In high-efficiency video coding (HEVC), motion estimation (ME) complexity is high. The ME complexity is greatly reduced by implementing a multiplication free one-bit transform (MF-1BT) in the HEVC encoder. Compared with the other one-bit transforms, the computational load of MF-1BT is less. The implementation of MF-1BT in a HEVC encoder greatly reduces the ME complexity in terms of ME time (MET) and total encoding time (ET). Experimental results show that the MF-1BT along with full search reduces the ME complexity in terms of percentage reduction in MET and ET by 89.03% and 87.53%, respectively, as compared with a conventional full search algorithm with a Bjontegaard delta-rate (BD-rate) of 0.1095% and Bjontegaard delta-peak signal-to-noise ratio (BD-PSNR) of 0.1311% in low delay-P main profile. The performance comparison of test zonal search (TZS) along with MF-1BT is evaluated by comparing it with the TZS algorithm in the fast search mode of the HEVC encoder. Hexagon and diamond search algorithm along with MF-1BT is also proposed in the fast search mode of the HEVC encoder to further reduce the MET and ET compared with the TZS algorithm of the HEVC encoder.