Gray code of absolute encoder！

When the number of positions is not a power of 2 the property to change only
one bits is lost in the passage from the last value to the first and vice versa. For
example if we want to bring about an absolute encoder with 12 positions/turn,
the code should be like the one shown in the table on the side:
one notes that at the passage between the positions 11 and 0 the
contemporary state change of 3 bit can involve reading errors and this is, as
previously seen, not acceptable.
The Gray - excess - code is used not to loose the characteristics of the
commutation of only one bit, making correspond the 0 position to the Gray
code relative to the value N, where N is the number that, subtracted from the
Gray code converted into binary code, supplies the exact position value.
The calculation of N number is:

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