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(12, 9) :

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 12 9 1 0 0 1
1 12 9 1 0 0 1 3 6 10 12 5 6
2 6 9 5 6 0 1 3 3 14 18 7 9
3 3 9 7 9 0 1 6 1 7 10 7 10 3 16 22 8 11
4 3 3 8 11 7 9 0
5 3 3 8 11 7 9 0
6 3 3 8 11 7 9 0
7 3 3 7 9 8 11 0
(7)(12) - (9)(9) = 3