Consider an index using extendible hashing for which:

Each bucket can hold up to $3$ records

The index is completely empty

The hashing function maps the d lowest$-$bits of each input to a bucket. For example, if $d=3$

then key $5(0101)$ and key $13(1101)$ have a matching hash $(101).$

Since the hash table is empty the initial global depth is :

We insert key $5,4,25,16,0,23$ in order,

The global directory depth $d$ of the index at this point is :

Then we insert key $31.$

The local depth d$\text{'}$ of the bucket that contains the key $31$ is now :

The local depth d$\text{'}$ of the bucket that contains the key $16$ is now :

The resulting global directory depth $d$ of the index now is :