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 Compliment of 5. Look at the image below:

Examples:

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

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

Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 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 
?> 