This talk discusses implementation of a novel method to convert quadrature samples into samples of angular movement of a digital laser gyroscope. Data processing module of a digital laser gyroscope includes accumulation unit, system of linear equations solver unit, a unit to compute ellipse parameters and a unit restoring time series. Those units are implemented in Verilog hardware description language for FPGA. Trials of the developed FPGA-based electronics demonstrated that it reduces by an order of magnitude the random error of angular velocity measurement, when averaging time of the gyro's output samples does not exceed one second.