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CS 232 Fall 2009 Practice Exam2.2 Solutions

# CS 232 Fall 2009 Practice Exam2.2 Solutions - CS 232...

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CS 232 Practice Exam 2: Solutions Fall 2009 1. Virtual Memory and Cache (30 points) : A byte addressable memory system has the following specifications: 40-bit virtual addresses, 32-bit physical addresses, two-level cache, 32-bit bus with a 1 cycle latency between L2 cache and memory, interleaved memory with two banks, each with a 10 cycle latency. The TLB and caches have the following specifications: TLB L1 cache L2 cache Hit time 2 cycles 1 cycle 15 cycles Hit rate 99% 75% 95% (a) If the page size is 512 bytes, fill in the sizes of the VPN and PPN fields: Page offset = log 2 512 = 9 bits. Hence VPN = 40 - 9 = 31 bits, PPN = 32 - 9 = 23 bits (b) The direct-mapped L1 cache holds 16 KB of data in 512 blocks, and has a write-through policy. How many bits does it take to implement this cache? Show your work for partial credit! Solution : The block size is 16 Kbytes 512 blocks = 32 bytes per block. Hence, the block offset is log 2 32 = 5 bits. Since the cache is direct-mapped, the number of sets is equal to the number of blocks i.e., 512. Thus the index is log 2 512 = 9 bits. Hence, the tag is 32 - 9 - 5 = 18 bits long. Since the cache is write-through, there are no dirty bits. Thus each block stores data, tag and valid bits. Hence, the total number of bits required to implement the cache is 512 × (32 × 8 + 18 + 1) (c) The L2 cache has the same block size as the L1 cache but holds 256 times as much data. It has a write-back policy, full LRU, and can be implemented using 4296 KB. What is the associativity of the L2 cache? Show your work for partial credit! Solution : Suppose the cache is 2 k -way associative. Since it has the same block size as L1 but holds 2 8 times more data, it must have 2 8 times as many blocks. Thus, it has 2 8 / 2 k = 2 8 - k as many sets, so the index field would be 8 - k bits longer (i.e., 17 + k bits long) and the tag would be 8 - k bits shorter (i.e., 10 + k bits long). Also, this cache has dirty bits. To implement full LRU, the cache needs m = log 2 (2 k )! LRU bits per set. Thus, the total number of bits to implement this cache is 2 8 × 512 × (32 × 8 + 10 + k + 1 + 1) + 2 8 - k .m = 4296 × 1024 × 8 bits. We can solve this for k and obtain the associativity 2 k . The problem on the exam will not involve such icky math, and you can always leave your answer as expressions . Do not simplify unless you absolutely have to.

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CS 232 Fall 2009 Practice Exam2.2 Solutions - CS 232...

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