The stability of Boolean networks and stabilization of Boolean control networks are discussed. By using the method of semi-tensor product of matrices and
the matrix expression of logic, the dynamics of Boolean network can be represented as a discrete-time dynamic system, then it is converted into an algebraic form. Then the one-to-one correspondence between the structure matrix of the algebraic form ad a digital transformation is established. Finally, by using the method of digital trasformation, necessary and sufficient conditions for the stability and stabilization of Boolean networks are obtained.