Fringe projection profilometry (FPP) using gray-scale patterns like sinusoidal stripes often encounters challenges for high dynamic range (HDR) applications. These challenges arise due to the presence of shiny surfaces or abrupt changes in reflectivity, leading to either reconstruction failure or substantial errors. We present a robust modulation and reconstruction method that divides the grayscale sinusoidal fringe into eight binary fringes and employs a differencing approach to mitigate HDR surface interference and enable demodulation, significantly reducing vulnerability to reflectivity fluctuations. The binary fringes differencing demodulation (BFDD) technique is presented to extract the relevant binary patterns from the camera images and integrate them into an 8-bit HDR gray stripe modulation. Binary modulation allows for simultaneous projection and image acquisition in just 0.2 seconds. The experimental results showed that this method achieves a remarkably high coverage rate in high-reflectivity 3D reconstruction. The method can also effectively mitigate negative impact due to abrupt changes in surface reflectivity, resulting in near-perfect ground truth consistency.