Title :
A novel redundant binary signed-digit (RBSD) Booth´s encoding
Author :
Besli, Nurettin ; Deshmukh, R.G.
Author_Institution :
Florida Inst. of Technol., Melbourne, FL, USA
Abstract :
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
Keywords :
adders; binary codes; digital arithmetic; redundancy; 2´s complement multiplication; Booth encoding; RBSD encoding; adder tree; negative multiples; partial products; radix-4; radix-8; redundant binary signed-digit encoding; wire crossing; Adders; Circuits; Computer applications; Decoding; Delay effects; Digital arithmetic; Encoding; Hardware; Signal processing algorithms; Wire;
Conference_Titel :
SoutheastCon, 2002. Proceedings IEEE
Conference_Location :
Columbia, SC
Print_ISBN :
0-7803-7252-2
DOI :
10.1109/.2002.995633