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(13, 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 13 4 1 0 0 1
1 4 13 0 1 1 0 9 2 4 14 2 7
2 2 13 2 7 1 0 11 1 6 20 3 10
3 1 13 3 10 1 0 12 1 4 10 4 10 6 Even Even 2 5
4 6 1 2 5 3 10 5 3 6 18 3 9
5 3 1 3 9 3 10 2 0 6 19 2 6 1 Even Even 1 3
6 1 1 1 3 3 10 0
7 1 1 1 3 3 10 0
(1)(13) - (3)(4) = 1