Droplets are versatile digital materials; they can be produced at high throughput, perform chemical reactions as miniature beakers and carry biological entities. Droplets have been manipulated with electric, optical, acoustic and magnetic forces, but all these methods use serial controls to address individual droplets. An alternative is algorithmic manipulation based on logic operations that automatically compute where droplets are stored or directed, thereby enabling parallel control. However, logic previously implemented in low-Reynolds-number droplet hydrodynamics is asynchronous and thus prone to errors that prevent scaling up the complexity of logic operations. Here we present a platform for error-free physical computation via synchronous universal logic. Our platform uses a rotating magnetic field that enables parallel manipulation of arbitrary numbers of ferrofluid droplets on permalloy tracks. Through the coupling of magnetic and hydrodynamic interaction forces between droplets, we developed AND, OR, XOR, NOT and NAND logic gates, fanouts, a full adder, a flip-flop and a finite-state machine. Our platform enables large-scale integration of droplet logic, analogous to the scaling seen in digital electronics, and opens new avenues in mesoscale material processing.
