In this paper, we investigate two- and one-dimensional honeycomb structures of boron antimony (BSb) using a first-principles plane wave method within the density functional theory. BSb with a two-dimensional honeycomb structure is a semiconductor with a 0.336 eV band gap. The vacancy defects, such as B, Sb, B + Sb divacancy, and B + Sb antisite disorder affect the electronic and magnetic properties of the 2D BSb sheet. All the structures with vacancies have nonmagnetic metallic characters, while the system with antisite disorder has a semiconducting band structure. We also examine bare and hydrogen-passivated quasi-one-dimensional armchair BSb nanoribbons. The effects of ribbon width (n) on an armchair BSb nanoribbon and hydrogen passivation on both B and Sb edge atoms are considered. The band gaps of bare and H passivated A-Nr-BSb oscillate with increasing ribbon width; this property is important for quantum dots. For ribbon width n = 12, the bare A-Nr-BSb is a nonmagnetic semiconductor with a 0.280 eV indirect band gap, but it becomes a nonmagnetic metal when B edge atoms are passivated with hydrogen. When Sb atoms are passivated with hydrogen, a ferromagnetic half-metallic ground state is observed with 2.09 mu(B) magnetic moment. When both B and Sb edges are passivated with hydrogen, a direct gap semiconductor is obtained with 0.490 eV band gap with disappearance of the bands of edge atoms.