Present paper reports electron impact total ionization cross sections (Qion) for all the components of DNA and RNA molecules from threshold to 2000 eV. We have employed spherical complex optical potential(SCOP) formalism to calculate the total inelastic cross sections and have deduced total ionization cross sections using complex scattering potential-ionization contribution (CSP-ic) method. DNA and RNA being the complex molecules, these cross sections are evaluated using the group additivity rule. The present results find good accord with the available previous theoretical estimates. In absence of experimental data for these biomolecules, the present theoretical estimates prove to be the reference data source. Qion for sugar phosphate backbone of RNA and for complete DNA and RNA units are reported for the first time in this work.