A new demodulation technique which can be used for the fiber optic acoustic sensor system using Sagnac interferometer is described. The theoretical limitation in dynamic range of the quadrature demodulation technique can be removed by the proposed BPSK(Binary Phase Shift Keying) demodulation technique. Full demodulation of input acoustic signal is possible with just simple electronics by eliminating the necessity of the high frequency phase modulation. This technique is suitable for digital signal processing of fiber optic sensor systems and can be applicable for other interferometers.