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# Subtract two numbers without using arithmetic operators

• Difficulty Level : Hard
• Last Updated : 07 Aug, 2021

Write a function subtract(x, y) that returns x-y where x and y are integers. The function should not use any of the arithmetic operators (+, ++, –, -, .. etc).
The idea is to use bitwise operators. Addition of two numbers has been discussed using Bitwise operators. Like addition, the idea is to use subtractor logic.

The truth table for the half subtractor is given below.

```X     Y     Diff     Borrow
0     0     0     0
0     1     1     1
1     0     1     0
1     1     0     0```

From the above table one can draw the Karnaugh map for “difference” and “borrow”.
So, Logic equations are:

```    Diff   = y ⊕ x
Borrow = x' . y ```

Following is implementation based on above equations.

## C++

 `// C++ program to Subtract two numbers``// without using arithmetic operators``#include ``using` `namespace` `std;` `int` `subtract(``int` `x, ``int` `y)``{``    ``// Iterate till there``    ``// is no carry``    ``while` `(y != 0)``    ``{``        ``// borrow contains common``        ``// set bits of y and unset``        ``// bits of x``        ``int` `borrow = (~x) & y;` `        ``// Subtraction of bits of x``        ``// and y where at least one``        ``// of the bits is not set``        ``x = x ^ y;` `        ``// Borrow is shifted by one``        ``// so that subtracting it from``        ``// x gives the required sum``        ``y = borrow << 1;``    ``}``    ``return` `x;``}` `// Driver Code``int` `main()``{``    ``int` `x = 29, y = 13;``    ``cout << ``"x - y is "` `<< subtract(x, y);``    ``return` `0;``}` `// This code is contributed by shivanisinghss2110`

## C

 `// C program to Subtract two numbers``// without using arithmetic operators``#include` `int` `subtract(``int` `x, ``int` `y)``{``    ``// Iterate till there``    ``// is no carry``    ``while` `(y != 0)``    ``{``        ``// borrow contains common``        ``// set bits of y and unset``        ``// bits of x``        ``int` `borrow = (~x) & y;` `        ``// Subtraction of bits of x``        ``// and y where at least one``        ``// of the bits is not set``        ``x = x ^ y;` `        ``// Borrow is shifted by one``        ``// so that subtracting it from``        ``// x gives the required sum``        ``y = borrow << 1;``    ``}``    ``return` `x;``}` `// Driver Code``int` `main()``{``    ``int` `x = 29, y = 13;``    ``printf``(``"x - y is %d"``, subtract(x, y));``    ``return` `0;``}`

## Java

 `// Java Program to subtract two Number``// without using arithmetic operator``import` `java.io.*;` `class` `GFG``{``    ``static` `int` `subtract(``int` `x, ``int` `y)``    ``{``        ` `    ``// Iterate till there``    ``// is no carry``    ``while` `(y != ``0``)``    ``{``        ``// borrow contains common``        ``// set bits of y and unset``        ``// bits of x``        ``int` `borrow = (~x) & y;` `        ``// Subtraction of bits of x``        ``// and y where at least one``        ``// of the bits is not set``        ``x = x ^ y;` `        ``// Borrow is shifted by one``        ``// so that subtracting it from``        ``// x gives the required sum``        ``y = borrow << ``1``;``    ``}``    ` `    ``return` `x;``}``    ` `    ``// Driver Code``    ``public` `static` `void` `main (String[] args)``    ``{``        ``int` `x = ``29``, y = ``13``;``        ` `        ``System.out.println(``"x - y is "` `+``                        ``subtract(x, y));``    ``}``}` `// This code is contributed by vt_m`

## Python3

 `def` `subtract(x, y):` `    ``# Iterate till there``    ``# is no carry``    ``while` `(y !``=` `0``):``    ` `        ``# borrow contains common``        ``# set bits of y and unset``        ``# bits of x``        ``borrow ``=` `(~x) & y``        ` `        ``# Subtraction of bits of x``        ``# and y where at least one``        ``# of the bits is not set``        ``x ``=` `x ^ y` `        ``# Borrow is shifted by one``        ``# so that subtracting it from``        ``# x gives the required sum``        ``y ``=` `borrow << ``1``    ` `    ``return` `x`  `# Driver Code``x ``=` `29``y ``=` `13``print``(``"x - y is"``,subtract(x, y))` `# This code is contributed by``# Smitha Dinesh Semwal`

## C#

 `// C# Program to subtract two Number``// without using arithmetic operator``using` `System;` `class` `GFG {``    ` `    ``static` `int` `subtract(``int` `x, ``int` `y)``    ``{``        ` `        ``// Iterate till there``        ``// is no carry``        ``while` `(y != 0)``        ``{``            ` `            ``// borrow contains common``            ``// set bits of y and unset``            ``// bits of x``            ``int` `borrow = (~x) & y;``    ` `            ``// Subtraction of bits of x``            ``// and y where at least one``            ``// of the bits is not set``            ``x = x ^ y;``    ` `            ``// Borrow is shifted by one``            ``// so that subtracting it from``            ``// x gives the required sum``            ``y = borrow << 1;``        ``}``        ` `        ``return` `x;``    ``}``    ` `    ``// Driver Code``    ``public` `static` `void` `Main ()``    ``{``        ``int` `x = 29, y = 13;``        ` `        ``Console.WriteLine(``"x - y is "` `+``                        ``subtract(x, y));``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output :

`x - y is 16`

Following is recursive implementation for the same approach.

## C++

 `#include ``using` `namespace` `std;` `int` `subtract(``int` `x, ``int` `y)``{``    ``if` `(y == 0)``        ``return` `x;``    ``return` `subtract(x ^ y, (~x & y) << 1);``}` `// Driver program``int` `main()``{``    ``int` `x = 29, y = 13;``    ``cout << ``"x - y is "``<< subtract(x, y);``    ``return` `0;``}` `// this code is contributed by shivanisinghss2110`

## C

 `#include` `int` `subtract(``int` `x, ``int` `y)``{``    ``if` `(y == 0)``        ``return` `x;``    ``return` `subtract(x ^ y, (~x & y) << 1);``}` `// Driver program``int` `main()``{``    ``int` `x = 29, y = 13;``    ``printf``(``"x - y is %d"``, subtract(x, y));``    ``return` `0;``}`

## Java

 `// Java  Program to subtract two Number``// without using arithmetic operator``// Recursive implementation.``class` `GFG {` `    ``static` `int` `subtract(``int` `x, ``int` `y)``    ``{` `        ``if` `(y == ``0``)``            ``return` `x;` `        ``return` `subtract(x ^ y, (~x & y) << ``1``);``    ``}` `    ``// Driver program``    ``public` `static` `void` `main(String[] args)``    ``{``        ``int` `x = ``29``, y = ``13``;``        ``System.out.printf(``"x - y is %d"``,``                            ``subtract(x, y));``    ``}``}` `// This code is contributed by ``// Smitha Dinesh Semwal.`

## Python3

 `# Python  Program to``# subtract two Number``# without using arithmetic operator``# Recursive implementation.` `def` `subtract(x, y):` `    ``if` `(y ``=``=` `0``):``        ``return` `x``    ``return` `subtract(x ^ y, (~x & y) << ``1``)` `# Driver program``x ``=` `29``y ``=` `13``print``(``"x - y is"``, subtract(x, y))` `# This code is contributed by``# Smitha Dinesh Semwal`

## C#

 `// C# Program to subtract two Number``// without using arithmetic operator``// Recursive implementation.``using` `System;` `class` `GFG {` `    ``static` `int` `subtract(``int` `x, ``int` `y)``    ``{``        ``if` `(y == 0)``            ``return` `x;` `        ``return` `subtract(x ^ y, (~x & y) << 1);``    ``}` `    ``// Driver program``    ``public` `static` `void` `Main()``    ``{``        ``int` `x = 29, y = 13;``        ``Console.WriteLine(``"x - y is "``+``                            ``subtract(x, y));``    ``}``}` `// This code is contributed by anuj_67.`

## PHP

 ``

## Javascript

 ``

Output :

`x - y is 16`