  We unveil the geometrical meaning of winding number and utilize it to
characterize the topological phases in one-dimensional chiral non-Hermitian
systems. While chiral symmetry ensures the winding number of Hermitian systems
being integers, it can take half integers for non-Hermitian systems. We give a
geometrical interpretation of the half integers by demonstrating that the
winding number $\nu$ of a non-Hermitian system is equal to half of the
summation of two winding numbers $\nu_1$ and $\nu_2$ associated with two
exceptional points respectively. The winding numbers $\nu_1$ and $\nu_2$
represent the times of real part of the Hamiltonian in momentum space
encircling the exceptional points and can only take integers. We further find
that the difference of $\nu_1$ and $\nu_2$ is related to the second winding
number or energy vorticity. By applying our scheme to a non-Hermitian
Su-Schrieffer-Heeger model and an extended version of it, we show that the
topologically different phases can be well characterized by winding numbers.
Furthermore, we demonstrate that the existence of left and right zero-mode edge
states is closely related to the winding number $\nu_1$ and $\nu_2$.
