The identity and timing of environmental stimulus play a pivotal role in living organisms in programming their signaling networks and developing specific phenotypes. The ability to unveil history-dependent signals will advance our understanding of temporally regulated biological processes. Here, we have developed a two-input, five-state DNA finite-state machine (FSM) to sense and record the temporally ordered inputs. The spatial organization of the processing units on DNA origami enables facile modulation of the energy landscape of DNA strand displacement reactions, allowing precise control of the reactions along predefined paths for different input orders. The use of spatial constraints brings about a simple, modular design for the FSM with a minimum set of orthogonal components and confers minimized leaky reactions and fast kinetics. The FSM demonstrates the capability of sensing the temporal orders of two microRNAs, highlighting its potential for temporally resolved biosensing and smart therapeutics.