arcgis desktop - Raster calculator : How to make 0 + NoData = 0?

I have a point data layer (vector) that I converted to a raster layer. I want to replace the NoData value (between each raster point) in the point raster layer by 0. So, I made a background raster layer (value = 0).

My plan was to add the background layer of 0 to the point raster layer, but as we can see in the + (Addition) tool page, a number (0) + NoData = NoData.

Any tips on how to achieve this?

I'm using ArcGIS 10.3, but I also have access to QGIS 2.10.

EDIT : I saw the QGIS Raster Calculator: Need values to be set to 0 instead of no data question, but I can't find the "Reclassify grid cells" tool. I just have "Reclassify grid values".

Answer

The simplest and fastest way to replace NODATA with something else, is map algebra/raster calculator:

It works on float and integer rasters. It is a good idea to specify type of output raster explicitly, using built-in functions Int or Float