The electronic structure of a crystalline boron carbide has an energy forbidden gap of ∼ 3 eV and is hence a good insulator. But, on the other hand, the electrical conductivity of boron carbide is measurable. It is therefore believed that the defects formation in boron carbide is responsible for its electrical conductivity and a theory of hopping conduction of bipolaron through localized defects were developed, accordingly. Although the bipolaron electrical conductivity model does not rely on any specific type of defect, the bipolaron formation in boron carbide is believed to be a defective CBB intraicosahedral chain in connection with an B11C icosahedron. The current study examined the existing theory of bipolaron electrical conductivity by performing a systematical study on the formation energies of the defects in boron carbide using a state-of-the-art ab-initio electronic structure method. The studied defects cover a) stoichiometric variations of carbon concentration, b) missing boron atoms, and c) distribution of carbon atoms in the materials. It is found that the ground state of a fully carbonated boron carbide consists of B11C icosahedra connected by CBC intraicosahedral chains, i.e. consistent with the reported structural model of B4C. When carbon concentration is reduced, however, the population of CBC chain is found to be intact, while the population of B11C icosahedron is reduced by the replacements of B12 icosahedron. This observation is fundamentally different from the existing model of boron-rich boron carbide. The localized states associated with missing boron atoms are identified and the electrical conductivity through these localized defects states is studied.