Calculations: Show all relevant work.

$1.$

Consider a disk and a file with the following characteristics: block size B $=256$ bytes; interblock gap size G $=56$ bytes; number of blocks per track $=40$; number of tracks per surface $=700.$ A disk pack consists of $12$ double$-$sided disks and rotates at $3200$ rpms$.$ The average seek time is $24$ msecs and block transfer time btt $=2$ msecs. The file contains r $=25000$ STUDENT records of fixed length. Each record has the following fields: NAME $(30$ bytes$),$ SSN $(9$ bytes$),$ ADDRESS $(20$ bytes$),$ PHONE $(9$ bytes$),$ SEX $(1$ byte$),$ DEPT $(6$ bytes$)$ and DEGREEPROG $(3$ bytes$).$ Block pointer $(6$ bytes$)$ and Record pointer $(8$ bytes$).$

a$)$ What is the blocking factor Bfr$.$

b$)$ Calculate the average number of block accesses needed to search for an arbitrary record in this file using a sequential storage.

c$)$ Calculate the average number of block accesses needed to search for an arbitrary record in the file, using a primary indexing. Index field is NAME.

d$)$ Calculate the number of blocks needed to store the file using B$+-$Tree indexing strategy with an average index capacity $70\%.$ How many blocks are needed for both indexes and data using a secondary index on ADDRESS? Calculate the average number of blocks accessed to access an arbitrary record.