Why do we normalise a signal (function)?

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http://www.seas.ucla.edu/dsplab/sqc/over.html
It says we have to normalize a signal before it is fed to a compander which reduces its dynamic range. But why don't we directly feed the compander block without normalizing the function first?

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Because the compander might saturate with too much signal, or it may not have enough sensitivity (or enough significant digits) for too little signal.
 
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janu203 said:
http://www.seas.ucla.edu/dsplab/sqc/over.html
It says we have to normalize a signal before it is fed to a compander which reduces its dynamic range. But why don't we directly feed the compander block without normalizing the function first?

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The channel, despite using companding, still has a given dynamic range so the input signal range needs to be appropriate if you want to avoid clipping or poor signal to noise ratio. Also, a number if sources could be passed through the same commander (say in a broadcast transmitter) so they need a reasonably constant loudness level.
[Edit: a lot of which @anorlunda has already said.]