The Midterm Solution - Suraj @ LUMS - Lahore University of ...

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Q 23. [15 marks] A microprocessor has an on-chip 2-way set associative cache with a totalcapacity of 8 kByte. Each line in cache can store sixteen 8-bit words. It has a totaladdressable space of 16 MBytes.Consider the following CPU instruction:Load AB1234ha) Which set number will this request be stored in cache? [2]Number of lines in a set (k) = 2Total capacity of the cache = 8 k ByteBlock size = 2 w = line size = sixteen 8 bit words = 16 bytesNumber of sets (v) = 2 d = Total capacity /( k x line size) = 256Total addressable space = = 2 s+w = 16 M bytesAddress length = (s + w) bits = 24 bitsThus, in the main memory address:Size of set = d = 8 bitsSize of a word = w = 4 bitsSize of a tag = (s-d) bits = 12 bitsTherefore, Load AB1234h will store the result in set number:23 hb) What will be its corresponding tag number? [2]The corresponding tag number will be : AB1 hIf the microprocessor had a direct mapped cache with half the capacity of the setassociative cache. Then,c) Which line number would the request be saved in? [2]If a microprocessor had a direct mapped cache with half the capacity of the set ofthe two –way set associative cache, then it would have a capacity of 4 kbytes andeffectively the same number of lines as the number of sets in the set associativecache, i.e.Number of lines in cache = m = 2 r = 256Thus, in the main memory address:Size of a line = r = 8 bitsSize of a word = w = 4 bitsSize of a tag = (s- r) bits = 12 bitsTherefore, Load AB1234h will store the result inline number:23 hPage 10 of 16
d) What will be the corresponding tag number [2]The corresponding tag number will once again be : AB1 hNow consider the case if the microprocessor had an associative cache with four times thecapacity of the direct mapped cache.e) Which line number would the request be saved in? [1]In associative mapping any block can be stored in any line depending upon the currentoccupancy and replacement algorithms. Thus, we cannot say for sure which linenumber the request will be saved in.f) What will be the corresponding tag number? [2]Address length = (s + w) bits = 24 bitsThus, in the main memory address:Size of a word = w = 4 bitsSize of a tag = s bits = 20 bitsTherefore, Load AB1234h will store the result with a tag number: AB123 hg) Which of the above caches will have the fastest access time.Justify your answer. [2]The direct cache will have the fastest access time, given a hit, i.e. the presence of therequested block in cache as only one comparison of the tag will determine whether therequisite block is present or absent. Whereas, in associative memory one would haveto compare the required tag with all tags in cache and in a set associative cache onewould have to compare the required tag with all tags in the set.h) Which of the above caches has the best overall performance consideringreplacement. [2]Of the three schemes under consideration, the set-associative cache will have the bestoverall performance considering replacement. Access time from main memory istypical much larger than the access time from cache. Thus, if a situation where morethan one block was alternatively required that mapped to the same line number.Direct mapping would require us to overwrite the blocks alternatively and this wouldbe highly inefficient (thrashing). Associative mapping overcomes this but one has togo through the entire cache comparing tags to search for a block. Set-associativecache requires a relatively short time to access a block because one only checks for arequired block by comparing tags within a set usually of size 2 or 4 whilst avoidingthrashingPage 11 of 16
Page 1 and 2: Lahore University Of Management Sci
Page 3: S. Masud & T. Jadoon Computer Organ
Page 7 and 8: Initial Contents of Memory in hex:R
Page 9: OR GateA15A14OR GateA133X8 DecoderA
Page 13 and 14: 0002 00 h0003 09 h0004 00 h0005 42
Page 15 and 16: Part C [15 marks]26. Which techniqu

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