Subtraction of two numbers using 2's Complement

Subtraction of two numbers using 2’s Complement

Difficulty Level : Hard
Last Updated : 13 Apr, 2021

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 Compliment 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“. 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

Method 2: Basic Approach or Brute Force Approach

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

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

Step-2: Add 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 substract
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 Compliment
    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 Compliment
        // 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 represnt
        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 substract
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 Compliment
    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 Compliment
        // 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 represnt
        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

C#

// C# code for above approach
using System;
 
class GFG{
     
// Program to substract
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 Compliment
    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 Compliment
        // 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 represnt
        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

Output

-00101

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