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

**Examples:**

Input: 12 Output: 11 Input: 6 Output: 5

**Method 1**

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.

- C

`// C code to subtract`

`// one from a given number`

`#include <stdio.h>`

`int`

`subtractOne(`

`int`

`x)`

`{`

` `

`int`

`m = 1;`

` `

`// Flip all the set bits`

` `

`// until we find a 1`

` `

`while`

`(!(x & m)) {`

` `

`x = x ^ m;`

` `

`m <<= 1;`

` `

`}`

` `

`// flip the rightmost 1 bit`

` `

`x = x ^ m;`

` `

`return`

`x;`

`}`

`/* Driver program to test above functions*/`

`int`

`main()`

`{`

` `

`printf`

`(`

`"%d"`

`, subtractOne(13));`

` `

`return`

`0;`

`}`

**Output:**

12

**Method 2 (If + is allowed)**

We know that the negative number is represented in 2’s complement form on most of the architectures. 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. 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 ]

Adding 2x on both the sides,

2x + ~x = x – 1

To obtain 2x, left shift x once.

`using`

`System;`

``

`class`

`GFG`

`{`

`` `static`

`int`

`subtractOne(`

`int`

`x)`

`` `{`

`` `return`

`((x << 1) + (~x));`

`` `}`

`` `/* Driver code*/`

`` `public`

`static`

`void`

`Main(String[] args)`

`` `{`

`` `Console.Write(`

`"{0}"`

`, subtractOne(13));`

`` `}`

`}`

**Output:**

12