Question

****************IN C PROGRAMMING****************

Sometimes even the smallest change in data can make a big difference. Luckily, there are algorithms that will let us not only detect when there has been an error(like checksums), but also correct when an error has occurred. These algorithms are called error-correcting codes.There are many examples of error correcting codes but one of the simplest examples is called a parity bit. A parity bit is just a single bit (1 or 0) that indicates whether a set of values has an even number of 1s (then the bit would be set to 0), or an odd number of 1s (then the bit would be set to 1).If you have a row of 1s and 0s, you can detect whether a single bit has been changed by checking the parity bit. But this won’t tell you anything about where the error is positioned.

Consider the following array of bits:

1 0 1 0 1 0 1 1

The parity bit of this array would be 1, since there are an odd number of 1s. If a single bit changed, the parity bit would be 0 (since a 1 was either added or removed).If you have a grid of 1s and 0s, you can detect whether a single bit has been changed by checking the parity bit of each row and each column. If you find a row that’s been changed and a column that’s been changed, then you know that the bit that was changed was at the intersection of that row and column. If a single bit changed, then you would be able to find the wrong bit, based on the wrong parity bits.

For this assignment you are going to calculate the parity for a 2D matirx of bits. As example:

This is a 3 by 4 matirx.

1 0 1 0    parity = 0 since there is an even number of 1's

1 0 1 1    parity = 1 since there is an odd number of 1's

1 1 1 1    parity = 0 since there is an even numnber of 1's

----------

1 1 1 0   is the parity of the above columns of rows

Your program should output the following:

Columns of Rows Parity: 1 1 1 0
Rows of Columns Parity: 0 1 0

Answer 1

According to given specifications, following C program is developed.

Source code:

Filename: parity.c

#include<stdio.h>

int main()
{
   int bits[10][10];
   int rows, cols;

   printf("\nEnter number of rows and columns of bit-grid: ");
   scanf("%d", &rows);
   scanf("%d", &cols);

   printf("\nEnter bits...\n");

   int i, j;
   for(i=0; i<rows; i++)
   {
   for(j=0; j<cols; j++)
   {
   scanf("%d", &bits[i][j]);
   }
   }

   int rows_parity[rows];
   int cols_parity[cols];

   // Process all rows and store parity of each row in rows_parity array
   for(i=0; i<rows; i++)
   {
       int count_one = 0;
       for(j=0; j<cols; j++)
       {
       if(bits[i][j]==1)
           count_one++;
       }

       if(count_one%2==0)
           rows_parity[i] = 0;
       else
           rows_parity[i] = 1;
   }

   // Process all columns and store parity of each column in cols_parity array
   for(j=0; j<cols; j++)
   {
       int count_one = 0;
       for(i=0; i<rows; i++)
       {

       if(bits[i][j]==1)
           count_one++;

       }

       if(count_one%2==0)
           cols_parity[j] = 0;
       else
           cols_parity[j] = 1;
   }

   printf("\nColumns Parity: ");
   for(i=0; i<cols; i++)
   {
       printf("%d ", cols_parity[i]);
   }

   printf("\nRows Parity: ");
   for(i=0; i<rows; i++)
   {
       printf("%d ", rows_parity[i]);
   }

   printf("\n");
   return 0;
}

Output screenshot