<p>Floating-gate memories (FGMs) show great promise for neuromorphic computing in efficient data-centric applications. However, their limited single-device state capacity remains insufficient for highly integrated precision computing. Here, we demonstrate 11-bit two-dimensional (2D) MoS₂ FGMs by contacting the 2D channels with bismuth electrodes, enabling 100 μA on-state current with 10⁸ on/off ratio and reducing the current noise by 3 times (approaching the equipment limits) due to the Schottky barrier-free interfaces. Moreover, we employed a dual-pulse state editing scheme enhancing the stability of our FGMs. The devices show as high as 2,249 distinct conductance levels (&gt;11-bit) while maintaining 230 ns operation speed, &gt;10⁴s retention, and &gt;10⁵ cycle endurance. Furthermore, the gate-injection operation prevents the influence from generated defects during cycling, maintaining low noise even after 10⁵ cycles and at 85 °C. Theoretical analysis reveals interfacial defects as the primary state-number limitation, suggesting 17-bit capacity is achievable through further trap density reduction. This work establishes 2D FGMs as promising candidates for high-bit-density, low-power neuromorphic hardware.</p>