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Problem Definition:

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

Examples:

Input: 6

Solution:

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)).

Code:

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

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