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(1, 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 1 13 1 0 0 1
1 1 13 1 0 0 1 12 1 1 1 1 1 6 14 2 7 1
2 6 1 7 1 1 0 5 3 20 2 10 1
3 3 1 10 1 1 0 2 0 11 1 11 1 1 24 2 12 1
4 1 1 12 1 1 0 0
5 1 1 12 1 1 0 0
6 1 1 12 1 1 0 0
7 1 1 1 0 12 1 0
(1)(1) - (0)(13) = 1