Is digitization of discrete valued signal necessary for it to be processed?
Your 1.5 and 4.4 are scaled integers (scaled to the nearest 10th).  C float variables are also a form of scaled integer (exponent indicating the scale factor).  So your data is still rounded to the nearest of smaller scaled integers.  

In binary digital computers everything gets converted and broken down into 1-bit integers (or sets of them) before processing by digital logic gates.

Analog computers work differently.