Bitwise Operators: Given a binary number, return the 1’s and 2’s complement of that number

Before getting into programming, we shall look at how to get 1’s and 2’s complement of a given binary number.

1’s Complement:

1’s complement of a number is achieved by flipping all the bits.

Example:

Original value			1’s Complement
	0			1
	1			0
	1100			0011
	1111			0000

2’s complement:

We get the 2’s complement, by adding 1 to the 1’s complement of the binary number.

2’s complement = 1’s complement + 1;

2’s complement is particularly important because, it is used to represent signed (-ve) numbers in binary. Positive number are stored as it is, but negative number will be stored in 2’s complement.

Example:

Original Value			1’s complement		2’s complement

10011001			01100110 	+1	 = 01100111	

Ok, now coming back to our question:

To get the 1’s complement, we flip the bits.

To get 2’c complement, flip all 1’s to 0 till me encounter first 0, then flip that 0 to 1.

Example:
Binary number is 1100

Then, 1’s complement is 0011

For 2’s complement:
Step 1: flip all the 1’s to 0 as: “0000”
Step 2: then flip first occurrence of 0 to 1 as “0100” gives us 2’s complement.
Note: The first occurrence of 0 is in the index 3 of 1’s complement.

C++ program:

#include<iostream>
#include<vector>
#include<string>

using namespace std;

char flip(char c)
{
	if(c == '0')
		return '1';
	else
		return '0';
}

void get_ones_twos_complement(string str)
{
	int len = str.size();

	string ones ;
	string twos ;

	for(int i = 0; i <len; i++ )
	{
		ones += flip(str[i]);
	}
	cout << "1's complement: " << ones << endl; 

	twos = ones;
	int i = 0;
	for ( i = len - 1; i > 0; i--)
	{
		if(ones[i] == '1')
			twos[i] = '0';
		else
		{
			twos[i] = '1';
			break;
		}

	}

	// This case is used to handle situations like "1111"
	// we add extra "1" on the left side
	if (i == -1)
		twos = '1'+twos;
	cout << "2's complement: " << twos << endl; 

}

int main()
{
	string binary = "1100";
	cout<<"Original binary number = "<<binary<<endl;
	get_ones_twos_complement(binary);

	return 0;
}

Output:

Original binary number = 1100
1's complement: 0011
2's complement: 0100