Question

Question 10 (10 points)

Consider a cache of 8 lines of 16 bytes each. Main memory is divided into blocks of 16 bytes each. That is, block 0 has bytes with addresses 0 through 15, and so on. Now consider a program that accesses memory in the following sequence of addresses:

• Loop three times: 10 through 20; 32 through 52.
• Once: 20 through 35.

Suppose the cache is organized as direct mapped. Memory blocks 0, 8, 16 and so on are assigned to line 1; blocks 1, 9, and so on to line 2; and so on. Compute the hit ratio during this process. Provide details regarding how you get the answer.

Question 11 (10 points)

Given a 8-bit word 00111001, suppose when the word is read from memory, the new check bits are calculated based on the fetched reading is 0001. Provide details regarding how you get the answer.

1. Is the data fetched correctly? (6 points)
2. If no, is the data bit or check bit goes wrong?( 3 points)
3. What is the additional checking bit that you need to store in the memory if you want to use it to detect two bits error? (1 point)

Answer 1

Q10.

Block size => 16 Bytes -> Block offset = log 16 = 4 bits. Let's see how address is stored in main memory block. Address Range Main Memory Block # 0-15 Block O 16 - 31 Block 1 32-47 Block 3 48 - 63 Block 4 A whole main memory block will be brought into one cache block. Let's see how many miss we have in each reference: 10 through 20 -> These address are occupied in block o and 1 of memory. So these 2 block of memory will be brought in cache leading to miss. One miss per block for loading into cache. Total 2 miss. (Block 0 and Block 1 of MM is brought in cache) 32 through 52 -> Total 2 miss (Block 1 and block 2 is brought in 1st and 2nd block of cache) Now since there is no block replacement, all reference for next 2 loop will be hit. Once : 20 - 35: This is also a hit since already the required block is present in cache. Now total # of reference =>3 *(11+21) + 16 = 112 Total # of miss = 2. So total #of hits = 112 - 2 =120 So Hit rate = 120/122 *100 = 98.36%

Please don't post so many questions at once. I have solved how much I have been asked to.

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