1. A motion detecting and motion compensation prediction circuit comprising: a frame memory carrying information regarding related image frames and providing outputs thereof to an integer pixel accuracy calculating unit that calculates relative position information of an object in different ones of said related image frames; a buffer memory accepting output from said frame memory and said integer pixel accuracy calculating unit; a pixel data input unit connected to said buffer memory and said frame memory for accepting data therefrom; an interpolated pixel data generating unit connected to and for accepting the output of said pixel data input unit; a subtractor accepting the output of said pixel data input unit and said interpolated pixel data generating unit and providing an output therefrom; a comparison unit accepting the output of said subtractor and providing a motion vector output to at least said buffer memory; wherein said buffer memory, said pixel data input unit, and said interpolated pixel data generating unit are operative during processing for the detection of a half-pixel accuracy motion vector based on a calculation result of said integer pixel accuracy calculating unit and during processing for generating a predictive-coded picture by using said motion vector.