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Superconducting digital circuits are promising technologies that can overcome bottlenecks in both classical and quantum computation due to their ultra-high operation speed and extremely low power dissipation. Superconducting nanowire cryotrons (nTrons) are emerging as one type of superconductor switching devices, offering advantages complementary to conventional Josephson junctions. Achieving monolithic integration of a reasonable number of nTrons into a functional digital circuit is a crucial step to extend its application. In this study, we constructed a monolithic integrated nTron-based binary encoder, which includes input fanout circuits, on-chip biasing, combinational logic routing and multi-gate nTrons. This represents a monolithic nTron digital circuit comprising 137 nTron gates, 424 resistors, 274 inductors, and 164 vias developed using a two-superconducting-layer fabrication process. The performance of this monolithic nTron encoder surpasses that of our previously demonstrated circuit with discrete nTron components. The maximum bias margin is 28% for the fanout circuit and 60% for the multi-gate nTron when using a signal generator, while the minimum timing jitter is 40 ps. The total power dissipation mainly from biasing resistors is 19.6 μW, making it more power efficient than RSFQ encoders. The encoder is then packaged and connected with a superconducting nanowire single-photon detector array for demonstrating its function of addressing pixel locations. Compared to the conventional readout, the nTron encoder shows a minimum readout error rate lower than 10−4 and reduces the readout RF lines from 15 to 4. The design and fabrication technologies could enrich integrated nTron digital circuits beyond current limits and promote their applications in classical and quantum systems. [ABSTRACT FROM AUTHOR]