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, 12) :

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 12 1 0 0 1
1 12 13 0 1 1 0 1 6 12 14 6 7
2 6 13 6 7 1 0 7 3 18 20 9 10
3 3 13 9 10 1 0 10 1 10 10 10 10 5 Even Even 5 5
4 5 3 5 5 9 10 2 0 14 15 2 2 1 Even Even 1 1
5 1 3 1 1 9 10 2 1 10 11 10 11 1 22 24 11 12
6 1 1 11 12 1 1 0
7 1 1 1 1 11 12 0
(1)(13) - (1)(12) = 1