Subtract two numbers without using arithmetic operators

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

Source: Wikipedia page for subtractor

Following is implementation based on above equations.

C

// C program to Subtract two numbers 
// without using arithmetic operators 
#include<stdio.h> 
  
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 arithetic operater 
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 arithetic operater 
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

<?php 
// PHP Program to subtract two Number 
// without using arithetic operater 
  
function 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; $y = 13; 
        echo "x - y is ", subtract($x,$y); 
  
// This code is contributed by Ajit 
?> 

Output :

x - y is 16

Following is recursive implementation for the same approach.

C

#include<stdio.h> 
  
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 arithetic operater 
// 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 arithetic operater 
// 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

<?php 
  
function subtract($x, $y) 
{ 
    if ($y == 0) 
        return $x; 
    return subtract($x ^ $y,  
                   (~$x & $y) << 1); 
} 
  
// Driver Code 
$x = 29; $y = 13; 
echo "x - y is ", subtract($x, $y); 
  
# This code is contributed by ajit  
?> 

Output :

x - y is 16

This article is contributed Dheeraj. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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