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(5, 13) :

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 5 13 1 0 0 1
1 5 13 1 0 0 1 8 1 1 1 1 1 4 14 6 7 3
2 4 5 7 3 1 0 1 2 20 8 10 4
3 2 5 10 4 1 0 3 1 Even Even 5 2
4 1 5 5 2 1 0 4 1 6 2 6 2 2 Even Even 3 1
5 2 1 3 1 5 2 1 1 16 6 8 3
6 1 1 8 3 5 2 0
7 1 1 8 3 5 2 0
(8)(5) - (3)(13) = 1