Question

4. (4pts) Assume that you have a direct-mapped cache with four-word blocks and a total size of 16 words that is initially empty, and that you will be given a series of word address references in the following order. Label each reference as a hit or a miss and show the content of the cache in each step. a). word address 21 Hit or Miss? What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address b). word address 41 (continuing from the previous step) Hit or Miss? What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address
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Answer 1

Given that cache size is 16 words and block size is 4 words. So, total number of blocks in cache is = Cache Size/Block Size = 16/4 = 4.

Cache offset need log(4) = 2 bits because block size is 4 words. (Least significant 2 bits are used for block offset)

And number of blocks are 4, so number of bits are for block indexing is log(4) = 2 bits.

And the remaining most significant bits are for tag.

a). word address 21 = (010101). Tag: 01, Block: 01, Word Offset: 01 Hit or Miss ? = Miss in block 1 What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address none 01(Tag) none none b). word address 41 (continuing from the previous step) = (101001). Tag: 10, Block = 10, Word offset = 01 Hit or Miss ? = Miss in block 2 What is the cache content at this point? Block number 0(00) 1 (01) 2 (10) 3 (11) none 10 01 Address none

c). word address 23 (continuing from the previous step) = (010111). Tag = 01, Block : 01, Word offset = 11 Hit or Miss? Hit in block 1 What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) none 01 10 none Address d). word address 8 (continuing from the previous step) =(001000). Tag = 00, Block: 10, Word Offset = 00. Hit or Miss? = Miss in block 2 (Replacement) What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address none 01 00 none

e). word address 43 (continuing from the previous step) = (101011). Tag: 10, Block number = 10 Word offset = 11 Hit or Miss? = Miss in block 2(replacement) What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address none 01 10 none f). word address 50 (continuing from the previous step) = (110010). Tag = 11, Block number: 00, Word offset = 10 Hit or Miss? = Miss in block o What is the cache content at this point? Block number 0 (00) 1 (01) 2 (10) 3 (11) Address 11 01 10 none

g). word address 25 (continuing from the previous step)= (011001. Tag = 01, Block number = 10, Word Offset = 01 Hit or Miss? Miss at block 2 (Replacement) stop: 0121003. Tag = 01, Block number = 10 What is the cache content at this point? 0 (0) 1 (01) 2 (10) 3 (11) Address 11 01 01 none h). word address 48 (continuing from the previous step)= (110000). Tag = 11. Block number = 00, Word Offset = 00 Hit or Miss? Hit at block o What is the cache content at this point? Block number 0(00) 1 (01) 2 (10) 3 (11) Address 01 01 none