A method and apparatuses for performing binary multiplication on signed and unsigned operands of various lengths is discussed herein. It is a concept that may be split into two parts, the first of which is the multiplication hardware itself, a compact, less than-full sized multiplier employing Booth or other type of recoding methods upon the multiplier to reduce the number of partial products per scan, and implemented in such a manner so that a multiplication operation with large operands may be broken into subgroups of operations that will fit into this mid-sized multiplier whose results, here called modular products, may be knitted back together to form a correct, final product. The second part of the concept is the supporting hardware used to separate the operands into subgroups and input the data and control signals to the multiplier, and the algorithms and apparatuses used to align and combine the modular products properly to obtain the final product. These algorithms used to obtain a result as specified by the operation may be as varied as the supporting hardware with which the multiplier may be used, making this multiplier a very flexible and powerful design.