> I'm wondering if the built-in ADC's are just simply horrible?

I've found the ADCs (on the F877 at least) to perform well

Are you using the recommended termination on the LM35 and
input requirements of the AD pin ?

http://www.national.com/pf/LM/LM35.html

You'll get much better resolution if you use a voltage reference
that covers the voltage range you expect from the LM35, but
not so high a resolution that noise becomes a problem

> My scaling is as follows:
>
> 0-5V for the voltage range (Vdd as reference)
> 0-1024 for the input value range (10bit ADC)

5000/1024 = 4.88mV / bit, = ~1/2dC resolution. The LM35 is
specced to +/- 1/4dC at room temperature (25dC)

> The output does of course rise when I heat the sensor, and drop
> back down as it cools, it's definately getting *some* value from
> the ADC...

Note that there is a thermal response curve for any temperature
changes. In still air this can be a couple of minutes

> I don't know of any offset register in the pic as there are only 4
> registers for the ADC in general, and none mention an offset i
> would need to set up

An "offset" is how you define it. The LM35 is designed to be a
direct output device, ie there is no voltage to discard as with
Kelvin sensors. As you say, a simple calculation on the ADC
reading should show the temperature

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