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Lecture 8 Addendum Booth Multipliers
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Source Jean-Pierre Deschamps, Gery Jean Antoine Bioul,
Gustavo D. Sutter, Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems, Chapter 12: Multipliers Section Booth multipliers
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Y Multiplicand Ym-1Ym-2 . . . Y1 Y0 X Multiplier xm-1xm-2 . . . x1 x0
Notation Y Multiplicand Ym-1Ym Y1 Y0 X Multiplier xm-1xm x1 x0 P Product (Y X ) p2m-1p2m p2 p1 p0 If multiplicand and multiplier are of different sizes, usually multiplier has the smaller size
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Radix-2 Booth Recoding yi = -xi + xi-1
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Radix-2 Booth Multiplier Basic Step
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Radix-2 Booth Multiplier Basic Step in Xilinx FPGAs
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Radix-2 Booth Multiplier
in Xilinx FPGAs
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Y Multiplicand Ym-1Ym-2 . . . Y1 Y0 X Multiplier xm-1xm-2 . . . x1 x0
Notation Y Multiplicand Ym-1Ym Y1 Y0 X Multiplier xm-1xm x1 x0 P Product (Y X ) p2m-1p2m p2 p1 p0 If multiplicand and multiplier are of different sizes, usually multiplier has the smaller size
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Radix-4 Booth Multiplier Basic Step
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zi/2 = -2xi+1 + xi + xi-1
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Radix-4 Booth Multiplier:
Left Shifter & Control
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