Why increasing block sizes in caches leads to decreased miss rate?

Question

My book about computer organization said that:

If size of a block is 1 word (4 bytes), it will encounter 10 misses when accessing 10 consecutive integers in an array.

If we set the size of a block to 2 words, we can achieve a reduction from 10 misses to maximum 6 misses when probing those 10 consecutive integers. (Assume an integer takes 4 bytes).

I don't get why it is 6 misses, I thought it would be more reasonable to be 5.

Answer 1

If the ten words you want to fetch happen to be aligned to the block boundaries, you'll only need to fetch 5 blocks, as shown here:

           ___
               Word 1000
           ___ Word 1001 ___
           1   Word 1002
           ___ Word 1003
           2   Word 1004
Cache      ___ Word 1005     The ten
Block      3   Word 1006     words you
Boundaries ___ Word 1007     want to
           4   Word 1008     fetch.
           ___ Word 1009
           5   Word 100A
           ___ Word 100B ___
               Word 100C
           ___ Word 100D
               Word 100E
           ___ Word 100F

However, if the ten words start in the middle of a cache block, then they span a total of six blocks, as shown here:

           ___
               Word 1000
           ___ Word 1001
           1   Word 1002 ___
           ___ Word 1003
           2   Word 1004
Cache      ___ Word 1005     The ten
Block      3   Word 1006     words you
Boundaries ___ Word 1007     want to
           4   Word 1008     fetch.
           ___ Word 1009
           5   Word 100A
           ___ Word 100B
           6   Word 100C ___
           ___ Word 100D
               Word 100E
           ___ Word 100F