Write a C program to read binary number from user and find twos complement of the binary number. How to find 2's complement of a binary number in C. Logic to find twos complement of a binary number in C program.

**Example**

**Input**

Input binary number: 01101110

**Output**

Twos complement: 10010010

## Required knowledge

Basic C programming, If else, For loop, String

Must know - Program to find ones complement

## What is twos complement?

Twos complement of an

-bit number is defined as the complement with respect to *N*`2`

. It is the result of subtracting the number from ^{N}`2`

, which in binary is one followed by ^{N}

zeroes.*N*

In simple words twos complement can be defined as sum of 1's complement of the binary number and 1.

## Logic to find twos complement

Below is the step by step descriptive logic to find twos complement of a binary string.

- Input a binary string from user. Store it in some variable say binary.
- Convert the binary string to ones complement. Store it in some variable say onesComp.
- Initialize another binary string variable to store twos complement, say twosComp = "".
- Initialize a variable to store carry bit during addition, say carry = 1. You may think now, why initialize carry to 1, why not 0? Since, we need to add only 1 to the binary string hence, I have initially assumed carry bit as the bit to be added.
- Run a loop from length of binary string to 1, decrementing 1 in each iteration. The loop structure should look like for(i=SIZE-1; i>=1; i--) (where SIZE is length of the binary string). You may think, why iterating in reverse order? Because addition is carried out in right to left order.
- Inside the loop there can be three cases:

**Case I:**If both current binary bit and carry bit are 1 then, put 0 to twos complement. Which is if(onesComp[i]=='1' && carry==1) then, twosComp[i] = '0', carry is still preserved to 1.

**Case II**: If current binary bit is 0 and carry bit is 1 then, put 1 to twos complement and set carry bit to 0. Which is if(onesComp[i]=='0' && carry==1) then, twosComp[i] = '1' and carry = 0.

**Case III:**If carry bit is 0, then assign the value of onesComp to twosComp.

## Program to find twos complement

```
/**
* C program to find 2's complement of a binary number
*/
#include <stdio.h>
#define SIZE 8
int main()
{
char binary[SIZE + 1], onesComp[SIZE + 1], twosComp[SIZE + 1];
int i, carry=1;
printf("Enter %d bit binary value: ", SIZE);
// Read 8-bit binary string
gets(binary);
/*
* Finds the 1's complement of the binary number
*/
for(i=0; i<SIZE; i++)
{
if(binary[i] == '1')
{
onesComp[i] = '0';
}
else if(binary[i] == '0')
{
onesComp[i] = '1';
}
}
onesComp[SIZE] = '\0';
/*
* Add 1 to the 1's complement
*/
for(i=SIZE-1; i>=0; i--)
{
if(onesComp[i] == '1' && carry == 1)
{
twosComp[i] = '0';
}
else if(onesComp[i] == '0' && carry == 1)
{
twosComp[i] = '1';
carry = 0;
}
else
{
twosComp[i] = onesComp[i];
}
}
twosComp[SIZE] = '\0';
printf("Original binary = %s\n", binary);
printf("Ones complement = %s\n", onesComp);
printf("Twos complement = %s\n", twosComp);
return 0;
}
```

Output

Enter 8 bit binary value: 01101100 Original binary = 01101100 Ones complement = 10010011 Twos complement = 10010100

Happy coding 😉

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