An operational NAND gate in Age of Empires II, built with the game's scenario editor. This one can also be built within the game in a two-player setup but it's a lot easier (so to speak) to just script it.

This one is designed to show its internal workings, and much simpler implementations are possible. Every bit is represented by two rails (grass for 0, a bridge for 1). Only one rail is active at a time, with a goat acting as the signal carrier. When the gate fires, the bit-goats are removed (they ded) and a new bit-goat is placed in its respective output rail.

To avoid race conditions, 'gate ready' rails (ice) are set, with a signal-goat in the rail closest to the gate indicating that it can start the calculation. In the above: in order for the AND gate to be active, the leftmost and bottom-most bit goats need to be near the pens (towards the inside of the map). This says that the gate is ready, but not that the UPSTREAM gate is ready. For that, the goat in the middle ice patch needs to be near the AND pen. When the gate fires, the goats are sent 'away' towards their upstream/downstream gates to signal readiness.

To read the gate: leftmost grass/bridge rails: 0/1 left-input for AND. Rightmost grass/bridge rails: right-input for AND. Middle rails: output of AND, input for NOT. In the gif, it computes AND(0, 1), places a goat in the middle grass rail (0), and NOT places a gate on the bridge (1).