[font color=\'#000000\']I agree that the longer exposure should give better S/N ratio. Can I change the example to 2 seconds at ISO 100 and 1/2 second at ISO 400 for simpler math?
The important point is that the aperture ratio is being held constant due to the adjustment in ISO setting, so light is gathered at the same rate.
The longer exposure will gather four as much light and so give four times the signal. This will produce twice as much photon shot noise (it is a square root law). The dark current noise will also be four times as much, but the spatial variation of it will be only twice as much (anothe square root law).
Thus overall, the noise should be less than four times as much, and so the signal to noise ratio should be better for the longer, lower ISO option. I am ignoring pre-amplifier noise, but that should be similar in either case, and so favors the longer exposure even more.[/font]