Algorithm Learning (6) converting----integer to Gray code

In the code of a group of numbers, if any two adjacent code is different from only one binary number, it is called the Gray Code, in addition, because the maximum number and the minimum number is only one digit difference, namely "end-to-end", so also called cyclic code or reflection code. In a digital system, code is often required to change in a certain order. For example, by increasing the number of natural numbers, if the number of 8421 yards, 0111 to 1000 when the four-bit changes, and in the actual circuit, 4-bit changes can not happen absolutely simultaneously, the count may appear in the short-term other code (1100, 1111, etc.). In certain cases, the circuit status error or input error may be caused. This error can be avoided by using gray code. Gray code is available in a variety of coding formats.

Gray code is available in various formats

decimal Number	4-bit natural binary code	4-bit typical gray code	Decimal Yusangre Code	decimal Empty six gray code	decimal Jump six gray code	Stepper 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	----	----	----	----

The typical gray code in the table is representative. If not specifically stated, Gray code refers to the typical gray code, which can be converted from the natural binary code. Conversion method Recursive generation Code table This method is based on the fact that Gray code is a reflection code, using the following rules of recursion to construct:

1. 1-bit gray code has two code words
Li class= "list-num-1-2 list-num-paddingleft-1" > (n+1) bit gray code in the former 2 n code word equals n-bit gray code word, sequentially written, prefixed 0
2. (n+1) Bit gray code in the rear 2n code word equals n-bit gray code word, written in reverse order, prefix 1
3. n+1 set of Gray code = n-Bit gray code set (sequential) plus prefix 0 + N-bit gray code set (reverse order) plus prefix 1

2-bit gray code	3-bit gray code	4-bit gray code	4-bit natural binary code
00011110	000001011010110111101100	0000000100110010011001110101010011001101111111101010101110011000	0000000100100011010001010110011110001001101010111100110111101111

XOR conversion binary code → Gray Code (Code): This method from the corresponding n-bit binary code word directly obtained n-bit gray code word, the steps are as follows:

1. Code word for n-bit binary, from right to left, numbered 0 to N-1
2. If the first and i+1 bits of the binary code word are the same, the corresponding gray code of the first bit is 0, otherwise 1 (when i+1=n, the nth bit of the binary word is considered 0, that is, the n-1 bit is unchanged)

The formula means: (G: Gray code, B: binary code)

For example: Binary code 0101, is 4 digits, so its conversion to the Gray code must also be 4 digits, it is advisable to turn into a binary code fifth bit 0, that is, 0 B3 B2 B1 b0. 0 XOR 0=0, so g3=00 xor 1=1, so g2=11 xor 0=1, so g1=10 xor 1=1, so G0=1 converted to a gray code of 0111

In fact, from the above Gray code xor or conversion method can be obtained a simple and easy algorithm, for example, for a 2 binary bit not more than 32 bits of the integer x, its gray code can be expressed as (x>>1) ^x.

Algorithm Demo:

#include <stdio.h>#include<stdlib.h>voidPrint_bin (unsignedintValueChar*tail);//print bit bit of a numberintMainintargcChar*argv[]) {unsignedinttemp;  for(unsignedintI=0; i<= the; i++) {printf ("%-4d:", i); Temp= (i>>1) ^i;//Conversion code is just one line, very simplePrint_bin (temp,"\ n"); }    return 0;}voidPrint_bin (unsignedintValueChar*tail) {     for(intI= to; i>=0; i--) {printf ("%d", (Value>>i) &1); }    if(tail) {printf ("%s", tail); }}

Compile run Result:

[Email protected]:~/documents/code$GCCTest.c-std=c99-o test.out[email protected]:~/documents/code$./Test.out0:000000000000000000000000000000001:000000000000000000000000000000012:000000000000000000000000000000113:000000000000000000000000000000104:000000000000000000000000000001105:000000000000000000000000000001116:000000000000000000000000000001017:000000000000000000000000000001008:000000000000000000000000000011009:00000000000000000000000000001101Ten:00000000000000000000000000001111 One:00000000000000000000000000001110 A:00000000000000000000000000001010 -:00000000000000000000000000001011 -:00000000000000000000000000001001 the:00000000000000000000000000001000

Algorithm Learning (6) converting----integer to Gray code