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  格雷码(Gray code),又叫循环二进制码或反射二进制码 在数字系统中只能识别0和1,各种数据要转换为二进制代码才能进行处理,格雷码是一种无权码,采用绝对编码方式,典型格雷码是一种具有反射特性和循环特性的单步自补码,它的循环、单步特性消除了随机取数时出现重大误差的可能,它的反射、自补特性使得求反非常方便。格雷码属于可靠性编码,是一种错误最小化的编码方式。

  因为,自然二进制码可以直接由数/模转换器转换成模拟信号,但某些情况,例如从十进制的3转换到4时二进制码的每一位都要变,使数字电路产生很大的尖峰电流脉冲。而格雷码则没有这一缺点,它是一种数字排序系统,其中的所有相邻整数在它们的数字表示中只有一个数字不同。它在任意两个相邻的数之间转换时,只有一个数位发生变化。它大大地减少了由一个状态到下一个状态时逻辑的混淆。另外由于最大数与最小数之间也仅一个数不同,故通常又叫格雷反射码或循环码。

 下表为几种自然二进制码与格雷码的对照表:

 
十进制数 自然二进制数 格雷码
0 0000 0000
1 0001 0001
2 0010 0011
3 0011 0010
4 0100 0110
5 0101 0111
6 0110 0101
7 0111 0100
8 1000 1100
9 1001 1101
10 1010 1111
11 1011 1110
12 1100 1010
13 1101 1011
14 1110 1001
15 1111 1000

一般的,普通二进制码与格雷码可以按以下方法互相转换:

  二进制码->格雷码(编码):从最右边一位起,依次将每一位与左边一位异或(XOR),作为对应格雷码该位的值,最左边一位不变(相当于左边是0);
  格雷码-〉二进制码(解码):从左边第二位起,将每位与左边一位解码后的值异或,作为该位解码后的值(最左边一位依然不变)。
View Code
 1 // Gray counter
 2 
 3 module gray_count
 4 (
 5     input clk, enable, reset,
 6     output reg [7:0] gray_count
 7 );
 8 
 9 // Implementation:
10 
11 // There's an imaginary bit in the counter, at q[-1], that resets to 1
12 // (unlike the rest of the bits of the counter) and flips every clock cycle.
13 // The decision of whether to flip any non-imaginary bit in the counter
14 // depends solely on the bits below it, down to the imaginary bit.    It flips
15 // only if all these bits, taken together, match the pattern 10* (a one
16 // followed by any number of zeros).
17 
18 // Almost every non-imaginary bit has a submodule instance that sets the
19 // bit based on the values of the lower-order bits, as described above.
20 // The rules have to differ slightly for the most significant bit or else 
21 // the counter would saturate at it's highest value, 1000...0.
22 
23     // q is the counter, plus the imaginary bit
24     reg q [7:-1];
25     
26     // no_ones_below[x] = 1 iff there are no 1's in q below q[x]
27     reg no_ones_below [7:-1];
28     
29     // q_msb is a modification to make the msb logic work
30     reg q_msb;
31     
32     integer i, j, k;
33     
34     always @ (posedge reset or posedge clk)
35     begin
36         if (reset)
37         begin
38         
39             // Resetting involves setting the imaginary bit to 1
40             q[-1] <= 1;
41             for (i = 0; i <= 7; i = i + 1)
42                 q[i] <= 0;
43                 
44         end
45         else if (enable)
46         begin
47             // Toggle the imaginary bit
48             q[-1] <= ~q[-1];
49             
50             for (i = 0; i < 7; i = i + 1)
51             begin
52                 
53                 // Flip q[i] if lower bits are a 1 followed by all 0's
54                 q[i] <= q[i] ^ (q[i-1] & no_ones_below[i-1]);
55             
56             end
57             
58             q[7] <= q[7] ^ (q_msb & no_ones_below[6]);
59         end
60     end
61     
62     
63     always @(*)
64     begin
65         
66         // There are never any 1's beneath the lowest bit
67         no_ones_below[-1] <= 1;
68         
69         for (j = 0; j < 7; j = j + 1)
70             no_ones_below[j] <= no_ones_below[j-1] & ~q[j-1];
71             
72         q_msb <= q[7] | q[6];
73         
74         // Copy over everything but the imaginary bit
75         for (k = 0; k < 8; k = k + 1)
76             gray_count[k] <= q[k];
77         end    
78         
79 endmodule

 

 

posted on 2012-10-05 15:12  sheller_liu  阅读(1882)  评论(0编辑  收藏  举报