Consider an extendible hashed index file, where each data page can hold at most three data entries.

a) Compute the binary representations of the following integers (hashed values):

2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Example: The binary representation of integer 2 is 10(2).

b) Show an extendible hashed index containing a directory (with two elements) that points to two buckets, where

one bucket contains the data entry 2* with h(2=10(2)) = 0, and

another bucket contains data entries 3*, 5* & 7*.

Please make sure that you explicitly show the global depth of the directory and the local depth of each data page/bucket.

c) What is the resulting extendible hashed index after each of the following data entries with keys: 11, 13, 17, 19, 23, 29 is inserted (one-by-one in the above order) into the extendible hashed index shown in Question 5(b)? Please make sure you show an extendible hashed index after each insertion (for a total of six indexes).