Just a quick sketch of a possible drive for a rod logic system. Each rod is attached to a compression spring. When the other end of the compression spring is pushed, if the rod is not inhibited, the rod should also be pushed nearly the same distance. If the rod is inhibited, then the spring compresses. The spring is pushed by means of a roller past which a track goes. The roller follows the track, pushing the rod at the right time. An additional set of springs is used to press the roller against the track, because the rod will not go back to the reset position by itself.
k1 is the spring constant of the return springs, and k2 is the spring constant for the rod spring.
The track could also be replaced with a cam gear, but in general we will have multiple levels of rods which need to be pushed in sequence, so a single track may be better.
With N rods inhibited, the force required to push the track past the rollers is given in the diagram above.