Connected logic gates can be operated on the levels of one molecule by making use of the special properties of high Rydberg states. Explicit experimental results for the NO molecule are provided as an example. A number of other options, including that of several gates concatenated so as to operate as a full adder, are discussed. Specific properties of high Rydberg states that are used are: their autoionization is delayed so that they can be distinguished from direct multiphoton ionization, during their long life such states also can decay by energy transfer to the molecular core in a way that can be controlled by the judicious application of very weak external electrical fields, and the Rydberg states can be detected by the application of an ionizing electrical field. The combination of two (or three) color photons with and without external weak fields allows the construction of quite elaborate logic circuit diagrams and shows that taking advantage of the different intramolecular dynamics of levels that differ by their excitation enables the compounding of logic operations on one molecular frame.