Quick Test of an ADC
Expecting a test input signal to produce a bit-accurate ADC output seems unreasonable. Instead you could create an exponential input voltage by turning on charging a capacitor through a resister. After reading in many period results over the expected rise time it shouldn't be hard to apply a test on the data comparing it to the easily predicted results for a gross ACD malfunction. At the very least it should be monotonically increasing and secondarily the delta between sample N and sample N+1 should be decreasing as N increases.