ECE 375: Digital Design II

Class 23

In the last class, we looked at signed multiplication. However, that design only works if for one negative numbers, not two.

Multiplication of Two Negative Numbers

A = 10110 => -10
X = 10101 => -11

K = 5

  p0    => 00_00000_00000
+ x0*a  => 11_10110_00000
------------------------
 2*p1   => 11_10110_00000

  p1    => 11_11011_00000
+ x1*a  => 00_00000_00000
------------------------
 2*p2   => 11_11011_00000

  p2    => 11_11101_10000
+ x2*a  => 11_10110_00000
------------------------
 2*p3   => 11_10011_10000

  p3    => 11_11001_11000
+ x3*a  => 00_00000_00000
------------------------
 2*p4   => 11_11001_11000

  p4    => 11_11100_11100
-- In the very last step, if the MSB of the multiplier is negative, you take the two's complement
  x4*a  => 10110
(x4*a)' => 01001
 -x4*a  => 00_01010_00000
------------------------
 2*p5   => 00_00110_11100
  p5    => 00_00011_01110 <=> 110

Hardware