19 X0, X1, AND X2 INDICATE EXACTLY ZERO, ONE, OR TWO 1’S IN A GROUP

10.19 X0, X1, and X2 indicate exactly zero, one, or two 1’s in a group. Y1, Y2, and Y3

are one-hot vectors indicating the first, second, and third 1.

=

0

X A

i i i:

1 bitwise precomputation

X

2 0

i i

g

0 0 0

X X X

−i j i k k j: : 1:

g g

= +

1 1 0 0 1 group logic

X X X X X

− −: : 1: : 1:i j i k k j i k k j

g g g

= + +

2 1 1 2 0 0 2

X X X X X X X

− − −i j i k k j i k k j i k k j: : 1: : 1: : 1:

Y A X

1 0