GATE CS 2020 Set 1 — Question 40
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Computer Organization & Architecture → Memory Hierarchy & Cache → Cache Numericals
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Question
A computer system with a word length of 32 bits has a 16 MB byte-addressable main memory and a 64 KB, 4-way set associative cache memory with a block size of 256 bytes. Consider the following four physical addresses represented in hexadecimal notation.A1 = 0x42C8A4, A2 = 0x546888, A3 = 0x6A289C, A4 = 0x5E4880Which one of the following is TRUE?
Correct answer
(B) A2 and A3 are mapped to the same cache set.
Solution
1.Determine Cache Parameters:
- Block size = 256 bytes = bytes. Offset bits = 8.
- Cache size = 64 KB = bytes.
- Number of blocks = .
- Associativity = 4-way.
- Number of sets = . Index bits = 6.
- Bits 0-7: Block Offset
- Bits 8-13: Set Index
- Bits 14-23: Tag
- Set Index = (Address >> 8) & 0x3F (mask for 6 bits)
- A1: 0x42C8A4 >> 8 = 0x42C8. Index = 0x42C8 & 0x3F = .
- A2: 0x546888 >> 8 = 0x5468. Index = 0x5468 & 0x3F = .
- A3: 0x6A289C >> 8 = 0x6A28. Index = 0x6A28 & 0x3F = .
- A4: 0x5E4880 >> 8 = 0x5E48. Index = 0x5E48 & 0x3F = .
- A1 and A4 map to set 8.
- A2 and A3 map to set 40.
- Option (B) is TRUE.
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