A computer system has a level-1 instruction cache (1-cache), a level-1 data…

2006

A computer system has a level-1 instruction cache (1-cache), a level-1 data cache (D-cache) and a level-2 cache (L2-cache) with the following specifications:

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The length of the physical address of a word in the main memory is 30 bits. The capacity of the tag memory in the I-cache, D-cache and L2-cache is, respectively,

Answer: A. 1 K x 18-bit, 1 K x 19-bit, 4 K x 16-bitAnswer: Key idea: tag bits = physical address bits - index bits - block-offset bits. The physical address given is a word address of 30 bits. I-cache (4K…

  1. A.

    1 K x 18-bit, 1 K x 19-bit, 4 K x 16-bit

  2. B.

    1 K x 16-bit, 1 K x 19-bit, 4 K x 18-bit

  3. C.

    1 K x 16-bit, 512 x 18-bit, 1 K x 16-bit

  4. D.

    1 K x 18-bit, 512 x 18-bit, 1 K x 18-bit

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Correct answer: A

Answer:

Key idea: tag bits = physical address bits - index bits - block-offset bits. The physical address given is a word address of 30 bits.

  • I-cache (4K words, direct mapped, block = 4 words):

    Number of lines = 4K / 4 = 1K ⇒ index = log2(1K) = 10 bits. Block offset = log2(4) = 2 bits. Tag = 30 - 10 - 2 = 18 bits. Tag memory = 1K × 18-bit.

  • D-cache (4K words, 2-way set-associative, block = 4 words):

    Total blocks = 4K / 4 = 1K. With 2-way, sets = 1K / 2 = 512 ⇒ index = log2(512) = 9 bits. Block offset = 2 bits. Tag = 30 - 9 - 2 = 19 bits. Number of tag entries = total blocks = 1K ⇒ tag memory = 1K × 19-bit.

  • L2-cache (64K words, 4-way set-associative, block = 16 words):

    Total blocks = 64K / 16 = 4K. With 4-way, sets = 4K / 4 = 1K ⇒ index = log2(1K) = 10 bits. Block offset = log2(16) = 4 bits. Tag = 30 - 10 - 4 = 16 bits. Number of tag entries = total blocks = 4K ⇒ tag memory = 4K × 16-bit.

Therefore, the tag memory capacities are: 1K × 18-bit, 1K × 19-bit, 4K × 16-bit.

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