# Subtract 1 without arithmetic operators C

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 0011001111). 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