C 2s Complement

The 2s complement in C is generated from the 1s complement in C. As we know that the 1s complement of a binary number is created by transforming bit 1 to 0 and 0 to 1; the 2s complement of a binary number is generated by adding one to the 1s complement of a binary number.

In short, we can say that the 2s complement in C is defined as the sum of the one's complement in C and one.

In the above figure, the binary number is equal to 00010100, and its one's complement is calculated by transforming the bit 1 to 0 and 0 to 1 vice versa. Therefore, one's complement becomes 11101011. After calculating one's complement, we calculate the two's complement by adding 1 to the one's complement, and its result is 11101100.

Let's create a program of 2s complement.

#include <stdio.h>
int main()
{
   int n;  // variable declaration
   printf("Enter the number of bits do you want to enter :");
   scanf("%d",&n);
   char binary[n+1];  // binary array declaration; 
   char onescomplement[n+1]; // onescomplement array declaration 
   char twoscomplement[n+1]; // twoscomplement array declaration
   int carry=1; // variable initialization
   printf("\nEnter the binary number : ");
   scanf("%s", binary);
   printf("%s", binary);
   printf("\nThe ones complement of the binary number is :");
   
   // Finding onescomplement in C
   for(int i=0;i<n;i++)
   {
       if(binary[i]=='0')
       onescomplement[i]='1';
       else if(binary[i]=='1')
       onescomplement[i]='0';
   }
   onescomplement[n]='\0';
   printf("%s",onescomplement);
  

printf("\nThe twos complement of a binary number is : ");

// Finding twoscomplement in C
for(int i=n-1; i>=0; i--)
    {
        if(onescomplement[i] == '1' && carry == 1)
        {
            twoscomplement[i] = '0';
        }
        else if(onescomplement[i] == '0' && carry == 1)
        {
            twoscomplement[i] = '1';
            carry = 0;
        }
        else
        {
            twoscomplement[i] = onescomplement[i];
        }
    }
twoscomplement[n]='\0';
printf("%s",twoscomplement);
return 0;
}

Output

Analysis of the above program,

• First, we input the number of bits, and it gets stored in the 'n' variable.
• After entering the number of bits, we declare character array, i.e., char binary[n+1], which holds the binary number. The 'n' is the number of bits which we entered in the previous step; it basically defines the size of the array.
• We declare two more arrays, i.e., onescomplement[n+1], and twoscomplement[n+1]. The onescomplement[n+1] array holds the ones complement of a binary number while the twoscomplement[n+1] array holds the two's complement of a binary number.
• Initialize the carry variable and assign 1 value to this variable.
• After declarations, we input the binary number.
• Now, we simply calculate the one's complement of a binary number. To do this, we create a loop that iterates throughout the binary array, for(int i=0;i<n;i++). In for loop, the condition is checked whether the bit is 1 or 0. If the bit is 1 then onescomplement[i]=0 else onescomplement[i]=1. In this way, one's complement of a binary number is generated.
• After calculating one's complement, we generate the 2s complement of a binary number. To do this, we create a loop that iterates from the last element to the starting element. In for loop, we have three conditions:
  • If the bit of onescomplement[i] is 1 and the value of carry is 1 then we put 0 in twocomplement[i].
  • If the bit of onescomplement[i] is 0 and the value of carry is 1 then we put 1 in twoscomplement[i] and 0 in carry.
  • If the above two conditions are false, then onescomplement[i] is equal to twoscomplement[i].