Consider the following multilevel index created $($on a primary key$)$ for the Twitter relation

containing $1$ billion $({10}^9)$ records:

Note that, inner index is a dense index while outer index is a sparse index. Inner index contains

an entry for each record of the relation. Outer index contains an entry for each block of the

inner index. Assume that $100$ index entries fit on a $4$ kilobyte block. The total memory size is

$4GB.$

A$)$ How much space is required $($in GBs$)$ by the inner index?

B$)$ What is the number of blocks required to store the outer index?

C$)$ Is it possible to store the outer or inner index in memory? An index can be stored in memory

if the total memory size is larger than the index size.

D$)$ Consider a case where we store the outer index in memory. What is the total number of

block transfers required to fetch a desired record block into the memory?