# Why sum of two binary numbers cannot be determined in $NC^0$ but in $AC^0$?

Why sum of two binary numbers cannot be determined in $$NC^0$$ but it can be determined in $$AC^0$$?

In an $$\mathsf{NC^0}$$ circuit, every output bit depends on a bounded number of input bits. But the $$k$$th bit of the output (counting from the LSB) depends on the first $$k$$th bits of each input.
To see that $$\mathsf{AC^0}$$ circuits can compute addition, we need to produce such a circuit. Hopefully you have seen such circuits, and otherwise perhaps you can construct them on your own. Give it a shot.
an $$NC^0$$ can only consider circuits of fan-in 2. If we try to adding with a Full-Adder with Lookahead Gatter to calculate the carry, needs every Full-Adder 3 Input signals. But in $$NC^0$$ are only 2 inputs allowed. If we try to replace Full-Adder with other logic gatters, we hurt the depth of the circuit.