b$)$ Consider a disk with block size $512$ bytes. A block pointer is $6$ bytes long, and a record pointer is $7$ bytes long. A file has $30,000$ EMPL OYE E records of fixed$-$length. E ach record has thefollowing fields: NAME $(30$ bytes$),$ SSN $(9$bytes$),$ DEPARTMENTCODE $(9$ bytes$),$ ADDRESS $(40$ bytes$),$ PH ONE $(9$ bytes$),$BIRTHDATE $(8$ bytes$),$ SEX $(1$ byte$),$ JOBCODE $(4$bytes$),$ SAL ARY $(4$ bytes, real number$).$ An additiond byte is used as a deletion marker.Assume that file is not ordered by the key field SSN and we need to create a secondary index on SSN$.$

$($i$)$ Find the number of levels needed, if wemake it into a multilevel index.

Data file

No$.$ of records $r=30000$

Block size $B=512$ bytes

Record size $R=115$ bytes

Blocking factor $bfr=\frac{B}{R}=\frac{512}{115}=4\mathrm{.}45=4$

Number of file blocks, $b=\frac{r}{b}fr=\frac{30000}{4}=7500$

Index file$-1^{st}$ level

No$.$ of records $r=30000$

Block size $B=512$ bytes

Record size $R=9$ bytes

Blocking factor $bfr=\frac{B}{R}=\frac{512}{9}=56$

Number of file blocks, $b=\frac{30000}{56}=536$

Index file$-2$nd level