Definition: Greycode (Gray Code)
An ordering of 2n binary numbers such that only one bit changes from one entry to the next.

Note:
Gray codes are useful in mechanical encoders since a slight change in location only affects one bit. Using a typical binary code, up to n bits could change, and slight misalignments between reading elements could cause wildly incorrect readings.
One Gray code for 3 bits is (000, 010, 011, 001, 101, 111, 110, 100). An n-bit Gray code corresponds to a Hamiltonian cycle on an n-dimensional hypercube. Note: Gray codes are not unique.
One way to construct a Gray code for n bits is to take a Gray code for n-1 bits with each code prefixed by 0 (for the first half of the code) and append the n-1 Gray code reversed with each code prefixed by 1 (for the second half).Here is an example of creating a 3-bit Gray code from a 2-bit Gray code:00 01 11 10 A Gray code for 2 bits
000 001 011 010 the 2-bit code with a zero prefix
10 11 01 00 the 2-bit code reversed
110 111 101 100 the reversed code with a one prefix
000 001 011 010 110 111 101 100 A Gray code for 3 bits (see NIST for more information)