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, 4) :

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 4 1 0 0 1
1 4 15 0 1 1 0 11 2 4 16 2 8
2 2 15 2 8 1 0 13 1 Even Even 1 4
3 1 15 1 4 1 0 14 1 2 4 2 4 7 Even Even 1 2
4 7 1 1 2 1 4 6 0 2 6 2 6 3 Even Even 1 3
5 3 1 1 3 1 4 2 0 2 7 2 7 1 6 22 3 11
6 1 1 3 11 1 4 0
7 1 1 3 11 1 4 0
(3)(15) - (11)(4) = 1