Dual-state genetic switches that can change their state in response to input signals can be used in synthetic biology to encode memory and control gene expression. A transcriptional toggle switch (TTS), with two mutually repressing transcription regulators, was previously used for switching between two expression states. In other studies, serine integrases have been used to control DNA inversion switches that can alternate between two different states. Both of these switches use two different inputs to switch ON or OFF. Here, we use mathematical modelling to design a robust one-input binary switch, which combines a TTS with a DNA inversion switch. This combined circuit switches between the two states every time it receives a pulse of a single-input signal. The robustness of the switch is based on the bistability of its TTS, while integrase recombination allows single-input control. Unidirectional integrase-RDF-mediated recombination is provided by a recently developed integrase-RDF fusion protein. We show that the switch is stable against parameter variations and molecular noise, making it a promising candidate for further use as a basic element of binary counting devices.