A novel redundant binary signed-digit (RBSD) Booth's encoding

This paper presents a novel redundant binary signed-digit Booth encoding (RBBE) for a multiplier, which directly generates the RBSD partial products and allows the use of Booth encoding for radix-4 and radix-8 without the need to generate any hard multiples. As for RBBE with higher than radix-8, the number of hard multiples is significantly reduced. Moreover, negation in RBSD requires only wire crossing of two bits of each digit and does not need any carry-propagate operation or sign-extension. Therefore, the generation of negative multiples or the multiplication of 2's complement numbers in RBSD form can be done without additional hardware. This leads to a faster and smaller size multiplier. A RBSD adder tree is used to accumulate these RBSD partial products and the result is in RBSD form. Although the carry-propagate addition is necessary for the conversion from RBSD to SB, this is not a disadvantage over a SB multiplier because the accumulation of SB partial products also requires the same carry-propagate addition to get the final result from the intermediate sum and carry at the last stage.