When you work in 16 bits mode, the pixel data have 16 bits/channel, thus 65536 shades per channel.
Your display has 8 or 10 bits/channel, thus 256 or 1024 shades per channel.
The way you convert the source data to the display is by resizing the color space. You have different strategies called render intent.
The more simple, the perceptive intent, is a proportionnal resizing :
- the 0 value of the source data is matched with the 0 value of the display,
- the 65535 value of the source is matched with the 255 value of the display.
- the n value of the source is matched with the n × (254 - 0) / (65535 - 0) of the display.
This is assuming that the color profile of the picture (let's say sRGB) is the same as the display. If not, you have to adjust the gamut in addition (dealing with the color values that the display will never be able to reproduce physically) and the computation is not that simple.
If the display (Eizo 16 bits) has more shades than the source image, Photoshop probably sends 8 or 10 bits data and then, on the operating system or on the screen itself, some algorithm resize them to 16 bits by doing the opposite operation : the n value of the source is matched with the n × (65535 - 0) / (254 - 0) value of the display.