1) 2-bit .tif with 3 as the NoData value. Only needs to express 0,1,NoData 2) 1-bit .tif with 0 as the NoData value. Only needs to express 1,NoData
No matter what sort of analysis I perform on these, they are always promoted to 8-bit with a noData value of 255. This is unacceptable because the file size balloons to 7gb with the promotion. I have found no solution to ensure bit depth is preserved. Having to use copy raster between every operation is not an option. I don't understand why this is happening, because I am not introducing any new values into the rasters through analysis.
Possibly set the geoprocessing environment NoData to PROMOTION. It's in the raster storage section. Based on the help, and if I'm understanding it correctly, that may do it. In the help, search for "nodata environment" (without quotes).