Adder of two 2-bit numbers

Hi, I'm Monika and I start my journey with electronic. I don't understand following task. Someone could explain me how to do it?

I need design an adder of two 2-bit numbers. The circuit provides an additional output W, which takes the state equals 1 when the result of the addition operation is greater than 3.
And I have to draw a suitable diagram for each circuit.

If you google full bit adder.. you should get one or two designs come up..

Some use XOR gates and others just NAND gates... They all show "carry" which is one when both inputs are 1... Making two, you just cascade..
there are diagrams of how to add several stages..