Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to construct Dirac spinors, considering the interchange between the Lorentz representation space (1/2, 0) and (0, 1/2) made by the magic of Pauli matrices and not by parity, as was commonly thought. As is well known, the parity operator is related with the Dirac dynamics, as can be seen in Speraņa L. D., Int. J. Mod. Phys. D, 2 (2014) 1444003. The major focus is to establish the relation between the Dirac dynamics with the parity operator, i.e., the reverse path shown in the paper by Speraņa.