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GATE 2025 CS (CS2) – Question 39

Computer Organization and Architecture · ALU and Control Unit Design · 2 marks · Multiple choice

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?

  1. 64 KB and 4 KB
  2. 128 KB and 16 KB
  3. 64 KB and 8 KB
  4. 128 KB and 6 KB

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Show answer and explanation

Correct answer: (A) 64 KB and 4 KB

Explanation

With a 1-byte block there is no offset, so the address is 4 + 12 = 16 bits and main memory is $2^{16}$ = 64 KB. The cache has $2^{12}$ blocks of 1 byte, which is 4 KB.