[Shiraz (Ray)]

I don't quite understand what you mean by signal being lost in background noise - apart from the dark current pedestal (which could possibly be considered to be noise), noise is simply variability in the signal - it is not something that in some way can obliterate the signal. Binning is just one way to average numerous independent measures of the signal to reduce the uncertainty (the noise). It doesn't matter if you do it on the chip or in software, the same signal will be there in either case.

Your analysis is correct in that perfect on-chip binning provides 2x the SNR of software binning. However, the 8300 does not do perfect binning - from a few sources, the single read noise in binning is somewhere around 1.3x that in 1x1 mode, so some of the SNR advantage is lost that way.

But the main point is that, if you get enough signal in the subs that shot noise dominates (and that is what you should aim for anyway), then it doesn't matter much what the read noise is in software or hardware binning. In your example let's take a more realistic signal of 1600 in each pixel, for which the total shot noise will be 80 with 2x2 binning. For your read noise of 10, the combined read/shot noise with on-chip binning would be 80.6 and for software binning 82.5 - ie there is only a minor advantage to on-chip binning. That very slight advantage would likely be overwhelmed by the increased single-event read noise in the on-chip binning mode of the CCD (this is certainly so for the 8300). In these circumstances software binning provides better dynamic range, a little bit more SNR and more flexibility.