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