The resistor has suffered a severe overload event. It would be prudent to determine what part it plays in the circuit. You can usually trace the tracks. Try to detrmine what could have led to the burn-up as replacing the resistor could just cause a repeat event with potential overload damage to another component. I have often found such damage caused by a shorted electrolytic capacitor, the resistor acts like a fuse in such cases and fries. Your resistor appears to have died a relatively non violent slow death as apposed to a dramatic and explosive overload. Hunt for the cause first.
I had a capacitor go short in my AVO Megger BM222 and the case was melted and charred by the heat produced by an associated SMD resistor. All this happened whilst it was sat in the off condition on a shelf ! The damn thing almost caught fire
As has been stated by Boredatwork, the ADC datasheet may help you with the purpose and value of the resistor. It may not be that critical depending upon it's purpose.
Or I would use a very high magnification microscope (analogue or USB digital type) to see if any remnants of the value remain on the burnt resistor. You can sometimes be lucky.
As a last ditch effort, I would fit a multi-turn high value trimpot (say 10K) across the resistors pads, then adjust it's value slowly from high to low and see what effect the resistor has on the opertion of the multimeter. From that you may be able to ascertain whether it is just a pull-up or a more important value that must be correct for calibration to be maintained.
As the resistor cooked quite well on what was probably a low voltage event I would expect it's value to be below 1K but that is just a guess on my part.
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