An Alternative Proof of Modified-Booth Recoding Algorithm Based on Number-Domain Transformations
V Rao · Journal of Circuits Systems and Computers · 2000
In this letter, the nonredundant radix-4 representation of two's complement numbers is exploited to develop an alternative proof for the modified-Booth recoding algorithm. This proof is established by showing that the modified-Booth recoding algorithm essentially amounts to successive transformations of the number from its two's complement to its nonredundant radix-4 representation and from its nonredundant radix-4 to its modified radix-4 signed-digit representation. The salient feature of these transformations is that the digits in the resulting modified radix-4 signed-digit number take on values from the same balanced digit-set, placing in evidence the main principle and motivation behind the modified-Booth recoding algorithm.