I have built a full adder that completes all calculations in 2 ticks. This differs from my very compact adders by not using XOR ot XNOR. I have compacted this design, but I believe there is a lot more room for improvement in future small versions of this adder. I built this using torches, dust, glass and target blocks.
This adder works via cross-inhibition and NOR gates. So there are two core rails; these are directly linked to the A and B inputs, respectively. Each core rail has a torch at the end, which directly acts on the sum output. Each core rail has a cross-inhibitor that uses a torch to invert the opposite rail's input onto the core rail it outputs on. When carry is turned on, this will directly inhibit both core rails, preventing an output sum. For all other cases, there are two NOR gates directly acting on the sum: the first one takes the inverted carry and the inverted OR of both A and B; the second NOR also takes the inverted carry and a signal made from the inverted A ORed with the inverted B.
The carry circuit has a NOR gate with inverted A and B inputs acting directly on Cout, followed by another NOR gate that also acts directly on Cout; this one has two inputs: the NOR of A and B, combined with the inverted carry.
This has been implemented in Java. I have uploaded a schematic on Planet Minecraft under the same title.
by Aggravating_Quiet_85