We propose a novel all-optical integrated thresholder called the dual resonator enhanced asymmetric Mach-Zehnder interferometer (DREAM). Unlike prior integrated photonic devices, the DREAM exhibits properties of stable binary decision making, outputting a constant “one” power value for signals above a certain power level and “zero” for signals of lower powers. This thresholding shape arises from the interference of complementary nonlinear effects of two microring resonators (MRR), one in each arm of a Mach-Zehnder interferometer (MZI). The proposed device performs several orders of magnitude better in size, decision latency, energy efficiency, and stability compared to fiber-based methods of optical thresholding. It is best suited for application in densely integrated systems where rapid conversion between analog and digital signal domains is ubiquitous, such as hybrid analog-digital and neuromorphic processing architectures. We derive analytical steady-state solutions to the nonlinear MRR, which enable design simulation, optimization, and automation of a continuous signal thresholder about three orders of magnitude faster than with numerical simulation. Additional numerical simulations indicate the possibility of a 50 GHz pulse thresholder with a 380 pJ switching threshold in a silicon-on-insulator (SOI) platform. The proposed circuit design techniques are potentially applicable to a wide range of materials, waveguide platforms, and resonator types, but for concreteness, we limit the focus of this paper to MRRs in SOI.