Add widget to an existing application

I am new in android and maybe my question is a bit stupid but I'd like to know if it's possible to add a widget to my activity application???

I already have my app, it's a kind of calculator, having DB (sqlite) and multiple screens but I need to give to user opportunity to interact with my app via an widget (kind of snack for my app).

Here is a schematic diagram:

I have to mention that step "2.4 Calculate result" will calculate how many times did we insert current day for all week.