binary addition / truth table?
what happens to the carry outs?


You can combine n full adder circuits to make an adder for n-bit numbers. When you do this, you connect the carry-out from each adder to the carry ins of the adder for the next most significant bit.

Here's an example adding 2 3-bit numbers, X = A + B:







simulate this circuit &ndash; Schematic created using CircuitLab


  why is the carry in an "input" of its own, shouldn't it be just x and y since the carry ins/outs usually belong to one operation distinct from the values we use?


It's more efficient to just calculate the sum of 3 bits in one operation than to add x and y, and then add cin in a 2nd step.