We describe a binary nonlinear optical correlator that uses a synthetic discrimination function (SDF) at the input plane to store the reference images. The SDF is displayed at the input plane side by side the input scene. The input scene, the SDF, and their joint power spectrum are thresholded to only two values. Thus, binary spatial light modulators can be used to implement the correlator. The correlation performance of the SDF-based binary nonlinear optical correlator is compared to that of the classical SDF-based correlator in the areas of correlation peak intensity, peak-to-sidelobe ratio, signal-to-noise ratio, and correlation width. We show that the SDF-based binary nonlinear optical correlator performs reasonably well. Furthermore, a single binary SLM can be used to read in sequentially the binarized input signals and the binarized joint power spectrum which results in a reduction in cost, size, and complexity of the system.