Give non-overlapping parts of 2 rasters a value 0 (QGIS)

in pure python this code does what you are asking for:

from osgeo import gdal    

ds = gdal.Open(yourotherraster)
band = ds.GetRasterBand(1)
arrA = band.ReadAsArray()
ds = gdal.Open('yourraster')
band = ds.GetRasterBand(1)
arrB = band.ReadAsArray()
arrB = np.where((arrA == 1), 2, arrB) #your condition
[cols, rows] = array.shape
driver = gdal.GetDriverByName("GTiff")
outdata = driver.Create('youroutputraster.tif', rows, cols, 1,
                                    gdal.GDT_UInt16)
outdata.SetGeoTransform(ds.GetGeoTransform())  ##sets same geotransform as input
outdata.SetProjection(ds.GetProjection())  ##sets same projection as input
outdata.GetRasterBand(1).WriteArray(array)
outdata.GetRasterBand(1).SetNoDataValue(0)  ##if you want these values transparent
outdata.FlushCache()  ##saves to disk!!
outdata = None
band = None
ds = None
i=0