Question

Below is a list of 8-bit memory address references, given as word addresses. Answer the following questions based on Section 5.3 of the textbook. 0x43, 0xc4, 0x2b, 0x42, Oxc5, 0x28, Oxbe, 0x05, 0x92, 0x2a, Oxba, Oxbd (a) For each of these references, identify the binary word address, the tag, and the index given a direct-mapped cache with 16 one-word blocks. Also list whether each reference is a hit or a miss, assuming the cache is initially empty. (b) For each of these references, identify the binary word address, the tag, the index, and the offset given a direct-mapped cache with two-word blocks and a total size of eight blocks. Also list if each reference is a hit or a miss, assuming the cache is initially empty. (c) You are asked to optimize a cache design for the given references. There are three direct- mapped cache designs possible, all with a total of 16 words of data. Which one is better for the above sequence of accesses? Justify your answer. 1. C1 has 1-word blocks, 2. C2 has 2-word blocks, and 3. C3 has 4-word blocks.

Answer 1

In a direct-mapped cache, the memory address is divided into the index, tag, and offset fields. For different cache configurations, the index, tag, and offset sizes vary. To optimize the cache design, you need to compare the hits and misses for each design option. In this case, C3 with 4-word blocks is the better cache design for the given references.

Step-by-step explanation:

In a direct-mapped cache, each memory address is divided into different fields: the index, tag, and offset.

(a) In a direct-mapped cache with 16 one-word blocks, the index size is 4 bits because 16 blocks can be represented by 4 bits. The tag size is 8 bits because each word address is 8 bits. The offset size is 4 bits because the word size is 8 bits. To determine if a reference is a hit or a miss, you compare the index field of the memory address with the index field of the cache block.

(b) In a direct-mapped cache with two-word blocks and a total size of eight blocks, the index size is 3 bits because 8 blocks can be represented by 3 bits. The tag size is 5 bits because each word address is 8 bits. The offset size is 3 bits because the block size is 2 words. To determine if a reference is a hit or a miss, you compare the index field and tag field of the memory address with the index field and tag field of the cache block.

(c) To optimize the cache design for the given references, we need to analyze the hits and misses for each design. Comparing the design options, C1 with 1-word blocks will have more misses because the block size is smaller. C2 with 2-word blocks will have fewer misses compared to C1, but still more than C3. C3 with 4-word blocks will have the fewest misses as it allows more data to be stored in each block. Therefore, C3 would be the better cache design for the given sequence of accesses.

Answer 2

a) For a direct-mapped cache with 16 one-word blocks:

Convert the memory addresses to binary word addresses.

Determine the number of index bits and tag bits for each reference.

Calculate the index and tag portions of the address.

Check whether the reference hits (if it matches the tag in the cache) or misses (if not present).

b) For a direct-mapped cache with two-word blocks and eight blocks:

Similarly, convert memory addresses to binary word addresses.

Calculate index, tag, and offset portions of the address.

Determine hits or misses based on the cache configuration.

c) To determine which cache design is better:

Calculate the total number of blocks and their sizes for each cache design (C1, C2, and C3).

Evaluate the number of hits and misses for the given sequence of accesses using each cache design.

Choose the cache design that yields the highest number of hits and fewer misses for the given sequence.

Remember, for optimization, consider the balance between the number of blocks and block size to minimize misses and maximize cache hits.