We investigated the surface orthogonal patterning and bidirectional self-assembly of binary hairy nanoparticles (NPs) constructed by uniformly tethering a single NP with multiple V-shaped AB diblock copolymers using Brownian dynamics simulations in a poor solvent. At low concentration, the chain collapse and microphase separation of binary polymer brushes can lead to the patterning of the NP surface into A- and B-type orthogonal patches with various numbers of domains (valency), n = 1-6, that adopt spherical, linear, triangular, tetrahedral, square pyramidal, and pentagonal pyramidal configurations. There is a linear relationship between the valency and the average ratio of NP diameter to the polymers' unperturbed root-mean-square end-to-end distance for the corresponding valency. The linear slope depends on the grafting density and is independent of the interaction parameters between polymers. At high concentration, the orthogonal patch NPs serve as building blocks and exhibit directional attractions by overlapping the same type of domains, resulting in self-assembly into a series of fascinating architectures depending on the valency and polymer length. Notably, the 2-valent orthogonal patch NPs have the bidirectional bonding ability to form the two-dimensional (2D) square NP arrays by two distinct pathways. Simultaneously patching A and B blocks enables the one-step formation of 2D square arrays via bidirectional growth, whereas step-by-step patching causes the directional formation of 1D chains followed by 2D square arrays. Moreover, the gap between NPs in the 2D square arrays is related to the polymer length but independent of the NP diameter. These 2D square NP arrays are of significant value in practical applications such as integrated circuit manufacturing and nanotechnology.