Patent ID: 6970113
Filing Date: 2005-11-29
Classification: H03M

Abstract:
1. A method of producing a reduced Gray code in n-many bits of 2k-many entries for a natural number k, the method comprising the steps of: (a) reflecting a Gray code in (n−1)-many bits and whose r-many ordered entries are (a, b, c, . . . , i, j) to produce an intermediate cyclic code of 2r-many ordered entries that are (a, b, c, . . . , i, j, j, i, . . . c, b, a), r being greater than k and wherein ( . . . , b, a, a, b, . . . ) and ( . . . , i, j, j, i, . . . ) are entries representing symmetrically reversed sequences in the ordering of the entries; (b) appending a first bit value to a selected location in each of the ordered entries (a, b, c, . . . , j) in the first half of the intermediate code to produce entries that are of n-many bits, and appending the complement of the first bit value to the selected location in each of the ordered entries (j, . . . c, b, a) in the second half of the intermediate code to produce entries that are of n-many bits, the combined appended versions of the first and second halves of the intermediate code forming a cyclic reflected binary Gray code of 2r-many entries; and (c) symmetrically discarding from the cyclic reflected binary Gray code of 2r-many entries of step (b) 2(r-k)-many consecutive entries corresponding to a symmetrically reversed sequence, leaving a cyclic reduced Gray code of 2k-many entries in n-many bits.