Summary form only given. The authors have previously (1988) integrated both a SQUID (superconducting quantum interference device) sensor and a superconducting feedback circuit on a single chip. In the present work, the authors describe the improvement of the dynamic range of the single-chip SQUID by more than two orders of magnitude; high sensitivity was also obtained. In the single-chip SQUID, the sensor is AC biased and produces a pulse sequence. The superconducting feedback circuit consists of a superconducting loop and a write gate, a two-junction interferometer. The gate adds a flux quantum to the loop when it receives a pulse from the sensor. The stored flux is fed back to the sensor through magnetical coupling. When a large input was applied, the loop stored flux quanta up to +or-2*10/sup 4/. This number is more than two orders of magnitude larger than the previous value, +or-10/sup 2/; however, it is reduced from the design value, +or-1.5*10/sup 5/. This reduction is due to the circulating current in the loop caused by the flux trappings. >