Physical Address Calculation Parameters
📌 Main memory size is 8 GB ($2^{33}$ bytes), resulting in a 33-bit physical address.
📌 Block size is 2 KB ($2^{11}$ bytes), requiring 11 bits for the block offset.
📌 Cache size is 4 MB ($2^{22}$ bytes), leading to $2^{11}$ cache lines (Cache Size / Block Size).

Physical Address Split Comparison
📌 Direct Mapping uses 11 bits for the tag, 11 bits for the line number, and 11 bits for the block offset (Tag:Line:Offset = 11:11:11).
📌 Fully Associative Mapping uses all $33 - 11 = 22$ bits for the tag, as there is no line/set field.
📌 4-Way Set Associative Mapping (assuming 4 lines/set, or $2^2$ lines/set) requires 9 bits for the set number, leaving 13 bits for the tag ($33 - 11 - 9 = 13$).

Comparative Analysis of Mapping Techniques
📌 The number of cache lines ($2^{11}$) remains constant across all mapping techniques as it depends only on cache and block size, not the mapping method.
📌 Tag Directory Size varies: Direct mapping needs $2^{11} \times 11$ tag bits, while Associative needs $2^{11} \times 22$ tag bits.
📌 The number of comparators required is 1 for Direct Mapping, $2^{11}$ for Fully Associative, and $K$ (4 in this example) for K-way Set Associative.

Key Points & Insights
➡️ For K-way Set Associative Mapping, $K=1$ is equivalent to Direct Mapping (each line is its own set).
➡️ If $K$ equals the total number of cache lines ($N$), it is equivalent to Fully Associative Mapping (only one set containing all lines).
➡️ The tag size dictates the type and size of the comparators needed to verify block presence within the cache.
➡️ Direct mapping is the least flexible, requiring only one comparison per access, while fully associative requires comparing against all cache lines.

📸 Video summarized with SummaryTube.com on Nov 09, 2025, 08:01 UTC