GATE CS 2026 Set 2 — Question 56
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Computer Organization & Architecture → Memory Hierarchy & Cache → Direct-Mapped Cache
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Question
Consider a system with 1 MB physical memory and a word length of 1 byte. The system uses a direct mapped cache, with block numbers starting from 0. The word with physical address 0xA2C28 is mapped to the cache block number . The maximum possible size of the cache (in KB) for this configuration is ___________. (answer in integer)Note: and
Correct answer
128 to 128
Solution
Physical memory = 1 MB = bytes. Thus, the physical address is 20 bits.
Word length = 1 byte.
Physical address = 0xA2C28 = .In a direct-mapped cache, the cache block number (Index) is calculated as:Let Block Size = bytes and Number of Cache Blocks = .
Given Index = .We need to find the maximum possible cache size, which is .
Let's test values for :
Word length = 1 byte.
Physical address = 0xA2C28 = .In a direct-mapped cache, the cache block number (Index) is calculated as:Let Block Size = bytes and Number of Cache Blocks = .
Given Index = .We need to find the maximum possible cache size, which is .
Let's test values for :
- If , then .
- .
- .
- The maximum value for is 11.
- Cache size = bytes = 128 KB.
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