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In this paper, we present a novel design for a signal processor based on rapid-single-flux-quantum (RSFQ) circuits for a compact neutron diffraction system with an array of 10B-enriched MgB2 nanowire neutron detectors. By introducing an RSFQ signal processor, the system is able to accommodate a large number of detectors and determine the kinetic energy of each incident neutron. The processor consists of quasi-one-junction SQUIDs (QOSs), time-to-digital converters, and a multiplexer. A QOS is connected to each detector that operates at 27 K. The QOS picks up a voltage impulse with a width smaller than 2 ns generated across a detector and creates an SFQ pulse for RSFQ signal processing. The diffraction patterns are determined by the position and the kinetic energy of the incident neutrons. The time-to-digital converter is used to measure these energies by the time-of-flight method. Time resolution down to tens of picoseconds is possible, even with an array of detectors, and it is easy to multiplex signals in the time domain. We successfully demonstrated the RSFQ signal processor in liquid helium, and also tested a prototype, consisting of the processor connected with four MgB2 nanowire detectors in a Gifford-McMahon cryocooler, by irradiating a focused pulsed laser instead of neutrons, and obtained preliminary experimental results.