Subtraction of two numbers using 2’s Complement

Given two numbers a and b. The task is to subtract b from a by using 2’s Complement method.
Note: Negative numbers represented as 2’s Complement of Positive Numbers.
For example, -5 can be represented in binary form as 2’s Complement of 5. Look at the image below: 

Examples: 

Input : a = 2, b = 3
Output : -1

Input : a = 9, b = 7
Output : 2 

To subtract b from a. Write the expression (a-b) as:  

(a - b) = a + (-b)

Now (-b) can be written as (2’s complement of b). So the above expression can be now written as:  

(a - b) = a + (2's complement of b)

So, the problem now reduces to “Add a to the 2’s complement of b“. The below image illustrates the above method of subtraction for the first example where a = 2 and b = 3. 

Below is the implementation of the above method: 

C++

#include <bits/stdc++.h>
using namespace std;

// function to subtract two values
// using 2's complement method
int Subtract(int a, int b)
{
    int c;

    // ~b is the 1's Complement of b
    // adding 1 to it make it 2's Complement
    c = a + (~b + 1);

    return c;
}

// Driver code
int main()
{
    int a = 2, b = 3;

    cout << Subtract(a, b)<<endl;

    a = 9; b = 7;
    cout << Subtract(a, b);

    return 0;
}

Java

class GFG
{

// function to subtract two values
// using 2's complement method
static int Subtract(int a, int b)
{
    int c;

    // ~b is the 1's Complement
    // of b adding 1 to it make
    // it 2's Complement
    c = a + (~b + 1);

    return c;
}

// Driver code
public static void main(String[] args)
{
    int a = 2, b = 3;

    System.out.println(Subtract(a, b));

    a = 9; b = 7;
    System.out.println(Subtract(a, b));
}
}

// This code is contributed
// by ChitraNayal

Python3

# python3 program of subtraction of
# two numbers using 2's complement .

# function to subtract two values
# using 2's complement method
def Subtract(a,b):

    # ~b is the 1's Complement of b
    # adding 1 to it make it 2's Complement
    c = a + (~b + 1)
    return c

# Driver code
if __name__ == "__main__" :

    # multiple assignments
    a,b = 2,3
    print(Subtract(a,b))

    a,b = 9,7
    print(Subtract(a,b))

C#

// C# program of subtraction of
// two numbers using 2's complement
using System;

class GFG
{
// function to subtract two values
// using 2's complement method
static int Subtract(int a, int b)
{
    int c;

    // ~b is the 1's Complement
    // of b adding 1 to it make
    // it 2's Complement
    c = a + (~b + 1);

    return c;
}

// Driver code
static void Main()
{
    int a = 2, b = 3;

    Console.WriteLine(Subtract(a, b));

    a = 9; b = 7;
    Console.WriteLine(Subtract(a, b));
}
}

// This code is contributed
// by mits

PHP

<?php
// function to subtract two values
// using 2's complement method
function Subtract($a, $b)
{

    // ~b is the 1's Complement
    // of b adding 1 to it make
    // it 2's Complement
    $c = $a + (~$b + 1);

    return $c;
}

// Driver code
$a = 2;
$b = 3;

echo Subtract($a, $b) . "\n";

$a = 9;
$b = 7;
echo Subtract($a, $b) . "\n";

// This code is contributed
// by ChitraNayal
?>

Javascript

<script>

// Function to subtract two values
// using 2's complement method
function Subtract(a, b)
{
    var c;

    // ~b is the 1's Complement of b
    // adding 1 to it make it 2's Complement
    c = a + (~b + 1);

    return c;
}

// Driver code
var a = 2, b = 3;
document.write( Subtract(a, b) + "<br>");

a = 9; b = 7;
document.write( Subtract(a, b));

// This code is contributed by itsok

</script>

Output

-1
2

Time complexity – O(nlog2(n))
Auxiliary Space – O(1)

Method 2: Basic Approach or Brute Force Approach

Subtraction of two Binary Numbers, subtract two binary numbers using 2’s Complement method. 

Step-1: Find the 2’s complement of the subtrahend. 

Step-2: Add the first number and 2’s complement of the subtrahend. 

Step-3: If the carry is produced, discard the carry. If there is no carry then take the 2’s complement of the result. 

Below is the implementation of the above approach.

C++

//C++ code for above approach
#include<iostream>
#include<bits/stdc++.h>
using namespace std;

// Program to subtract
void Subtract(int n, int a[],
                       int b[])
{

    // 1's Complement
    for(int i = 0; i < n; i++)
    {

        //Replace 1 by 0
        if(b[i] == 1)
        {
            b[i] = 0;
        }

        //Replace 0 by 1
        else
        {
            b[i] = 1;
        }
    }

    //Add 1 at end to get 2's Complement
    for(int i = n - 1; i >= 0; i--)
    {
        if(b[i] == 0)
        {
            b[i] = 1;
            break;
        }
        else
        {
            b[i] = 0;
        }
    }

    // Represents carry
    int t = 0;
    for(int i = n - 1; i >= 0; i--)
    {

        // Add a, b and carry
        a[i] = a[i] + b[i] + t;

        // If a[i] is 2
        if(a[i] == 2)
        {
            a[i] = 0;
            t = 1;

        }

        // If a[i] is 3
        else if(a[i] == 3)
        {
            a[i] = 1;
            t = 1;
        }
        else
            t = 0;
    }

    cout << endl;

    // If carry is generated
    // discard the carry
    if(t==1)
    {

       // print the result
       for(int i = 0; i < n; i++)
       {

         // Print the result
         cout<<a[i];
       }
    }

    // if carry is not generated
    else
    {

        // Calculate 2's Complement
        // of the obtained result
        for(int i = 0; i < n; i++)
        {
            if(a[i] == 1)
                a[i] = 0;
            else
                a[i] = 1;
        }
        for(int i = n - 1; i >= 0; i--)
        {
            if(a[i] == 0)
            {
                a[i] = 1;
                break;
            }
        else
            a[i] = 0;
        }

        // Add -ve sign to represent
        cout << "-";

        // -ve result
        // Print the resultant array
        for(int i = 0; i < n; i++)
        {
            cout << a[i];
        }
    }
}

// Driver Code
int main()
{
    int n;
    n = 5;
    int a[] = {1, 0, 1, 0, 1},
        b[] = {1, 1, 0, 1, 0};

    Subtract(n,a,b);
    return 0;
}

Java

// Java code for above approach
import java.io.*;

class GFG{

// Program to subtract
static void Subtract(int n, int a[], int b[])
{

    // 1's Complement
    for(int i = 0; i < n; i++)
    {

        // Replace 1 by 0
        if (b[i] == 1)
        {
            b[i] = 0;
        }

        // Replace 0 by 1
        else
        {
            b[i] = 1;
        }
    }

    // Add 1 at end to get 2's Complement
    for(int i = n - 1; i >= 0; i--)
    {
        if (b[i] == 0)
        {
            b[i] = 1;
            break;
        }
        else
        {
            b[i] = 0;
        }
    }

    // Represents carry
    int t = 0;
    for(int i = n - 1; i >= 0; i--)
    {

        // Add a, b and carry
        a[i] = a[i] + b[i] + t;

        // If a[i] is 2
        if (a[i] == 2)
        {
            a[i] = 0;
            t = 1;
        }

        // If a[i] is 3
        else if (a[i] == 3)
        {
            a[i] = 1;
            t = 1;
        }
        else
            t = 0;
    }

    System.out.println();

    // If carry is generated
    // discard the carry
    if (t == 1)
    {

        // Print the result
        for(int i = 0; i < n; i++)
        {

            // Print the result
            System.out.print(a[i]);
        }
    }

    // If carry is not generated
    else
    {

        // Calculate 2's Complement
        // of the obtained result
        for(int i = 0; i < n; i++)
        {
            if (a[i] == 1)
                a[i] = 0;
            else
                a[i] = 1;
        }
        for(int i = n - 1; i >= 0; i--)
        {
            if (a[i] == 0)
            {
                a[i] = 1;
                break;
            }
        else
            a[i] = 0;
        }

        // Add -ve sign to represent
        System.out.print("-");

        // -ve result
        // Print the resultant array
        for(int i = 0; i < n; i++)
        {
            System.out.print(a[i]);
        }
    }
}

// Driver Code
public static void main (String[] args)
{
    int n;
    n = 5;
    int a[] = {1, 0, 1, 0, 1};
    int b[] = {1, 1, 0, 1, 0};

    Subtract(n, a, b);
}
}

// This code is contributed by avanitrachhadiya2155

Python3

# Python implementation of above approach

# Program to subtract
def Subtract(n, a, b):

    # 1's Complement
    for i in range(n):

        # Replace 1 by 0
        if (b[i] == 1):
            b[i] = 0

        # Replace 0 by 1
        else:
            b[i] = 1

    # Add 1 at end to get 2's Complement
    for i in range(n - 1, -1, -1):

        if (b[i] == 0):
            b[i] = 1
            break
        else:
            b[i] = 0

    # Represents carry
    t = 0
    for i in range(n - 1, -1, -1):

        # Add a, b and carry
        a[i] = a[i] + b[i] + t

        # If a[i] is 2
        if (a[i] == 2):
            a[i] = 0
            t = 1

        # If a[i] is 3
        elif (a[i] == 3):
            a[i] = 1
            t = 1
        else:
            t = 0

    print()

    # If carry is generated
    # discard the carry
    if (t == 1):

        # Print the result
        for i in range(n):

            # Print the result
            print(a[i],end="")

    # If carry is not generated
    else:

        # Calculate 2's Complement
        # of the obtained result
        for i in range(n):
            if (a[i] == 1):
                a[i] = 0
            else:
                a[i] = 1
        for i in range(n - 1, -1, -1):
            if (a[i] == 0):
                a[i] = 1
                break
            else:
                a[i] = 0

        # Add -ve sign to represent
        print("-",end="")

        # -ve result
        # Print the resultant array
        for i in range(n):
            print(a[i],end="")

# Driver Code
n = 5
a=[1, 0, 1, 0, 1]
b=[1, 1, 0, 1, 0]
Subtract(n, a, b)

# This code is contributed by shinjanpatra

C#

// C# code for above approach
using System;

class GFG{

// Program to subtract
static void Subtract(int n, int[] a, int[] b)
{

    // 1's Complement
    for(int i = 0; i < n; i++)
    {

        // Replace 1 by 0
        if (b[i] == 1)
        {
            b[i] = 0;
        }

        // Replace 0 by 1
        else
        {
            b[i] = 1;
        }
    }

    // Add 1 at end to get 2's Complement
    for(int i = n - 1; i >= 0; i--)
    {
        if (b[i] == 0)
        {
            b[i] = 1;
            break;
        }
        else
        {
            b[i] = 0;
        }
    }

    // Represents carry
    int t = 0;
    for(int i = n - 1; i >= 0; i--)
    {

        // Add a, b and carry
        a[i] = a[i] + b[i] + t;

        // If a[i] is 2
        if (a[i] == 2)
        {
            a[i] = 0;
            t = 1;
        }

        // If a[i] is 3
        else if (a[i] == 3)
        {
            a[i] = 1;
            t = 1;
        }
        else
            t = 0;
    }

    Console.WriteLine();

    // If carry is generated
    // discard the carry
    if (t == 1)
    {

        // Print the result
        for(int i = 0; i < n; i++)
        {

            // Print the result
            Console.Write(a[i]);
        }
    }

    // If carry is not generated
    else
    {

        // Calculate 2's Complement
        // of the obtained result
        for(int i = 0; i < n; i++)
        {
            if (a[i] == 1)
                a[i] = 0;
            else
                a[i] = 1;
        }
        for(int i = n - 1; i >= 0; i--)
        {
            if (a[i] == 0)
            {
                a[i] = 1;
                break;
            }
            else
                a[i] = 0;
        }

        // Add -ve sign to represent
        Console.Write("-");

        // -ve result
        // Print the resultant array
        for(int i = 0; i < n; i++)
        {
            Console.Write(a[i]);
        }
    }
}

// Driver Code
static public void Main()
{
    int n;
    n = 5;
    int[] a = {1, 0, 1, 0, 1};
    int[] b = {1, 1, 0, 1, 0};

    Subtract(n, a, b);
}
}

// This code is contributed by rag2127

Javascript

<script>
// Javascript code for above approach

    // Program to subtract
    function Subtract(n,a,b)
    {
        // 1's Complement
    for(let i = 0; i < n; i++)
    {

        // Replace 1 by 0
        if (b[i] == 1)
        {
            b[i] = 0;
        }

        // Replace 0 by 1
        else
        {
            b[i] = 1;
        }
    }

    // Add 1 at end to get 2's Complement
    for(let i = n - 1; i >= 0; i--)
    {
        if (b[i] == 0)
        {
            b[i] = 1;
            break;
        }
        else
        {
            b[i] = 0;
        }
    }

    // Represents carry
    let t = 0;
    for(let i = n - 1; i >= 0; i--)
    {

        // Add a, b and carry
        a[i] = a[i] + b[i] + t;

        // If a[i] is 2
        if (a[i] == 2)
        {
            a[i] = 0;
            t = 1;
        }

        // If a[i] is 3
        else if (a[i] == 3)
        {
            a[i] = 1;
            t = 1;
        }
        else
            t = 0;
    }

    document.write("<br>");

    // If carry is generated
    // discard the carry
    if (t == 1)
    {

        // Print the result
        for(let i = 0; i < n; i++)
        {

            // Print the result
            document.write(a[i]);
        }
    }

    // If carry is not generated
    else
    {

        // Calculate 2's Complement
        // of the obtained result
        for(let i = 0; i < n; i++)
        {
            if (a[i] == 1)
                a[i] = 0;
            else
                a[i] = 1;
        }
        for(let i = n - 1; i >= 0; i--)
        {
            if (a[i] == 0)
            {
                a[i] = 1;
                break;
            }
        else
            a[i] = 0;
        }

        // Add -ve sign to represent
        document.write("-");

        // -ve result
        // Print the resultant array
        for(let i = 0; i < n; i++)
        {
            document.write(a[i]);
        }
    }
    }

    // Driver Code
    let n = 5;
    let a=[1, 0, 1, 0, 1];
    let b=[1, 1, 0, 1, 0];
    Subtract(n, a, b);


// This code is contributed by patel2127
</script>

Output

-00101

Time complexity : O(N)

Auxiliary Space : O(1)