Assume that you will use simple parity protection in Exercises 6.24 through 6.27. Specifically, assume that you will be computing one parity block for each file in the file system. Further, assume that you will also use a 20- byte MD5 checksum per 4 KB block of each file. We first tackle the problem of space overhead. According to recent studies [Douceur and Bolosky 1999], these file size distributions are what is found in modern PCs:

The study also finds that file systems are usually about half full. Assume you have a 37 GB disk volume that is roughly half full and follows that same distribution, and answer the following questions:
a. How much extra information (both in bytes and as a percent of the volume) must you keep on disk to be able to detect a single error with checksums?
b. How much extra information (both in bytes and as a percent of the volume) would you need to be able to both detect a single error with checksums as well as correct it?
c. Given this file distribution, is the block size you are using to compute checksums too big, too little, or just right?

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I KB 2 KB 4 KB 8 K6 K 32 KB 64 K 128 KB 256 KB512 KB21 MB 26,6% | 110% | 11.2% | 10.9% | 9.5% | 8.5% | 7. l % | 51% | 3.74 | 2.4% | 4.0%