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, 5) :

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 5 1 0 0 1
1 12 5 1 0 0 1 7 6 6 12 3 6
2 6 5 3 6 0 1 1 3 8 18 4 9
3 3 5 4 9 0 1 2 1 4 10 4 10 1 Even Even 2 5
4 1 3 2 5 4 9 2 1 6 14 1 2 1 6 14 3 7
5 1 1 3 7 2 5 0
6 1 1 3 7 2 5 0
7 1 1 3 7 2 5 0
(3)(12) - (7)(5) = 1