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.

**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. The same analogy holds for decrement. Note that this method works only if the numbers are stored in 2’s complement form. Like addition, Write a function Add() that returns sum of two integers. To subtract 1 from a number x (say 0011001000), flip all the bits after the rightmost 1 bit (we get 001100**1** 111). Finally, flip the rightmost 1 bit also (we get 0011000111) to get the answer. The function should not use any of the arithmetic operators (+, ++, –, -, … etc). Sum of two bits can be obtained by performing XOR (^) of the two bits. Carry bit can be obtained by performing AND (&) of two bits. We can extend this logic for integers. If x and y don’t have set bits at same position(s), then bitwise XOR (^) of x and y gives the sum of x and y. To incorporate common set bits also, bitwise AND (&) is used. Bitwise AND of x and y gives all carry bits. We calculate (x & y) << 1 and add it to x ^ y to get the required result. The idea is to use subtractor logic. Write a program to subtract one from a given number. The idea is to use bitwise operators. Like addition, Write a function Add() that returns sum of two integers. The function should not use any of the arithmetic operators (+, ++, –, -, … etc). Sum of two bits can be obtained by performing XOR (^) of the two bits. Carry bit can be obtained by performing AND (&) of two bits. We can extend this logic for integers. If x and y don’t have set bits at same position(s), then bitwise XOR (^) of x and y gives the sum of x and y. To incorporate common set bits also, bitwise AND (&) is used. Bitwise AND of x and y gives all carry bits. We calculate (x & y) << 1 and add it to x ^ y to get the required result. The idea is to use subtractor logic. The use of operators like ‘+’, ‘-‘, ‘*’, ‘/’, ‘++’, ‘–‘ …etc. are not allowed.

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.

`<?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);`

`?>`

**Output:**

14