misses.
By using the cache with 8 lines it will have only 1 conflict miss.
So by increasing block size the no of cache lines decreases which may lead to increased conflict misses.

Answer 1

Number of tags bits remains same it is true but it does not means conflict miss will remain constant.

If block size is increased keeping cache size constant then conflict miss can remain constant or can increase.

Let Main memory have 4 block of 2 word each and cache have 2 block of one word each 

MM block 0	MM block 1	MM block 2	MM block 3
0	2	4	6
1	3	5	7

Cache block 0	Cache block 1
0	2
1	3

MM block 0 and 1 are mapped with cache block 0 similarly MM block 2 and 3 are mapped with cache block 1.

now consider following request 0,7,0,7,0,7....... 

Number of conflict miss 0

Now we increase block size 1 block = 4 words

MM block 0	MM block 1
0	4
1	5
2	6
3	7

Cache Block 0

0

1

2

3

Now for same request 0,7,0,7,0,7..... conflict miss rise 

In short

It depends on word or byte sequence not on mapping technique

https://courses.cs.washington.edu/courses/cse378/02sp/sections/section9-2.html

Comments

In your second paragraph you are saying it might remain same or decrease.

In last sentence you are saying it might rise.

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corrected, check now