How to get rectangle with two values in converting polygon to raster?

Question

I have 112 vector polygon shapefiles. I want to convert every single one to raster layer but instead of getting layer with same shape as vector polygon, I want to get rectangle in which cells that match vector polygon have value 1, and all other cells in rectangle have value 0. And that rectangle for every raster layer should have same size because I want to overlap and sum all 112 raster layers together to get final raster layer in which I will have value gradation among cells between 1 (where is only one of primary raster layers lay) and 112 (where all 112 raster layers overlapping).

Is there a simple way to do that? I don't know how to get rectangle in converting polygon to raster.

I'm using ArcMap 10.0

Here is scheme what I want:

I have many polygons that overlapping but all are inside of boundary of Croatia shape. And I want every polygon have the same extent when converted in raster (red rectangle). At the end I should get final raster layer that look like this schematic:

Answer 1

This is definitely clumsy, but without knowing more about your data this should work:

Each polygon needs to have some field with a value of 1, if your shapefiles don't already have this, then you will have to batch add fields to the lot. Then use the Union tool to union ALL of your polygons, this will create individual polys for each overlapping area. With this new dataset you can add a field called SUM, and then calculate it as the sum of all your ID fields.
If you don't already have a rectangle of your desired area, use the Minimum Bounding Geometry tool to draw a rectangle around your largest feature. Use the Erase tool to remove the overlap area of this bounding rectangle with your unioned polygons (the bounding rectangle is the input feature). Finally, Merge the erased bounding rectangle with the unioned polygons, now you have a set of polygons that completely cover your desired area with a field, SUM, that indicates how many polys are present (after merging the bounding rectagle's SUM value will be 0).
All that is left is to make it a raster with the Convert Polygon to Raster tool using SUM as the value field.