A receiver including: a data processing circuit, in a training mode, to compare a multi-level signal with first and second voltage signals, and to generate data density signals; a counter circuit to count the data density signals to generate counting values; a control circuit to store, in a register set, a voltage range, counting values corresponding to the voltage range and a control code associated with a first level of the first voltage signal and a second level of the second voltage signal, the voltage range being based on the first and second voltage signals; and a voltage generation circuit, in the training mode, to apply the first and second voltage signals to the data processing circuit and to increase the first level and the second level by a difference between the first and second control signals in response to the control code from the control circuit.