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U of I CS 232 - Problem 1: Virtual and Physical addresses

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CS232 Fall 2006 Virtual Memory November 6, 2006Problem 1: Virtual and Physical addressesA memory system has the following components:Cache: 4-way set-associative, size = 64 KB, write-back policy, block size = 16 wordsTLB: 128 entries, 2-way set associativePhysical address: 32 bits, byte-addressableVirtual address: 50 bits, byte-addressablePage table: Two-level, Level-1 table has 220entriesPage size: 4 KB(a) Compute the lengths of the following fields:Page Offset = bitsLevel-1 Virtual Page Number (VPN) = bitsLevel-2 Virtual Page Number = bitsPhysical Page Number (PPN) = bits(b) For the cache, the bits for the index and block-offset fields come from the virtual address, and bitsfor the tag field come from the physical address that the virtual address is translated into.Compute the lengths of each of the following fields:Block offsetIndexTag (Careful! Remember that the tag is used to differentiate two blocks that have a common index.Since the index comes from the virtual address whereas the tag comes from the physical address,what should the tag field be?)(c) For the TLB, the index is bits long and the tag is bits long.1CS232 Fall 2006 Virtual Memory November 6, 2006Problem 2: Average access timeAssume the following specifications for components of the the memory system from Problem 1:Memory: Interleaved with 16 banks, word addressable, access time for each bank = 14 cyclesMemory bus: Width = 1 word, latency = 1 cycleTLB: Hit time = 2 cycles, miss rate = 1%Page table: Page-fault rate = 0.01%Hard disk: Time to replace a page = 106cyclesCache: Hit time = 1 cycle, miss rate = 2%, 50% of replaced blocks are dirty(a) On a TLB miss, compute how many cycles it takes to read the PPN from the page table or determinethat it does not exist in the page table. In other words, compute the hit time of the page table.Hint: The page table is in memory. How many accesses to memory does it take to recover the PPN?Can these accesses be interleaved (pipelined) in the manner described in class?(b) Compute the average number of cycles to translate a VPN into a PPN. In other words, compute theAMAT of the TLB. Hint: Remember that the TLB, page-table and disk form a hierarchy.(c) Compute the time needed to load a cache-block from memory into the cache. In other words, computethe cache miss penalty.(d) Compute the average time needed per memory access in the above system, assuming a 2 GHz


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U of I CS 232 - Problem 1: Virtual and Physical addresses

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