$3.$ Suppose that a disk unit has the following parameters: seek time s $=20$ msec; rotational delay rd $=10$ msec; block transfer time btt $=1$ msec; block size B $=2400$ bytes; interblock gap size G $=600$ bytes, number of blocks per track $=50,$ number of tracks per surface $=300,$ disk pack of $25$ double$-$sided disks. An EMPLOYEE file has the following fields: Ssn$,9$ bytes; Last$\_$name, $20$ bytes; First$\_$name, $20$ bytes; Middle$\_$init, $1$ byte; Birth$\_$date, $10$ bytes; Address, $35$ bytes; Phone, $12$ bytes; Supervisor$\_$ssn$,9$ bytes; Department, $4$ bytes; Job$\_$code, $4$ bytes; deletion marker, $1$ byte. The EMPLOYEE file has r $=30,000$ records, fixed$-$length format, and unspanned blocking. Write appropriate formulas and calculate the following values for the above EMPLOYEE file:

a$.$ Calculate the record size R $($including the deletion marker$),$ the blocking factor bfr$,$ and the number of disk blocks b$.$

b$.$ Calculate the total capacity of a track.

c$.$ Calculate the useful capacity of a track.

d$.$ Calculate the total capacity of a cylinder.

e$.$ Calculate the useful capacity of a cylinder.

f$.$ Calculate the total capacity of all cylinders.

g$.$ Calculate the useful capacity of all cylinders.

h$.$ Calculate the wasted space in each disk block because of the unspanned organization.

i$.$ Calculate the transfer rate tr and the bulk transfer rate btr for this disk unit $($see Appendix B for definitions of tr and btr$).$

j$.$ Calculate the average number of block accesses needed to search for an arbitrary record in the file, using linear search.

k$.$ Calculate in msec the average time needed to search for an arbitrary record in the file, using linear search, if the file blocks are stored on consecutive disk blocks.

l$.$ Calculate in msec the average time needed to search for an arbitrary record in the file, using linear search, if the file blocks are not stored on consecutive disk blocks.

m$.$ Assume that the records are ordered via some key field. Calculate the average number of block accesses and the average time needed to search for an arbitrary record in the file, using binary search.