1. Lecture 8 Addendum
Booth
Multipliers

2. 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

3. 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

4. Radix-2 Booth Recoding
yi = -xi + xi-1

5. Radix-2 Booth
Multiplier
Basic Step

6. Radix-2 Booth
Multiplier
Basic Step
in Xilinx FPGAs

7. Radix-2 Booth Multiplier
in Xilinx FPGAs

8. 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

9. Radix-4 Booth
Multiplier
Basic Step

10. zi/2 = -2xi+1 + xi + xi-1

11. Radix-4 Booth Multiplier:
Left Shifter & Control