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(15, 8) :

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 15 8 1 0 0 1
1 8 15 0 1 1 0 7 4 8 16 4 8
2 4 15 4 8 1 0 11 2 Even Even 2 4
3 2 15 2 4 1 0 13 1 Even Even 1 2
4 1 15 1 2 1 0 14 1 2 2 2 2 7 Even Even 1 1
5 7 1 1 1 1 2 6 0 2 3 2 3 3 10 18 5 9
6 3 1 5 9 1 2 2 0 6 11 6 11 1 14 26 7 13
7 1 1 7 13 1 2 0
(7)(15) - (13)(8) = 1