This technical note proposes a quadratic programming (QP)-based method for identification of finite impulse response (FIR) dynamic systems from quantized or binary data. The main idea of the proposed method is to reformulate this identification problem, usually viewed as a nonlinear estimation problem with discontinuous nonlinearities, in the form of a standard QP problem, which is a convex optimization problem and can be solved efficiently. The so-called complete input conditions to ensure the unique solution of the QP problem are developed, and the consistency of the estimated parameters is established under the complete input conditions. Numerical examples demonstrate the effectiveness of the proposed method.