Suppose our file system has files of 10 sizes, with equal numbers of files of si

Question

Suppose our file system has files of 10 sizes, with equal numbers of files of size 1K, 2K, 4K, 8K,..., 512K. Compute the space utilization for each of the ten block sizes 1K, 2K,..., 512K (the same powers of 2 as the file sizes). Then, identify the correct space efficiency, to three decimal places, for one of these block sizes in the list below.

A. If the block size is 4K, the space efficiency is .998.

B. If the block size is 64K, the space efficiency is .077.

C. If the block size is 256K, the space efficiency is .020.

D. If the block size is 64K, the space efficiency is .761.

Explanation / Answer

Total space to be allocated is 2^10-1=1023

The memory allocated depends on the block size so if we need to allocate 1K memory and we have 4K blocks so it will allocate 4K blocks even if the requirement is 1K hence 3K is wasted so space efficiency in this case will be 1/4=0.25

If the block size is 1K then the efficiency is 1

If the block size is 2K then the efficiency is 1023/1024

If the block size is 4K then the efficiency is 1023/1028

If the block size is 8K then the efficiency is 1023/1040

If the block size is 16K then the efficiency is 1023/1072

If the block size is 32K then the efficiency is 1023/1152

If the block size is 64K then the efficiency is 1023/1344

If the block size is 128K then the efficiency is 1023/1792

If the block size is 256K then the efficiency is 1023/2816

If the block size is 512K then the efficiency is 1023/5120

Hence the correct option is D

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