A new algorithm named the eight-section (ES) method for carrying out the interpolation for a magneto-resistive (MR) encoder is successfully developed and fabricated in a digital chip. It is known that a conventional magneto-resistive (MR) encoder employs the interpolation method, which converts incoming front-end analog signals in harmonics in sinusoids/co-sinusoids to moving displacement via calculating arc-tangents. This conventional interpolation requires divisions to be carried out for the displacement, which often leads to large noises while conducting digital computation, eventually undermining significantly the accuracy of the MR sensor. The proposed interpolation of eight-section (ES) is designed specially without divisions in the digital computation, leading to higher precision than the conventional interpolation conducting the computation of arc-tangents. The digital computation chip designed by this study consists of a cycle counter, two decimators for incoming analog signals of the MR sensor, a correcting circuit, and the proposal ES interpolation unit. The designed chip is successfully fabricated by TSMC 0.18-μm CMOS process, the area of which is 1643 × 1676 μm. The chip is than calibrated by a reference interferometer by experiments for further improving the measurement accuracy. The precision finally results in measuring displacement reaches as accurate as within 1.065 μm, which is much favorable to the existing performance around 2 μm by the conventional interpolation.