Minecraft wiki entry for Logic_gates, associated text: The half adder is nearly identical to the full adder, except the second XOR gate is removed and the output from the first XOR gate becomes S. There is no carry in (C'), but the carry out (C) circuit is still on top of the first XOR gate and provides a carry to the first full adder. Some ALUs will not use a half adder for the first bit, to support INCREMENT (allow a carry in on the first bit).