Cache Memory-

 

Before you go through this article, make sure that you have gone through the previous article on Cache Memory.

 

We have discussed-

• Cache memory is a random access memory.
• It lies on the path between the processor and the main memory.
• It bridges the speed mismatch between the fastest processor and the slower main memory.

 

Also Read- Cache Mapping Techniques

 

Cache Lines-

 

Cache memory is divided into equal size partitions called as cache lines.

 

• While designing a computer’s cache system, the size of cache lines is an important parameter.
• The size of cache line affects a lot of parameters in the caching system.

 

The following results discuss the effect of changing the cache block (or line) size in a caching system.

 

Result-01: Effect of Changing Block Size on Spatial Locality-

 

The larger the block size, better will be the spatial locality.

 

Explanation-

 

Keeping the cache size constant, we have-

 

Case-01: Decreasing the Block Size-

 

• A smaller block size will contain a smaller number of near by addresses in it.
• Thus, only smaller number of near by addresses will be brought into the cache.
• This increases the chances of cache miss which reduces the exploitation of spatial locality.
• Thus, smaller is the block size, inferior is the spatial locality.

 

Case-02: Increasing the Block Size-

 

• A larger block size will contain a larger number of near by addresses in it.
• Thus, larger number of near by addresses will be brought into the cache.
• This increases the chances of cache hit which increases the exploitation of spatial locality.
• Thus, larger is the block size, better is the spatial locality.

 

Result-02: Effect of Changing Block Size On Cache Tag in Direct Mapped Cache-

 

In direct mapped cache, block size does not affect the cache tag anyhow.

 

Explanation-

 

Keeping the cache size constant, we have-

 

Case-01: Decreasing the Block Size-

 

• Decreasing the block size increases the number of lines in cache.
• With the decrease in block size, the number of bits in block offset decreases.
• However, with the increase in the number of cache lines, number of bits in line number increases.
• So, number of bits in line number + number of bits in block offset = remains constant.
• Thus, there is no effect on the cache tag.

 

Example-

 

 

Case-02: Increasing the Block Size-

 

• Increasing the block size decreases the number of lines in cache.
• With the increase in block size, the number of bits in block offset increases.
• However, with the decrease in the number of cache lines, number of bits in line number decreases.
• Thus, number of bits in line number + number of bits in block offset = remains constant.
• Thus, there is no effect on the cache tag.

 

Example-

 

 

Result-03: Effect of Changing Block Size On Cache Tag in Fully Associative Cache-

 

In fully associative cache, on decreasing block size, cache tag is reduced and vice versa.

 

Explanation-

 

Keeping the cache size constant, we have-

 

Case-01: Decreasing the Block Size-

 

• Decreasing the block size decreases the number of bits in block offset.
• With the decrease in number of bits in block offset, number of bits in tag increases.

 

Case-02: Increasing the Block Size-

 

• Increasing the block size increases the number of bits in block offset.
• With the increase in number of bits in block offset, number of bits in tag decreases.

 

Result-04: Effect of Changing Block Size On Cache Tag in Set Associative Cache-

 

In set associative cache, block size does not affect cache tag anyhow.

 

Explanation-

 

Keeping the cache size constant, we have-

 

Case-01: Decreasing the Block Size-

 

• Decreasing the block size increases the number of lines in cache.
• With the decrease in block size, number of bits in block offset decreases.
• With the increase in the number of cache lines, number of sets in cache increases.
• With the increase in number of sets in cache, number of bits in set number increases.
• So, number of bits in set number + number of bits in block offset = remains constant.
• Thus, there is no effect on the cache tag.

 

Example-

 

 

Case-02: Increasing the Block Size-

 

• Increasing the block size decreases the number of lines in cache.
• With the increase in block size, number of bits in block offset increases.
• With the decrease in the number of cache lines, number of sets in cache decreases.
• With the decrease in number of sets in cache, number of bits in set number decreases.
• So, number of bits in set number + number of bits in block offset = remains constant.
• Thus, there is no effect on the cache tag.

 

Example-

 

 

Result-05: Effect of Changing Block Size On Cache Miss Penalty-

 

A smaller cache block incurs a lower cache miss penalty.

Explanation-

 

• When a cache miss occurs, block containing the required word has to be brought from the main memory.
• If the block size is small, then time taken to bring the block in the cache will be less.
• Hence, less miss penalty will incur.
• But if the block size is large, then time taken to bring the block in the cache will be more.
• Hence, more miss penalty will incur.

 

Result-06: Effect of Cache Tag On Cache Hit Time-

 

A smaller cache tag ensures a lower cache hit time.

Explanation-

 

• Cache hit time is the time required to find out whether the required block is in cache or not.
• It involves comparing the tag of generated address with the tag of cache lines.
• Smaller is the cache tag, lesser will be the time taken to perform the comparisons.
• Hence, smaller cache tag ensures lower cache hit time.
• On the other hand, larger is the cache tag, more will be time taken to perform the comparisons.
• Thus, larger cache tag results in higher cache hit time.

 

PRACTICE PROBLEM BASED ON CACHE LINE-

 

Problem-

 

In designing a computer’s cache system, the cache block or cache line size is an important parameter. Which of the following statements is correct in this context?

1. A smaller block size implies better spatial locality
2. A smaller block size implies a smaller cache tag and hence lower cache tag overhead
3. A smaller block size implies a larger cache tag and hence lower cache hit time
4. A smaller bock size incurs a lower cache miss penalty

 

Solution-

 

Option (D) is correct. (Result-05)

 

Reasons-

 

Option (A) is incorrect because-

• Smaller block does not imply better spatial locality.
• Always, Larger the block size, better is the spatial locality.

 

Option (B) is incorrect because-

• In direct mapped cache and set associative cache, there is no effect of changing block size on cache tag.
• In fully associative mapped cache, on decreasing block size, cache tag becomes larger.
• Thus, smaller block size does not imply smaller cache tag in any cache organization.

 

Option (C) is incorrect because-

• “A smaller block size implies a larger cache tag” is true only for fully associative mapped cache.
• Larger cache tag does not imply lower cache hit time rather cache hit time is increased.

 

Next Article- Magnetic Disk | Important Formulas

 

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