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.

1. #include <stdio.h>  
2. int main()  
3. {  
4.    int n;  // variable declaration  
5.    printf("Enter the number of bits do you want to enter :");  
6.    scanf("%d",&n);  
7.    char binary[n+1];  // binary array declaration;   
8.    char onescomplement[n+1]; // onescomplement array declaration   
9.    char twoscomplement[n+1]; // twoscomplement array declaration  
10.    int carry=1; // variable initialization  
11.    printf("\nEnter the binary number : ");  
12.    scanf("%s", binary);  
13.    printf("%s", binary);  
14.    printf("\nThe ones complement of the binary number is :");  
15.      
16.    // Finding onescomplement in C  
17.    for(int i=0;i<n;i++)  
18.    {  
19.        if(binary[i]=='0')  
20.        onescomplement[i]='1';  
21.        else if(binary[i]=='1')  
22.        onescomplement[i]='0';  
23.    }  
24.    onescomplement[n]='\0';  
25.    printf("%s",onescomplement);  
26.     
27.   
28. printf("\nThe twos complement of a binary number is : ");  
29.   
30. // Finding twoscomplement in C  
31. for(int i=n-1; i>=0; i--)  
32.     {  
33.         if(onescomplement[i] == '1' && carry == 1)  
34.         {  
35.             twoscomplement[i] = '0';  
36.         }  
37.         else if(onescomplement[i] == '0' && carry == 1)  
38.         {  
39.             twoscomplement[i] = '1';  
40.             carry = 0;  
41.         }  
42.         else  
43.         {  
44.             twoscomplement[i] = onescomplement[i];  
45.         }  
46.     }  
47. twoscomplement[n]='\0';  
48. printf("%s",twoscomplement);  
49. return 0;  
50. }  

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].