Add 1 to a given number

Write a program to add one to a given number. The use of operators like ‘+’, ‘-‘, ‘*’, ‘/’, ‘++’, ‘–‘ …etc are not allowed.
Examples:

Input:  12
Output: 13

Input:  6
Output: 7

This question can be approached by using some bit magic. Following are different methods to achieve the same using bitwise operators.

Method 1
To add 1 to a number x (say 0011000111), flip all the bits after the rightmost 0 bit (we get 0011000000). Finally, flip the rightmost 0 bit also (we get 0011001000) to get the answer.

C

// C++ code to add add
// one to a given number 
#include <stdio.h>

int addOne(int x)
{
    int m = 1;
    
    // Flip all the set bits 
    // until we find a 0 
    while( x & m )
    {
        x = x ^ m;
        m <<= 1;
    }
    
    // flip the rightmost 0 bit 
    x = x ^ m;
    return x;
}

/* Driver program to test above functions*/
int main()
{
    printf("%d", addOne(13));
    getchar();
    return 0;
}

Java

// Java code to add add
// one to a given number 
class GFG {

    static int addOne(int x)
    {
        int m = 1;
        
        // Flip all the set bits 
        // until we find a 0 
        while( (int)(x & m) == 1)
        {
            x = x ^ m;
            m <<= 1;
        }
    
        // flip the rightmost 0 bit 
        x = x ^ m;
        return x;
    }
    
    /* Driver program to test above functions*/
    public static void main(String[] args)
    {
        System.out.println(addOne(13));
    }
}

// This code is contributed by prerna saini.

Python3

# Python3 code to add 1
# one to a given number 
def addOne(x) :
    
    m = 1;
    # Flip all the set bits
    # until we find a 0 
    while(x & m):
        x = x ^ m
        m <<= 1
    
    # flip the rightmost 
    # 0 bit 
    x = x ^ m
    return x

# Driver program
n = 13
print addOne(n)

# This code is contributed by Prerna Saini.

C#

// C# code to add one
// to a given number 
using System;

class GFG {

    static int addOne(int x)
    {
        int m = 1;
        
        // Flip all the set bits 
        // until we find a 0 
        while( (int)(x & m) == 1)
        {
            x = x ^ m;
            m <<= 1;
        }
    
        // flip the rightmost 0 bit 
        x = x ^ m;
        return x;
    }
    
    // Driver code
    public static void Main()
    {
        Console.WriteLine(addOne(13));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP code to add add
// one to a given number 


function addOne($x)
{
    $m = 1;
    
    // Flip all the set bits 
    // until we find a 0 
    while( $x & $m )
    {
        $x = $x ^ $m;
        $m <<= 1;
    }
    
    // flip the rightmost 0 bit 
    $x = $x ^ $m;
    return $x;
}

// Driver Code
echo addOne(13);

// This code is contributed by vt_m.
?>


Output:

14

Method 2
We know that the negative number is represented in 2’s complement form on most of the architectures. We have the following lemma hold for 2’s complement representation of signed numbers.



Say, x is numerical value of a number, then

~x = -(x+1) [ ~ is for bitwise complement ]

(x + 1) is due to addition of 1 in 2’s complement conversion

To get (x + 1) apply negation once again. So, the final expression becomes (-(~x)).

C

#include<stdio.h>

int addOne(int x)
{
   return (-(~x));
}

/* Driver program to test above functions*/
int main()
{
  printf("%d", addOne(13));
  getchar();
  return 0;
}

Java

// Java code to Add 1 to a given number
class GFG
{
    static int addOne(int x)
    {
         return (-(~x));
    }
    
    // Driver program
    public static void main(String[] args)
    {
        System.out.printf("%d", addOne(13));
    }
}

// This code is contributed 
// by Smitha Dinesh Semwal

Python3

# Python3 code to add 1 to a given number

def addOne(x):
    return (-(~x));


# Driver program 
print(addOne(13))

# This code is contributed by Smitha Dinesh Semwal

C#

 // C# code to Add 1 
// to a given number
using System;

class GFG
{
    static int addOne(int x)
    {
        return (-(~x));
    }
    
    // Driver program
    public static void Main()
    {
        Console.WriteLine(addOne(13));
    }
}

// This code is contributed by vt_m.

PHP

<?php
// PHP Code to Add 1 
// to a given number

function addOne($x)
{
return (-(~$x));
}

// Driver Code
echo addOne(13);

// This code is contributed by vt_m.
?>


Output:

14

Example

Assume the machine word length is one *nibble* for simplicity.
And x = 2 (0010),
~x = ~2 = 1101 (13 numerical)
-~x = -1101

Interpreting bits 1101 in 2’s complement form yields numerical value as -(2^4 – 13) = -3. Applying ‘-‘ on the result leaves 3. Same analogy holds for decrement. See this comment for implementation of decrement.
Note that this method works only if the numbers are stored in 2’s complement form.

Thanks to Venki for suggesting this method.

Please write comments if you find the above code/algorithm incorrect, or find better ways to solve the same problem






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