hi,
You say that you want to work over a range of 20C thru 30C, the LM35 will output a voltage of 0.2V and 0.3V at these limits, thats a range of 0.1V
If you input this 0.1V change into the PIC's adc directly you would see an adc count of:
[0.2v/5v] *1023 = 41 counts to [0.3/5v]*1023 =61 counts which is only a 20 count change.
So at best you could only display to 1.0Cdeg.
To give a bigger change count change you need to amplify the LM35 output by say by at least a factor of 4, this would then give an adc count of 80.
Which gives a resolution of 0.25Cdeg
If you wanted to display 0.1Cdeg resolution you would multiply the 0.1V range by 9.77 times
This would give [0.977v/5v]*1023 = 200 counts.
Do you follow.?