GrayCodeExample.txt
GrayCode flips only one bit with each increment or decrement.
The Base2Sum and GraySum is the number of 1's in GrayCode.
If n is the number of bits, there are n! combinations or reorderings.
ReOrdering the Gray bits reorders the classifications.

Bits = 6
Base10	Base2		GrayCode	GraySum == Number of 1's in GrayCode
0		000000		000000		0
1		000001		000001		1
2		000010		000011		2
3		000011		000010		1
4		000100		000110		2
5		000101		000111		3
6		000110		000101		2
7		000111		000100		1
8		001000		001100		2
9		001001		001101		3
10		001010		001111		4
11		001011		001110		3
12		001100		001010		2
13		001101		001011		3
14		001110		001001		2
15		001111		001000		1
16		010000		011000		2
17		010001		011001		3
18		010010		011011		4
19		010011		011010		3
20		010100		011110		4
21		010101		011111		5
22		010110		011101		4
23		010111		011100		3
24		011000		010100		2
25		011001		010101		3
26		011010		010111		4
27		011011		010110		3
28		011100		010010		2
29		011101		010011		3
30		011110		010001		2
31		011111		010000		1
32		100000		110000		2
33		100001		110001		3
34		100010		110011		4
35		100011		110010		3
36		100100		110110		4
37		100101		110111		5
38		100110		110101		4
39		100111		110100		3
40		101000		111100		4
41		101001		111101		5
42		101010		111111		6
43		101011		111110		5
44		101100		111010		4
45		101101		111011		5
46		101110		111001		4
47		101111		111000		3
48		110000		101000		2
49		110001		101001		3
50		110010		101011		4
51		110011		101010		3
52		110100		101110		4
53		110101		101111		5
54		110110		101101		4
55		110111		101100		3
56		111000		100100		2
57		111001		100101		3
58		111010		100111		4
59		111011		100110		3
60		111100		100010		2
61		111101		100011		3
62		111110		100001		2
63		111111		100000		1

GrayCodeExample.txt