GATE CS 2025 Set 2 — Question 39
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Computer Organization & Architecture → Memory Hierarchy & Cache → Cache Numericals
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Question
For a direct-mapped cache, 4 bits are used for the tag field and 12 bits are used to index into a cache block. The size of each cache block is one byte. Assume that there is no other information stored for each cache block.Which ONE of the following is the CORRECT option for the sizes of the main memory and the cache memory in this system (byte addressable), respectively?
Correct answer
(A) 64 KB and 4 KB
Solution
Given:
The physical address size is the sum of Tag, Index, and Offset bits:The size of the main memory is determined by the physical address space:2. Cache Memory Size:
The number of cache lines (blocks) is determined by the index bits:The size of the cache memory (data capacity) is:Thus, the main memory size is 64 KB and the cache memory size is 4 KB.Option (A) matches these values.
- Tag bits () = 4
- Index bits () = 12
- Block size = 1 byte
The physical address size is the sum of Tag, Index, and Offset bits:The size of the main memory is determined by the physical address space:2. Cache Memory Size:
The number of cache lines (blocks) is determined by the index bits:The size of the cache memory (data capacity) is:Thus, the main memory size is 64 KB and the cache memory size is 4 KB.Option (A) matches these values.
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