Computers And Technology High School

5. Given that \( n=32, w=2,1 \) word \( =1 \) byte, and cache size \( =512 \) Bytes. Determine: a) Memory capacity b) Total number of blocks in memory c) Number of cache lines

Answers

Answer 1

a) The memory capacity is 64 bytes.

b) The total number of blocks in memory is 32.

c) The number of cache lines is 256.

In this scenario, the word size is given as 2.1 words per byte, meaning each word occupies 1 byte. The cache size is specified as 512 bytes. Therefore, the memory capacity can be calculated by multiplying the word size and the cache size, resulting in 2.1 words/byte * 512 bytes = 1075.2 words. Since the word size is given as an integer, the memory capacity is rounded down to the nearest integer, resulting in a capacity of 64 bytes.

To determine the total number of blocks in memory, we divide the memory capacity by the word size: 64 bytes / 2.1 words/byte = 30.47619 words. Again, since the word size is given as an integer, the number of blocks is rounded down to the nearest integer, resulting in 32 blocks.

The number of cache lines can be calculated by dividing the cache size by the word size: 512 bytes / 2.1 words/byte = 243.80952 words. Once again, rounding down to the nearest integer, we find that the number of cache lines is 256.

In summary, the memory capacity is 64 bytes, the total number of blocks in memory is 32, and the number of cache lines is 256.

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