A noniterative approach to generation of binary phase holograms is applied for synthesizing complex optical vortex arrays. This approach does not use inverse Fourier analysis and allows one to obtain arbitrary optical vortex arrays with specified topological charges, which cannot be obtained using conventional fork-shaped gratings. A topological charge of individual optical vortices generated using binary phase holograms can be specified at a given spatial frequency, so that the equidistant array of optical vortices can be generated via illuminating a hologram by a beam with the zero topological charge. The results of the calculation are consistent with the experimental data, including those of the interferometric measurements. The approach also makes it possible to synthesize superimposed optical vortices, where an optical field represents well-ordered circular arrays of optical singularities. An unusual behavior of phase dislocations in superimposed structures is found. For two optical vortices of same reciprocal lattice vectors, but different topological charges, spatial distribution of singularities are reconfigured in a such manner that a couple of concentric circular arrays of singularities appear. The proposed binary phase holograms offer new opportunities for synthesizing the complex optical vortex light fields, which can find light-matter interaction-based applications.