Have a look here
https://www.photomet...-basics/binning
CCD 4 times the signal, 1 time the read noise
CMOS 4 times the signal, 2 times the read noise.
In practice, this is sensor dependent because the hardware can average or sum the pixels (will get back to this later).
and here
https://andor.oxinst...y-ccd-detectors
The internals of the fits file of a 14-bits camera provides some insight - the acquired data is simply shifted by 2 bits (multiplied by 4) in the camera in order to get 16 bits integer values in the fits files (300 s dark)
Filename: dark300.fit
No. Name Ver Type Cards Dimensions Format
0 PRIMARY 1 PrimaryHDU 34 (3008, 3008) int16 (rescales to uint16)
(3008, 3008)
INSTRUME: ZWO ASI533MC Pro
[[2800 2796 2796 ... 2796 2788 2804]
[2796 2800 2796 ... 2796 2796 2800]
[2800 2796 2792 ... 2800 2804 2792]
...
[2776 2792 2800 ... 2796 2804 2804]
[2796 2804 2808 ... 2792 2800 2796]
[2796 2800 2800 ... 2792 2804 2804]]
Contains numbers not divisible by 4: False
Since summing and averaging 4 numbers that are divisible by 4 obviously gives a number that is divisible by 4 you can see where this is going.
Now looking at a native 16-bits camera, we get on the same 300 sec dark
No. Name Ver Type Cards Dimensions Format
0 PRIMARY 1 PrimaryHDU 41 (6248, 4176) int16 (rescales to uint16)
(4176, 6248)
INSTRUME: ZWO ASI2600MC Pro
[[499 494 500 ... 499 505 498]
[498 514 499 ... 501 497 489]
[499 494 502 ... 507 511 493]
...
[505 503 523 ... 499 505 506]
[508 500 509 ... 503 510 504]
[499 505 499 ... 498 505 506]]
Contains numbers not divisible by 4: True
See the difference?
Futhermore, here's what a calibration frame might end up looking like when it is actually used for calibration (it has been rescaled to 32-bit floats)
No. Name Ver Type Cards Dimensions Format
0 PRIMARY 1 PrimaryHDU 126 (9576, 6388) float32
(6388, 9576)
INSTRUME: ZWO ASI6200MM Pro
[[0.00763523 0.00765812 0.00764191 ... 0.00769341 0.00760185 0.00765145]
[0.00763523 0.00765812 0.00766575 ... 0.00762856 0.00763809 0.00764954]
[0.00764286 0.00760662 0.00763714 ... 0.00764668 0.00760948 0.00766384]
...
[0.00769436 0.00759422 0.00768292 ... 0.00762474 0.00767147 0.00765717]
[0.00766384 0.00763714 0.00764668 ... 0.00764096 0.00764858 0.0076257 ]
[0.0076524 0.00766003 0.0076524 ... 0.00763142 0.00764858 0.0076257 ]]
But without knowing exactly the internals of the on-chip binning and the exact algorithms used by the calibration software you can't really quantify an eventual gain in practice.
Going back to the hardware summing or averaging binning strategy (depends on camera electronics, configuration options available, etc...) there are a couple of things you need to take into account
a 14-bit camera summing could be OK, but keep in mind that since you get a sum of 4 numbers that are divisible by 4 you are still getting a maximum 16384 levels (at the very maximum and not linearly) and you do run the risk of overflowing.
a 14-bit camera averaging will not overflow, but it will still give you a maximum number of 16384 levels.
One could possibly argue that by oversampling the number of photons hitting the area, you are increasing the resolution of your photon counter but you will still end up with 16384 electrons maximum (at unity gain)
Bottom line: don't bother with the false hope of increasing actual FWC by 4 per advertisement material.