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(13, 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 13 9 1 0 0 1
1 13 9 1 0 0 1 4 0 1 1 1 1 2 10 14 5 7
2 2 9 5 7 0 1 7 1 14 20 7 10
3 1 9 7 10 0 1 8 1 7 11 7 11 4 16 24 8 12
4 4 1 8 12 7 10 3 2 Even Even 4 6
5 2 1 4 6 7 10 1 1 Even Even 2 3
6 1 1 2 3 7 10 0
7 1 1 7 10 2 3 0
(7)(13) - (10)(9) = 1