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, 11) :

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