Uniform Shift Multiplication Algorithms Without Overflow

In this correspondence the problem of performing the multiplication by recoding the multiplier is considered. A special recoding for fractional numbers in two´s complement form is presented, that generates a class of uniform shift multiplication algorithms having the property that every partial product is always in the open interval (-1,1). Both the scan of the multiplier from the least to the most significant bit and the scan in the opposite direction are considered.