Utilizing computer-generated holograms is a promising technique because these holograms can theoretically generate arbitrary waves with high light efficiency. In phase-only spatial light modulators, encoding complex amplitudes into phase-only holograms is a significant issue, and double-phase holograms have been a popular encoding technique. However, they reduce the light efficiency. In this study, our complex amplitude encoding, called binary amplitude encoding (BAE), and conventional methods including double-phase hologram, iterative algorithm, and error diffusion methods were compared in terms of the fidelity of reproduced light waves and light efficiency, considering the applications of lensless zoomable holographic projection and vortex beam generation. This study also proposes a noise reduction method for BAE holograms that is effective when the holograms have different aspect ratios. BAE is a non-iterative method, which allows holograms to be obtained more than 2 orders of magnitude faster than iterative holograms; BAE has about 3 times higher light efficiency with comparable image quality compared to double-phase holograms.