Abstract In this work, we implement a fast non-iterative method for the generation of binary amplitude Fresnel holograms and demonstrate their application in a holographic projection scheme based on a digital micromirror device. To achieve this, we perform the binarization of phase-only holograms generated using an optimized Fresnel random phase. We analyze the quality of the resulting binary amplitude holograms and compare them with holograms obtained with the conventional iterative Fresnel algorithm as a function of the number of iterations and the propagation distance. Additionally, we evaluate the diffraction efficiency in both methods. We demonstrate that the holograms produced with our method present significantly advantages in computation speed without a significant reduction in the reconstruction quality. Both experimental and numerical results confirm the effectiveness of our proposal.