This paper presents an exact formula for the entanglement of formation for all mixed states of two qubits with no more than two non-zero eigenvalues. The entanglement of formation is defined as the minimum average entanglement of a set of pure states that can be used to create a given mixed state. For a mixed state ρ, the entanglement of formation E(ρ) is given by E(ρ) = 𝓔(c), where c is the concurrence of ρ, defined as max(0, 2λ_max - TrR), with λ_max being the largest eigenvalue of R(ρ), and R(ρ) being a function of ρ defined as sqrt(sqrt(ρ)ρ*sqrt(ρ)). The concurrence is a measure of entanglement that is invariant under local unitary transformations. The paper also provides evidence that this formula may apply to all states of this system. The formula is derived using a magic basis for two-qubit systems and involves a matrix R that measures the "degree of equality" between ρ and its complex conjugate. The paper also discusses the implications of the formula for quantum computing and quantum cryptography, and suggests that it may be generalized to larger systems.This paper presents an exact formula for the entanglement of formation for all mixed states of two qubits with no more than two non-zero eigenvalues. The entanglement of formation is defined as the minimum average entanglement of a set of pure states that can be used to create a given mixed state. For a mixed state ρ, the entanglement of formation E(ρ) is given by E(ρ) = 𝓔(c), where c is the concurrence of ρ, defined as max(0, 2λ_max - TrR), with λ_max being the largest eigenvalue of R(ρ), and R(ρ) being a function of ρ defined as sqrt(sqrt(ρ)ρ*sqrt(ρ)). The concurrence is a measure of entanglement that is invariant under local unitary transformations. The paper also provides evidence that this formula may apply to all states of this system. The formula is derived using a magic basis for two-qubit systems and involves a matrix R that measures the "degree of equality" between ρ and its complex conjugate. The paper also discusses the implications of the formula for quantum computing and quantum cryptography, and suggests that it may be generalized to larger systems.