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