We present a new framework for implementing real-time embedded safety-critical controllers which utilizes hybrid computing to address the issue of limited computational resources, a problem that is particularly prevalent in microrobotics. In our approach, the nominal stabilizing control algorithm is implemented digitally while the safety-critical quadratic program is solved via a dedicated analog resistor array. We apply this hybrid computing architecture to a simulated collision avoidance task for a micro-aerial vehicle and show the benefit relative to a purely-digital implementation. By leveraging analog quadratic programming on the Crazyflie 2.1 micro quadrotor, a reduction in overall processing time from 8.9 ms to 0.6 ms is estimated for this computationally-limited system. We further display the viability of our proposed safety-critical control framework through real-time flight demonstrations, utilizing a novel prototype analog circuit tethered to the Crazyflie. The flight results confirm the functionality of the control structure and prototype circuit while highlighting the overall capabilities of hybrid computing.