Please write a Python program to implement the base expansion algorithm and test other input values of $y$ and $L$ in the base expansion algorithm to understand and internalize how this algorithm is working.

Based on the Python program that you created in question $1,$ please improve your program code to convert the following base $10$ values to their equivalent binary values in normalized form assuming $L=5$ bits for the fractional part.

$2\mathrm{.}375$

$\frac{1}{7}$

$21/2$

$($from math import pi$)$