This paper studies the simple dynamic binary neural network characterized by the signum activation function, ternary weighting parameters and integer threshold parameters. The network can be regarded as a digital version of the recurrent neural network and can output a variety of binary periodic orbits. The network dynamics can be simplified into a return map, from a set of lattice points, to itself. In order to store a desired periodic orbit, we present two learning algorithms based on the correlation learning and the genetic algorithm. The algorithms are applied to three examples: a periodic orbit corresponding to the switching signal of the dc-ac inverter and artificial periodic orbit. Using the return map, we have investigated the storage of the periodic orbits and stability of the stored periodic orbits.