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


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++

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#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;
}

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Java

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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

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Python3

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# 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))

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C#

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// 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

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PHP

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<?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
?>

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Output:

-1
2


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