associative mapping

Question

Consider 32 KB 4-way set associative cache with 64-byte block size. CPU generates 32 bits physical address . A 4-to-1 multiplexer has a latency of 1 ns while a k bit comparator has a latency of 2k ns. The hit latency of the cache organization is?

Should we calculate using 4 comparators or just one?

Comments

cache size =32KB = 2¹⁵

block size = 64 B = 2⁶

number of lines = 32 K/ 64 = 512 = 2⁹

number of sets = 512 / 4= 128 = 2⁷

4 ways  , so 4 comparator. each of 19 bits since tag are compared,

but all are working parallally so only time consider for one comparator,

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19 bits comparator used since multiplexer select the set and comparator compare tag of each set.

Answer 1

Cache Size=32KB

Block Size=64B

4-way set associative

No. of sets =2^15/(2^6*2^2)=2^7

Hence Tag Bit=19, Set Bit=7, Word Bit=6

So we need total 4 comparators each of  Size 19 bit.

But, when we calculate Latency of Comparator then we take only one comparator latency (Since all Comparator works in parallel).

Total latency= Delay of One 19-bit Comparator + Delay of one 4:1 Multiplexer (it is used for OR-ing the 4 comparators)  

                    =2*kns+1ns

                   =2*19 +1

                   =39ns