Radix 4 Booth Multiplication To improve the performance of multiplication process encoding is used Booth encoder plays an important role in Booth's multiplier as it reduces the number of partial product stages Consider the multiplication of two N bit numbers multiplicand X and multiplier Y in two's complement form as N 2 X xN 12N 1 ai 2i 1 i 0 N 2 Y yN 12N 1 bi 2i 2 i In this structure each group is encoded and decoded by selecting by 1 2 or 0 instead of shifting and adding for every column of the multiplier term and multiplying to obtain the same result which is shown in table 2 1 Table 2 1 Function table of Booth Multiplier Radix 4 booth encoder performs the process of encoding the multiplicand based on multiplier bits Using overlapping technique 3 bits at a time is compared Grouping of the multiplier bit to obtain the encoding value starts from the LSB of the multiplier and the first block only uses two bits of the multiplier and assumes a zero for the third bit as shown in figure 2 2 111000110 Figure 2 2 3 bit pairing as per booth recoding The number of partial products can be reduced to n 2 if two n bits numbers are multiplied if n is even number or n 1 2 if n is an odd number by using modified radix 4 booth multiplier

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