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An 8KB direct mapped write-back cache is organized as multiple blocks, each of size 32-bytes. The processor generates 32-bit addresses. The cache controller maintains the tag information for each cache block comprising of the following.
1 Valid bit
1 Modified bit
As many bits as the minimum needed to identify the memory block mapped in the cache.
 
Q. What is the total size of memory needed at the cache controller to store metadata (tags) for the cache?
  • a)
    4864 bits
  • b)
    6144bits
  • c)
    6656bits
  • d)
    5376bits
Correct answer is option 'D'. Can you explain this answer?
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An 8KB direct mapped write-back cache is organized as multiple blocks,...
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An 8KB direct mapped write-back cache is organized as multiple blocks,...
Explanation:

Given,
Cache size = 8KB = 2^13 Bytes
Block size = 32 Bytes = 2^5 Bytes
Total number of blocks = Cache size / Block size = 2^13 / 2^5 = 2^8 blocks

Tag information for each block:
Valid bit = 1 bit
Modified bit = 1 bit
Memory block identification bits = Minimum bits required to identify memory block mapped in the cache

Number of bits required to identify memory block mapped in the cache:
As the cache is direct mapped, only one block can be mapped to a particular cache index. Hence, the number of bits required to identify the memory block mapped in the cache = Number of index bits.
Number of index bits = log2 (Total number of blocks) = log2 (2^8) = 8 bits

Total number of bits required to store tag information for each block:
= Valid bit + Modified bit + Memory block identification bits
= 1 + 1 + 8
= 10 bits

Total memory needed at the cache controller to store metadata (tags) for the cache:
= Total number of blocks * Total number of bits required to store tag information for each block
= 2^8 * 10 bits
= 2560 bits
= 320 Bytes

Therefore, the correct answer is option D, i.e., 5376 bits.
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An 8KB direct mapped write-back cache is organized as multiple blocks, each of size 32-bytes. The processor generates 32-bit addresses. The cache controller maintains the tag information for each cache block comprising of the following.1 Valid bit1 Modified bitAs many bits as the minimum needed to identify the memory block mapped in the cache.Q.What is the total size of memory needed at the cache controller to store metadata (tags) for the cache?a)4864 bitsb)6144bitsc)6656bitsd)5376bitsCorrect answer is option 'D'. Can you explain this answer?
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