A modulator for generating a control code in response to a frequency control word is provided. The modulator includes an adder, an accumulator, a next state generation unit, and a code generation unit. The adder generates a frequency error signal by calculating a difference between the frequency control word and the control code. The accumulator generates a phase error signal by accumulating the frequency error signal. The phase error signal includes an integer part and a fractional part. The integer part of the phase error signal is a current state signal. The next state generation unit generates a next state signal according to a characteristic probability distribution determined by the fractional part of the phase error signal. The code generation unit generates the control code in response to the current state signal and the next state signal.