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Hamming code example

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Hamming code example
PostPosted: Thu Jan 11, 2007 12:57 pm     Reply with quote

I was looking for an example yesterday on Hamming codes. I found this post:

It was really helpful. I modified the code a little, and thought I'd share the code (with formatting intact):


BYTE codeToData (BYTE code);
BYTE correctCode(BYTE code);
BYTE decode(BYTE code);
BYTE dataToCode(BYTE data);

/* struct for Hamming(8,4)
     Hamming codes from */
struct {
     int nData; // 4-bit data (0 to 15), bytes will be handled nibble-by-nibble
     BYTE nCode; // 7-bit Hamming code with extra parity bit.
HammingCodes[16] = {
     {0, 0b00000000},
     {1, 0b10000111},
     {2, 0b10011001},
     {3, 0b00011110},
     {4, 0b10101010},
     {5, 0b00101101},
     {6, 0b00110011},
     {7, 0b10110100},
     {8, 0b01001011},
     {9, 0b11001100},
     {10, 0b11010010},
     {11, 0b01010101},
     {12, 0b11100001},
     {13, 0b01100110},
     {14, 0b01111000},
     {15, 0b11111111}
/* end of Hamming(8,4) struct */

main() {
     /* testing hamming */
     BYTE test[3];
     BYTE result;
     test[0]=0b01001011; // correct - should return "8" as the decoded data
     test[1]=0b00001011; // single bit error
     test[2]=0b10001011;  // double bit error

     while(TRUE) {
          for(i=0;i<3;i++) {
               result = decode(test[i]);
               if(result!=0xFF) printf("Test number %x, Original: %x, Decoded data: %x\r\n",i,test[i],result);
               else printf("More than one error in data\r\n");
          delay_ms(4000); // 4000 was chosen arbitrarily
     /* end of testing hamming */

BYTE decode(BYTE code) {
     BYTE j;
     j = codeToData(code);
     if(j!=0xFF) return j; // the corresponding code was found
     else { // code wasn't found
          j = correctCode(code); // try to correct a single bit error
          if(j==0xFF) return 0xFF; // there was more than a single bit error
          else return codeToData(j); // fixed it!  Get the data and be done!

BYTE codeToData(BYTE code) {
     BYTE j;

     for (j = 0; j < 16; j++) {
          if (code == HammingCodes[j].nCode) {
               // Got it! Return the 4-bit data
               return j;
     // Not a code!
     return 0xFF;

BYTE correctCode(BYTE code) {
     BYTE n, j, mask;

     // Flip each bit and see if we can fix it!
     mask = 1;
     for (j=0;j<8;j++) {
          n = codeToData(code ^ mask);
          if (n != 0xFF) {
               // Corrected it!
               return code ^ mask;
          mask <<= 1;
     // More than single bit error - return 0xFF to signify inability to correct
     return 0xFF;

/* This function takes data (0-15) and converts it to a hamming code */
BYTE dataToCode(BYTE data) {
     if (data >= 0 && data < 16) {
          return HammingCodes[data].nCode;
     return 0xFF; // incorrect range of data passed as parameter

I did pluck it out of context in another program I tested it in, so hopefully I didn't break anything or forget something. Please let me know if that's the case.

It's really cool to see the code recover completely from a single-bit error, and detect a two-bit error.

There might be a more efficient way to do this - I'd be interested in seeing it if there is a much more efficient way.


Last edited by evsource on Thu Jan 11, 2007 2:46 pm; edited 1 time in total
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