X = 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
Y = 00 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15
X ↔ Y

Ext-GCD(9, 13) :

i GCD Bezout AOdd : AEven :
A B ax ay bx by |A-B| A↔B Sx Sy ax
Sx'
ay
Sy'
A
A/2
ax
ax + Y
ay
ay + X
ax
ax/2
ay
ay/2
0 9 13 1 0 0 1
1 9 13 1 0 0 1 4 1 1 1 1 1 2 14 10 7 5
2 2 9 7 5 1 0 7 1 20 14 10 7
3 1 9 10 7 1 0 8 1 11 7 11 7 4 24 16 12 8
4 4 1 12 8 10 7 3 2 Even Even 6 4
5 2 1 6 4 10 7 1 1 Even Even 3 2
6 1 1 3 2 10 7 0
7 1 1 3 2 10 7 0
(3)(9) - (2)(13) = 1