Now we know why you are building these gadgets at home - it's your new career leading to one of these 
At work we use EEPROM calibration for zero and scale, allowing the use of cheap 1% 50ppm resistors to make a product accurate to ~ 0.1%.
BTW there is going to be money to be made in producing replacement modules for the KC225. If you look at that PDF I posted and count the stuff that is no longer made... the pitch accelerometer is one of them. I bought two KC225 computers from a US dealer a few years ago for $500 each, with fresh Honeywell paperwork, and have them on the shelf.
I often wonder about doing some avionics product, and while we have discussed all the usual barriers to entry here many times, I do think the one opportunity, for a nice small business, is products like these Davtrons. Simple well defined functionality, and the approval should be easy. In fact you could PMA it, though (when I investigated PMA) it is difficult for a non US based company because you need to host a bunch of FAA inspectors for a week or two. Very few (any?) PMAd parts are made in Europe. The Big Q is whether there is much demand for oddball products such as these...
Yeah, if you can make a sensor which is inaccurate but very stable in short- and long-term, and supply a table of corrections, that's neat
These Bosch guys are pretty smart ... that's why they have a fleet of Canadair Challengers in the hangar next to ours :-)
Yeah, if you can make a sensor which is inaccurate but very stable in short- and long-term, and supply a table of corrections, that's neat 
I can't see any cheap baro sensor being accurate to say 1 mb except over a small range and if calibrated at some point in that range. It would imply linearity and stability to better than 0.1%.
Mr. Bosch claims a typical absolute accuracy of his little sensor of +/-1hPa (or 30ft!) over the calibrated range of 1100 to 300hPa (sea level to FL 300). Every sensor has a set of individual calibration data that are stored on an internal EEPROM. (see page 6 of the datasheet: http://www.arduinoeverything.com/wp-content/uploads/2011/12/BST-BMP085-DS000-05.pdf). I find that pretty amazing for a device that probably costs no more than one Euro.
I can't see any cheap baro sensor being accurate to say 1 mb except over a small range and if calibrated at some point in that range. It would imply linearity and stability to better than 0.1%.
So if you want approx sea level QNH, no problem, and if you want the QNH at the top of Mt Everest, again no problem because the height there is known very accurately (by now).
But you won't get say 1 millibar accuracy all the way from SL to say FL300, cheaply.
Whether this matters is another thing. Example: the KFC225 autopilot contains a baro transducer. It uses an encoding altimeter (KEA130A) to capture a preset altitude but after the capture it uses the internal one to hold altitude. The output of the internal one is not at all accurate, but it goes to a 16-bit ADC so they get a resolution of better than 1ft. Looking at the GPS altitude data recorded over a long flight, it seems stable enough, which is all that matters. Commercially, the component (now obsolete) cost about €50-100. Schematic
You would also need to add an EEPROM...
The ATmega328 comes with 2kBytes of non volatile RAM / EEPROM on board, that should be sufficient.
The Davtron 655 would be more interesting to do and it gets closer to Achim's original requirement
No problem, you would need the barometric sensor and just two more formulas to program. In a pressurised aircraft one would have to connect it to the static source (or install a second one for that purpose).
Which sensor do you use? The better ones are factory calibrated.
My board has a BMP085 sensor (from Bosch). It comes with on-board factory calibration data that has to be applied to every sample. I have not tested it's accuracy yet.
BTW: My homegrown "QNH indicator" without calibration of any kind (!) shows exactly the QNH of EDDS airport which is about 13NM away. I just rechecked with the latest METAR.
Which sensor do you use? The better ones are factory calibrated.
I use an MS5534 from Intersema/Measurement Specialities in my aircraft, in cabin air and not connected to the static port, and I've found its reading to differ less than 100ft from the static port instruments over the whole altitude range of the aircraft (i.e. up to ~F140). I find this quite remarkable, given that the two altimeters also start to differ around 50ft at higher altitudes.
You would also need to add an EEPROM e.g. 93c46 so the unit powers up in the last selected mode. The Davtrons always reset to the top option, which is annoying.
The Davtron 655 would be more interesting to do and it gets closer to Achim's original requirement. It needs the pressure altitude and gets it via 10-wire Gray code. It would be much better to get it via ARINC429 digital, which comes out of a GTX330 or similar.
It still can't do the QNH; for that one needs GPS data.
I doubt if any constants in the universe are known to 24 bits...
The constants maybe not. But you still can measure your variables with that kind of precision. In the datasheet they write:
APPLICATIONS
CARDIAC DIAGNOSTICS
DIRECT THERMOCOUPLE INTERFACES
BLOOD ANALYSIS
INFRARED PYROMETERS
LIQUID/GAS CHROMATOGRAPHY
PRECISION PROCESS CONTROL
I'm not familiar with any of those, so I don't know if they really require that amount of precision.
The temp probe would be the existing probe. The display would probably be LED, dot matrix.
That should make your project fairly easy then. A rainy-Sunday-afternoon exercise. One button to query (C/F/Voltage), serially attached sensor and some kind of "half intelligent" display like this:
(Siemens RED PD4436)
I doubt if any constants in the universe are known to 24 bits... mass of the electron? Some 24-bit ADCs can be very linear though. Making a bit of real equipment which actually makes use of more than about 20 bits is almost impossible.
The temp probe would be the existing probe. The display would probably be LED, dot matrix.
