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, 7) :

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 7 1 0 0 1
1 1 7 1 0 0 1 6 1 1 1 1 1 3 8 2 4 1
2 3 1 4 1 1 0 2 0 5 1 5 1 1 12 2 6 1
3 1 1 6 1 1 0 0
4 1 1 6 1 1 0 0
5 1 1 6 1 1 0 0
6 1 1 6 1 1 0 0
7 1 1 1 0 6 1 0
(1)(1) - (0)(7) = 1