What Is the Gray Code?

The typical binary Gray code (Binary Gray Code) is referred to as the Gray code. It was named after the "Pulse Code Communication" patent of Frank Gray (18870913-19690523) published in 1953. It was originally used for communication. -Digital conversion and position-Digital conversion in progress. French telecommunications engineer Jean-Maurice-Émile Baudot (18450911-19030328) used a baud code equivalent to a variant of it. An 8-element binary mechanical counter designed by George Stibitz in 1941 coincided with the counting law of Gray code counters.

In the encoding of a group of numbers, if any two adjacent codes have only one digit binary number, this encoding is called Gray Code, and because there is only one digit between the maximum and minimum numbers Different, that is, "end to end", so it is also called cyclic code or reflection code . ^[2]

Gray codes have multiple encoding forms

Decimal	4-bit natural binary code	4-digit typical Gray code	Decimal Remaining Gray Code	Decimal empty six gray code	Decimal Six Jump Gray Code	Step code
0	0000	0000	0010	0000	0000	00000
1	0001	0001	0110	0001	0001	00001
2	0010	0011	0111	0011	0011	00011
3	0011	0010	0101	0010	0010	00111
4	0100	0110	0100	0110	0110	01111
5	0101	0111	1100	1110	0111	11111
6	0110	0101	1101	1010	0101	11110
7	0111	0100	1111	1011	0100	11100
8	1000	1100	1110	1001	1100	11000
9	1001	1101	1010	1000	1000	10000
10	1010	1111	----	----	----	----
11	1011	1110	----	----	----	----
12	1100	1010	----	----	----	----
13	1101	1011	----	----	----	----
14	1110	1001	----	----	----	----
15	1111	1000	----	----	----	----

Typical Gray codes in the table are representative. Unless otherwise specified, Gray codes refer to typical Gray codes , which can be converted from natural binary codes.

• Gray code is a reliability code , which is a kind of error minimization

  The French engineer Jean-Maurice- & Eacute; mlle Baudot used the Baud code in 1880 as a variant of the typical Gray code. ^[3]

  According to the characteristics of Gray code, that is, for two adjacent decimal numbers, the corresponding two Gray codes differ only by one binary bit. In addition, there is only one binary bit difference between the maximum and minimum numbers. The following is a Gray code c implementation that uses a binary number of length n to represent the decimal number m. The running result is shown in the right figure:

   #include <stdio.h> voidmain () {intm, n, i, j, b, p, bound; intgr [14]; // Enter n, m and determine whether m is legal bound = 1; printf ("Pleaseinputtwonumber: n, m \ n "); scanf ("% d,% d ", & n, & m); for (i = 1; i <= n; i ++) bound * = 2; if (m <0 || m> = bound) {printf ("Dataerror!"); exit (0);} b = 1; for (i = 0; i <n; i ++) {p = 0; b * = 2; for (j = 0; j <= m; j ++) {if (j% bb / 2 == 0) p = 1-p;} gr [i] = p;} printf ("m ="); for (i = n-1; i> = 0; i--) {printf ("% d", gr [i]);} printf ("\ n");} 

  Pascal program for Gray code decoding:

    var
   x, y, i: longint;
   begin
   readln (x);
   fori: = 30downto0do
   begin
   y: = (xand (1shli)) xor ((xand (1shl (i + 1))) shr1);
   x: = xandnot (1shli) ory;
   end;
   writeln (x);
   end.
   2
   var
   x, i, n: longint;
   begin
   readln (n);
   x: = n;
   fori: = 1to31do
   begin
   x: = xshr1;
   n: = nxorx;
   end;
   writeln (n);
   end.