L-3.8: Fully Associative Mapping with examples in Hindi | Cache Mapping | Computer Organisation

Summary

In this video, we explore the concept of **Fully Associative Mapping** in caching, following up from the previous discussion on **Direct Mapping**. We compare the advantages and disadvantages of both mapping techniques, emphasizing that Fully Associative Mapping reduces **conflict misses** and increases **cache hits** by allowing blocks to be stored in any cache line. However, it introduces the need for more comparisons and a larger tag size. Through examples and detailed breakdowns, we discuss how physical addresses are divided into **tag** and **block offset** to ensure efficient memory access and cache management.

Takeaways

• 😀 Direct Mapping vs Fully Associative Mapping: In this video, the presenter compares direct mapping and fully associative mapping in cache memory, highlighting key differences and benefits.
• 😀 Fully Associative Mapping: In fully associative mapping, any block can be placed in any cache line, unlike direct mapping where each block has a fixed cache line.
• 😀 No Conflict Misses: A major advantage of fully associative mapping is the elimination of conflict misses, leading to increased cache hits.
• 😀 Cache Configuration: The main memory has 128 words, divided into 32 blocks of 4 words each, while the cache has a total size of 16 words with 4 words per line.
• 😀 Tag Bit Calculation: The physical address in this example consists of 7 bits, with 5 bits representing the tag and 2 bits representing the block offset.
• 😀 Block Placement Flexibility: In fully associative mapping, blocks can be placed anywhere in the cache, making it more flexible compared to direct mapping.
• 😀 Increased Comparisons: A disadvantage of fully associative mapping is the need to compare the tag bits with all cache lines to find a match, resulting in more comparisons compared to direct mapping.
• 😀 Block Offset: The block offset is 2 bits, as there are 4 words per block. This determines the memory location within each block.
• 😀 Cache Hits and Misses: The video explains how a cache hit occurs when the CPU finds the requested block in the cache, and a cache miss occurs when it is not found.
• 😀 Overall Efficiency: Despite the increased number of comparisons, fully associative mapping generally leads to more cache hits, making it more efficient than direct mapping in many cases.

Q & A

What is the main difference between direct mapping and fully associative mapping in cache memory?

In direct mapping, each block of main memory is mapped to a fixed line in the cache, meaning each block has a predetermined location. In contrast, fully associative mapping allows any block to be placed in any cache line, providing more flexibility and reducing conflict misses.

How does fully associative mapping help reduce conflict misses?

Fully associative mapping allows any block to be placed in any available cache line, ensuring that empty cache lines are utilized efficiently. This flexibility reduces the chances of conflict misses, as blocks can be placed in whichever line is available, rather than being restricted to a specific line.

What are the components of a physical address in the fully associative mapping example?

In the fully associative mapping example, the physical address consists of two parts: the block offset and the block number (tag). The block offset is used to identify a specific word within a block, while the block number (tag) identifies which block is stored in the cache.

How many bits are needed to represent the physical address in this example?

The physical address is 7 bits in total. This consists of 5 bits for the block number (tag) and 2 bits for the block offset, as there are 32 blocks and each block contains 4 words.

What is the role of the tag in fully associative mapping?

The tag in fully associative mapping identifies which block is currently stored in a particular cache line. Since any block can be placed in any line, the tag helps the cache system determine if the requested block is present by comparing it with the tags stored in the cache.

Why is there no line number in the address structure for fully associative mapping?

In fully associative mapping, the block can be placed in any line in the cache, meaning there is no need for a line number in the address structure. The entire block number serves as the tag, allowing for flexible placement of blocks in any cache line.

How does fully associative mapping impact cache hits and misses?

Fully associative mapping increases the likelihood of cache hits because any block can be placed in any cache line, reducing the chances of conflict misses. However, a cache miss occurs if the requested block is not found in the cache, and the system must fetch it from main memory.

What is the disadvantage of fully associative mapping in terms of tag bits?

The disadvantage of fully associative mapping is that it requires more bits for the tag. Since any block can be placed in any cache line, the tag must represent all 32 possible blocks, requiring 5 bits, which is larger compared to direct mapping.

What is the trade-off between the number of comparisons in direct mapping and fully associative mapping?

In direct mapping, only one comparison is needed to check if a block is in the cache, as each block has a fixed line. However, in fully associative mapping, multiple comparisons are needed because any block can be stored in any cache line, requiring the tag to be compared with all cache lines.

Why does fully associative mapping require more comparisons than direct mapping?

Fully associative mapping requires more comparisons because the block can be stored in any of the cache lines. To check for a hit, the tag must be compared with all the tags in the cache, unlike direct mapping where only one comparison is needed due to the fixed position of each block.