Made-easy test series

Question

Cache can hold 512KB. Data is transferred between main memory and Cache Block of 32B each. Main memory consists of 4GB. If cache memory is 2-way set associative then the hexadecimal main memory address (ABABABAB)_H is mapped to which cache set?

Answer give by them is Line offset= 2B5B and Set offset= 1D5D.

I understood how they got set offset value but didn't understand how they got the answer for line offset.

Please help.

Answer 1

See first of all we have to see the CPU generated address format based on the constraints given

No of lines = Cache size  / cache blocksize 

                =  512 K B /  32 B

                =  2¹⁴

No of sets hence  = 2¹³

Hence no of set bits  =  13 bits

Block offset  = log₂ (32)   =  5 bits

So no of tag bits  =  32 - 13 - 5  =  14 bits

Given memory address : A B A B A B A B  

                   = 1010 1011 1010 1011 1010 1011 1010 1011

So set bits (middle 13 bits after 14 tag bits)  =  11 1010 1011 101 which can be rewritten as 

                                                                 =  0001 1101 0101 1101

                                                                 =  1 D 5 D

Hence set offset   =  1 D 5 D

There is no line offset concept in set associative cache as given a set , a line can be mapped to any of the ways..

Comments

Your last statement "There is no line offset concept in set associative cache as given a set, a line can be mapped to any of the ways" 

You mean to say beacuse the question is about set associative mapping so they gave line offset value just randomly i.e. 2B5B?

Had it been a direct mapping then we would find line offset value right? 

As number of lines is 2¹⁴ so there is 14bits for line. Hence leaving first 13bits for tag, we have 14bits for line which again give us the same value 1D5D.

Am I correct?

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I mean to say given a set the main memory block can be allocated to any of the cache blocks within a set..

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Ya, i know that part. Just am still not clear about 2B5B value for line concept.

Please clarify that part.