Is digitization of discrete valued signal necessary for it to be processed? While reading the book DSP by Proakis and Manolakis i came across the concept of digitization of signals. The Author states that Digitization(rounding  it off to nearest integer) of signal is necessary in order for it to be processed by computer. If i write the following code :-

float signal[5]={ 1.5 , 1 , 4.4 , 3 , 2 , 3 };
for(int i=0;i&lt;5;i++){
    signal[i]*=2;
}


However, In this above code I am able to process the signal without rounding it off to the nearest integer. Please help me clear my doubt.
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.