Add 1 to a given number | GeeksforGeeks

Write a program to add one to a given number. You are not allowed to use operators like ‘+’, ‘-’, ‘*’, ‘/’, ‘++’, ‘–’ …etc.
Method 1
To add 1 to a number x (say 0011000111), we need to flip all the bits after the rightmost 0 bit (we get 0011000000). Finally, flip the rightmost 0 bit also (we get 0011001000) and we are done.

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;

}

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.

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

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

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

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