but that is what i thought my question was at the beginning of this post ... how many bits in the 'small' space and is it different than a 'larger' space. But from what I've read here and elsewhere, bits are not used to define the colorspace. Yes adobeRGB has more colors than sRGB but they both have to get 'shoehorned' into an image that 'only' has 16 bits to store a shade of red. A 16 bit image in Adobe RGB can only have one of 2^16 shades of red at a given pixel. A 16 bit image in sRGB likewise can only have one of 2^16 shades of red. Manipulating an image in either space still gives a number that has to fall within 0 and 2^16 for R,G, and B for each pixel, no?.The number is then translated to a different number by the 'colorspace adjuster' just before the image is shipped to the display driver. sRGB and aRGB have different colors so the image is 'scaled more' when being displayed as aRGB. Where/how is a 'colorspace handicap' applied when we manipulate an image? Yes, sRGB is a subset of aRGB. Converting to either space will result in 'color scaling' but isnt that AFTER all the manipulations are done?
Okay, I think I understand where you're coming from. And you're right, it's a little confusing.
A few things that might help:
Primaries like RG & B in an additive systems can only go from completely off to 100% on — kind of like a light on a dimmer switch. 100% is the most saturated red you'll get – in an 8-bit representation you'll call that [255, 0, 0] or in 16-bit [65535, 0, 0]. Those values between 0 and 1.0 are what is represented by the math: with 8 bit images you get 256 steps between 0 and 1.0 with 16 bit you get 2^16 steps between 0 and 1.0. But whether it's an 8 bit or 16 bit representation it doesn't make sense to turn the dimmer to a number below zero or above 100%. Adding more steps between 0 and 100& doesn't change the extremes of the system—or to put another way doesn't change the gamut.
Another way to think about it that reflects how colorimetry actually works is to start with an RGB color like sRGB [255, 0, 0] and convert to XYZ. It makes it easier to see that 255 isn't just an abstract number in this context; it is tied to the the XYZ value of the sRGB primaries. That's why this specifies a precise color metric value and not just an integer. In XYZ (and D65 white point) that color lands right around XYZ[.41, .21, .02]. From there you can convert to Adobe RGB and you'll get something around [.85, .002, .0006] - basically the AdobeRGB red primary at 85%. In an 8 bit representation this would be about [219, 0, 0] or in 16-bit [56361, 131, 39]. That all works well because the sRGB primary is within the gamut of AdobeRGB. You can specify the same XYZ coordinate in both working spaces.
If you try to to the opposite — start with AdobeRGB[255, 0 0] and go to sRGB you run into trouble. Converting to XYZ you get XYZ[.58, .30, .03]. Now when you try to go from here to sRGB you end up with RGB values[1.4, 0.002, 0.223] (without gamma correction). You need your red primary to fire at 140% (or in 8-bit terms 357) to hit this XYZ value, which by definition it can't do. Whether you encode that in 8 bits or 16 bits you still can't have a primary at 140%.
I think a good simple, analogy for all this is stereo volume. I might have an average stereo system, which when I turn the volume up to 10 (its highest setting) is about 100dB. It's going to be 100dB at full blast whether my volume control has detents at every integer giving me ten steps or every 10th of an integer giving me 100 steps between 0 and 10. My friend has a rock concert set up also with a volume knob that goes to 10. But when his is set at 10 it produces 150bD. Again it doesn't matter how many steps his volume knob has, full blast is full blast. He can simulate my full blast of 100dB by turning his volume knob down a couple notches until the system is producing a 100dB, but there's nothing I can do on my system to produce 150db. His system has a larger volume 'gamut.' If both our knobs have detents at integers, I can take some comfort that between 0 and 100dB I can dial finer distinctions that he can because my 10 steps are spread from 0 to 100, while his are ten steps over 150dB.