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(11, 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 11 12 1 0 0 1
1 12 11 0 1 1 0 1 6 12 12 6 6
2 6 11 6 6 1 0 5 3 Even Even 3 3
3 3 11 3 3 1 0 8 1 4 3 4 3 4 16 14 8 7
4 4 3 8 7 3 3 1 2 20 18 10 9
5 2 3 10 9 3 3 1 1 22 20 11 10
6 1 3 11 10 3 3 2 1 14 13 2 2 1 Even Even 1 1
7 1 1 11 10 1 1 0
(11)(11) - (10)(12) = 1