3. Assuming a cache of 4096 blocks, a four-word block size, each word contains 4 bytes, and a 64-bits memory address. Memory is byte addressable, and random block replacement policy and write back policy are implemented. Find the total number of tag bits for caches that are a) direct-mapped b) 2-way set associative c) 4-way set associative d) Fully associative

3. Assuming a cache of 4096 blocks, a four-word block size, each word contains 4 bytes, and a 64-bits memory address. Memory is byte addressable, and random block replacement policy and write back policy are implemented. Find the total number of tag bits for caches that are a) direct-mapped b) 2-way set associative c) 4-way set associative d) Fully associative

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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A computer of 32 bits has a cache memory of 64 KB with a cache line size of 64 bytes. The cache access time is 20 ns, and the miss penalty is 120 ns. The cache is 2-way associative. a) What is the number of cache lines? b) What is the number of cache sets? c) What is the number of lines per set? d) Draw a scheme of this cache. e) Calculate the time to read a word in case of miss.
2-Caches are important to providing a high-performance memory hierarchy to processors. Below is a list of 32-bit memory address references, given as word addresses. a. For each of these references, identify the binary address, the tag, and the index given a direct-mapped cache with two-word blocks and a total size of 4 blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. 42, 180, 46, 185, 189, 3, 181, 43, 6, 189, 65, 190 b. For each of these references, identify the binary address, the tag, and the index given a direct-mapped cache with four-word blocks and a total size of 4 blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. c. For each of these references, identify the binary address, the tag, and the index given a two way associative cache with two-word blocks and a total size of 4 blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty d. For each of these…
For a direct-mapped cache design with a 32-bit address, the following bits of the address are used to access the cache.Tag Index Offset31–10 9–5 4–01. What is the cache block size (in words)?2. How many entries does the cache have?3. What is the ratio between total bits required for such a cache implementation over the data storage bits?Starting from power on, the following byte-addressed cache references are recorded. Address 0 4 16 132 232 160 1024 30 140 3100 180 2180 How many blocks are replaced? What is the hit ratio? List the fi nal state of the cache, with each valid entry represented as a record of <index, tag, data>
Assume a direct-mapped cache that holds 4096 bytes, in which each block is 16 bytes.Assuming that an address is 32 bits and that cache is initially empty:a. Complete the table that follows. (You should use hexadecimal numbers for allanswers).b. Which, if any, of the addresses will cause a collision (forcing the block that was justbrought in to be overwritten) if they are accessed one right after the other? Explain
For a direct-mapped cache design with a 32-bit address, the following bits ofthe address are used to access the cache. We assume that each word has 4 bytes. Hints:this is a multiword block direct-mapped cache because each cache block (i.e., each cacheline or each cache entry) contains multiple words. The width of the “Byte offset” segmentis 2 (i.e., the lowest two bits of a 32-bit address), which indicates that each word has 4bytes. The width of the “Block offset” segment (i.e., from the 2nd bit to the 5th bit of a 32-bit address) determines the number of words per cache line. A) What is the cache line size (in words)? B) How many entries does the cache have? C) What is the ratio between total bits required for such a cacheimplementation over the data storage bits?
For a direct-mapped cache design with 64-bit addresses, the following bits of the address are used to access the cache: Tag Index Offset 63-13 12-4 3-0 a. What is the cache block size (in bytes)?b. What is the cache size (in bytes)?c. What is the total number of bits (including valid bit, tag bits and data array bits) to implement this cache?d. For the same block and cache sizes, you want to implement a 4-way set-associative cache, what is the number of index bit and the number of tag bits?
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Cache Mapping Technique 1. Suppose a computer usingdirect-mapped cache has 2 bytes of byte=addressable main memory and a cache of32 blocks, where each cache block contains 16 bytes.a) How many blocksof main memory are there?b) What is theformat of a memory address as seen by the cache; that is, what are the sizes ofthe tag, block, and offset fields?c) To which cacheblock will the memory address 0x0DB63 map?2. Suppose a computer using fullyassociative cache has 2 bytes of byte-addressable main memory and a cache of128 blocks, where each cache block contains 64 bytes.a) How many blocksof main memory are there?b) What is theformat of a memory address as seen by the cache; that is, what are the sizes ofthe tag and offset fields?c) To which cacheblock will the memory address 0x01D872 map?3. A 2-way set-associative cacheconsists of four sets. Main memory contains 2K blocks of 8 bytes each and byte addressingis used.a) Show the mainmemory address format that allows us to map addresses from…
Suppose a computer using direct mapped cache has 232 byte of byte-addressable main memory, and a cache of 1024 blocks, where each cache block contains 32 bytes. a) How many blocks of main memory are there? b) What is the format of a memory address as seen by the cache, i.e., what are the sizes of the tag, block, and offset fields? c) To which cache block will the memory address 0x000063FA map?
.2: Below is a list of 32-bit memory address references, given as word addresses. 3, 180, 43, 2, 191, 88, 253 For each of these references, identify the binary address, the tag, and the index given a direct- mapped cache with 16 one-word blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. For each of these references, identify the binary address, the tag, and the index given a direct-mapped cache with 2-word blocks and a total size of 8 blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. For each of these references, identify the binary address, the tag, and the index given a direct-mapped cache with 4-word blocks and a total size of 8 blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty.
“Prefetching” is a technique that leverages predictable address patterns to speculatively bring in additional cache blocks when a particular cache block is accessed. One example of prefetching is a stream buff er that prefetches sequentially adjacent cache blocks into a separate buff er when a particular cache block is brought in. If the data is found in the prefetch buff er, it is considered as a hit and moved into the cache and the next cache block is prefetched. Assume a two-entry stream buff er and assume that the cache latency is such that a cache block can be loaded before the computation on the previous cache block is completed. What is the miss rate for the address stream above?Cache block size (B) can aff ect both miss rate and miss latency. Assuming a 1-CPI machine with an average of 1.35 references (both instruction and data) per instruction, help find the optimal block size given the following miss rates for various block sizes. 8: 4% 16: 3% 32: 2% 64: 1.5% 128: 1%…
A two-level cache hierarchy of L1 and L2 with 2 and 3 blocks respectively is designed. Both L1 and L2 are fully-associative with LRU replacement policy. A sequence of references (block addresses from left to right, denoted as letters) is given in the table. Both caches are empty initially. You need to simulate the contents of L1 and L2 for the given sequence. Note that each request goes to L1 first. A request is issued to L2 only if it misses L1. In case of a L2 hit, the requested block is fetched from L2 and placed into L1, both in the MRU position. In case of a L2 miss, the block is loaded from memory into both L1 and L2 caches in the MRU position. The cache contents are displayed by the block addresses from MRU position to LRU position, separated by a comma.