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.

$2.$ 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.

$2\mathrm{.}375$

$1/7$

$21/2$

$($from math import pi$)$