Gray codes

The gray levels of an m-bit gray-scale image can be represented as an array a[m] of bits. Images can be stored as collections of binary images called bitplanes.

An alternative approach is to represent the image by an m-bit Gray code. The gray code g[m] can be computed from:

   int n = m-1;
   g[n] = a[n];
   while (n--) g[n] = a[n] ^ a[n+1];

Gray code examples

4-bit codes

The following table enumerates a 4-bit set of gray levels and the corresponding Gray codes. Both decimal (n, k) and base-2 representations are given. Gray codes have the unique feature that successive code words differ in only one bit position.

   n binary   gray   k
   0   0000   0000   0
   1   0001   0001   1
   2   0010   0011   3
   3   0011   0010   2
   4   0100   0110   6
   5   0101   0111   7
   6   0110   0101   5
   7   0111   0100   4
   8   1000   1100  12
   9   1001   1101  13
  10   1010   1111  15
  11   1011   1110  14
  12   1100   1010  10
  13   1101   1011  11
  14   1110   1001   9
  15   1111   1000   8

Gray codes are often used in angular encoder wheels, because the one-bit change per transition applies even to the transition from 15 to 0 (wraparound).

Shown below are encoder wheels where bit-planes are encoded in annular rings, The maximum angular frequency of the Gray code is half that of the binary code.