The change above involves moving from a 32 bit floating point linear gamma to an 8 bit integer non linear gamma colour space. To minimise the visible on screen impact - flatten all layers first, then use the Exposure and Gamma method as shown by Stephen.
You have to accept though that no display currently made can include the full range of the 32 bit float linear image, so when working in 32 bit you are not seeing the full range of the image on screen. That is why you have a preview exposure control at the bottom left of the window when working in 32 bit linear so you can select which part of the dynamic range is visible on screen while you work on it.
Controls to convert from 32 bit to an 8bit/16 bit gamma space are designed to give you choices as to what will be captured in the final 8 bit/16 bit image, and what will be discarded. Conversions between 16 bit and 8 bit are much simpler as they both have the same range, just divided into a different number of steps.
Dave