In this note, the dynamical behaviors of Euler's discretization of the equivalent control based sliding-mode control (SMC) systems are studied. We show that if the discretized SMC system is asymptotically stable, then every trajectory converges to a period-2 cycle. Bounds for the steady states are derived, which allow one to estimate the maximum chattering amplitude for a given value of the time step. The analysis and results are verified with several computer simulations.