Question $1.(50$ marks$)$

Suppose that you have formatted your disk with a block size of $4096$ bytes and assume

that we have $10,000$ SMARTPHONE records of fixed length. A block pointer is $10$

bytes long $(P=10),$ and a record pointer is $6$ bytes long $(Pr=6.$ Each SMARTPHONE

record has the following fields: Brand $(16$ bytes$),$ Model $(20$ bytes$),$ Color $(10$ bytes$),$

Size $(60$ bytes$),$ Weight $(10$ bytes$),$ Price $(8$ bytes$),$ Year $(4$ bytes$),$ and Remarks $(160$

bytes$).$ The file is ordered by the key field Brand, and we want to construct a primary

index on Brand.

Justify your answers and state any assumptions that you make!

$($a$)$ Calculate the blocking factor $($bfr$)$ and the number of file blocks needed to store the

SMARTPHONE records. Assume that records are stored unspanned. How much

space remains unused per block? $[10$ marks$]$

$($b$)$ Calculate the index blocking factor bfri. $[5$ marks$]$

$($c$)$ Assume that the primary index is a single$-$level index. Calculate the number of

index entries and the number of index blocks. $[10$ marks$]$

$($d$)$ Suppose we are going to retrieve a record based on the value of Brand. What is

the number of block accesses needed to search for a record without using the

primary index? And what is the number of block accesses using the single$-$level

index in subquestion $($c$)?[10$ marks$]$

$($e$)$ Now, suppose that we want to make the primary index a multilevel index. How

many levels are needed and what is the total number of blocks required by the

multilevel index? $[10$ marks$]$

$($f$)$ Consider the multilevel index from subquestion $($e$).$ What is the number of block

accesses needed to search for and retrieve a record from the file, given its Brand

value? $[5$ marks$]$