Nanoparticles with biocomputing capabilities could potentially be used to create sophisticated robotic devices with a variety of biomedical applications, including intelligent sensors and theranostic agents. Deoxyribonucleic acid - DNA / Ribonucleic acid - RNA based computing techniques have already been developed that can offer a complete set of Boolean logic functions and have been used, for example, to analyse cells and deliver molecular payloads. However, the computing potential of particle-based systems remains relatively unexplored. Here, we show that almost any type of nanoparticle or microparticle can be transformed into autonomous biocomputing structures that are capable of implementing a functionally complete set of Boolean logic gates - YES, NOT, AND and OR - and binding to a target as result of a computation. The logic-gating functionality is incorporated into self-assembled particle/biomolecule interfaces - demonstrated here with proteins - and the logic gating is achieved through input-induced disassembly of the structures. To illustrate the capabilities of the approach, we show that the structures can be used for logic-gated cell targeting and advanced immunoassays.