Higher precision with less digits?

Question

Consider an ideal digital milliammeter (zero resistance, zero uncertainty on AD converter input) with realistic (noisy, hysteresic, etc.) AD converter output and a \$3½\$ -digit display. Often when we measure something and the measured value is near the transition between two readings, e.g. \$0.002\; \mathrm{mA}\$ vs \$0.003\; \mathrm{mA}\$, the display (the far-right (last) digit in this case) starts to blink/alternate between the two numbers.

Most of people presume that if you see the number \$0.003\$ for a longer time than \$0.002\$, it means something like: "absolute distance of the real value of input is closer to \$0.003\$ than to \$0.002\$". In other words it means you can round the result to \$0.003\; \mathrm{mA}\$.

Besides the fact that you should use a more precise apparatus in this case, is this practice recommended? And can we use the blinking itself to get a higher precision past the digit precision?

For example: if \$0.002\$ appears half of the time and \$0.003\$ also, we might assess the real value is close to \$0.0025\$. However this gets questionable anywhere off this point and I suppose the display behaviour is different from device to device. Engineers, what are your thoughts?

Answer 1

No, you never attempt to extrapolate beyond the displayed digits of a single reading.

In fact, the situation is much worse than you think. A "realistic" (as you say) ADC has several sources of error, which are usually specified in terms of offset error, gain error, and non-linearity. You must read the datasheet for the ADC or meter that you use. If you do, you will probably discover that the accuracy of the meter is something like \$\pm 0.005\$ mA for an indicated value of \$0.002\$ mA. Yes, the error is typically much larger than the resolution. Whenever you record or report a measured value you must also report the error in that measurement.

I should mention that if you understand the statistics of the noise in the readings you may be able to oversample to achieve higher effective precision. A good engineer doesn't do this by just "estimating" by eyeball, but by actually recording a number of measurements and averaging.

Answer 2

You need to draw a distinction between absolute accuracy, and incremental accuracy.

Any meter tends to have a resolution significantly better than its absolute accuracy. For instance, the +/- last digit of a 3.5 digit DVM is often swamped in absolute accuracy by the calibration error. If you expect the reading to be the same in several months (long term drift), or at different ambient temperatures, or with the battery in the DMM swinging between high and low voltage, then good luck.

If however, over a short period, you have a reading that flicks between 0.002 and 0.003 50% each or 10%/90% each, then you can confidently assume that there is a slight difference in input voltages, at a sub-LSB level. But you can't assume that either voltage is accurately what it claims it is, beyond the accuracy specification of your DMM.