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redundant binary booth recoding vhdl code
#1

students from engineering college ece department
we are doing a project on this topic we want how to solve redundant binary booth multiplier problem and vhdl code.
A Modified Partial Product
Generator for Redundant Binary
Multipliers
Xiaoping Cui, Weiqiang Liu, Senior Member, IEEE,
Xin Chen, Earl E. Swartzlander, Jr., Life Fellow, IEEE
and Fabrizio Lombardi, Fellow, IEEE
Abstract—Due to its high modularity and carry-free addition, a
redundant binary (RB) representation can be used when designing
high performance multipliers. The conventional RB multiplier requires
an additional RB partial product (RBPP) row, because an
error-correcting word (ECW) is generated by both the radix-4 Modified
Booth encoding (MBE) and the RB encoding. This incurs in an
additional RBPP accumulation stage for the MBE multiplier. In this
paper, a new RB modified partial product generator (RBMPPG) is
proposed; it removes the extra ECW and hence, it saves one RBPP
accumulation stage. Therefore, the proposed RBMPPG generates
fewer partial product rows than a conventional RB MBE multiplier.
Simulation results show that the proposed RBMPPG based designs
significantly improve the area and power consumption when the
word length of each operand in the multiplier is at least 32 bits;
these reductions over previous NB multiplier designs incur in a
modest delay increase (approximately 5%). The power-delay product
can be reduced by up to 59% using the proposed RB multipliers
when compared with existing RB multipliers.
Index Terms—Redundant binary, modified Booth encoding, RB
partial product generator, RB multiplier
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#2
The use of redundant binary arithmetic (RB) in the design of high-speed digital multipliers is beneficial due to its great modularity and its incorporation without support. To reduce the number of partial products, a modified cabin coding algorithm with high radix content is desired. However, their use is hampered by the complexity of generating the hard multiples and the overhead resulting from the negative multiples and the conversion of normal binary number (NB) to RB. This document proposes a new RB Booth coding scheme to avoid these problems. The idea is to polarize two adjacent coded Booth digits to directly form a partial product RB to avoid the hard multiple of the high-booth Booth coding without incurring any correction vector. The proposed method leads to a lower coding and decoding complexity than the newly proposed RB cab encoder. The results of synthesis using the standard Artisan TSMC 0.18 cell library show that the RB multipliers designed with our proposed Booth coding algorithm exhibit on average 14% more speed and 17% less energy delay product than the existing multiplication algorithms for a power range of two word lengths from 8 to 64 b.
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