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(6, 12) → Twos = 1 → Ext-GCD(3, 6) :

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