Digital low-dropout (LDO) regulators are popular in research today as compact power supply solutions. This paper provides a unique approach to analyze digital LDO feedback mechanics and stability, to reduce voltage ripple and extend operating speed over the state-of-the-art. A novel error-subtracting counter is proposed to exponentially improve the response time of any digital LDO, to keep the loop stable outside the typical operating limits, and to increase power-supply rejection (PSR). This leverages the fact that digital LDOs are fundamentally one-bit relaxation oscillators in steady-state. Theory and simulations show how the analog-to-digital (ADC) and digital-to-analog converters (DAC) in these systems affect stability. When compromised, a digital LDO produces uncontrolled sub-clock oscillations at the output that the proposed error-subtracting counter removes.