# 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 the above method:

## C++

 `#include ` `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)<

## 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

 ` `

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++

 `//CPP code for above approach ` `#include ` `#include ` `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<= 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; ` `}`

Output

`-00101`

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