Logical operations using biological molecules, such as DNA computing or programmable diagnosis using DNA, have recently received attention. Challenges remain with respect to the development of such systems, including label-free output detection and the rapidity of operation. Here, we propose integration of biological nanopores with DNA molecules for development of a logical operating system. We configured outputs "1" and "0" as single-stranded DNA (ssDNA) that is or is not translocated through a nanopore; unlabeled DNA was detected electrically. A negative-AND (NAND) operation was successfully conducted within approximately 10 min, which is rapid compared with previous studies using unlabeled DNA. In addition, this operation was executed in a four-droplet network. DNA molecules and associated information were transferred among droplets via biological nanopores. This system would facilitate linking of molecules and electronic interfaces. Thus, it could be applied to molecular robotics, genetic engineering, and even medical diagnosis and treatment.