# C Program to subtract two Number without using arithetic operater Recursive implementation

Write a function subtract(x, y) that returns x-y where x and y are integers. The function should not use any of the arithmetic operators (+, ++, –, -, … etc).
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 truth table for the half subtractor is given below.

X Y Diff Borrow
0 0 0 0
0 1 1 1
1 0 1 0
1 1 0 0
From the above table one can draw the Karnaugh map for “difference” and “borrow”.
So, Logic equations are:

``````Diff   = y ⊕ x
Borrow = x' . y
``````

Following is recursive implementation for the same approach.

`#include<stdio.h>`

`int` `subtract(` `int` `x, ` `int` `y)`

`{`

` ` `if` `(y == 0)`

` ` `return` `x;`

` ` `return` `subtract(x ^ y, (~x & y) << 1);`

`}`

`// Driver program`

`int` `main()`

`{`

` ` `int` `x = 29, y = 13;`

` ` `printf` `(` `"x - y is %d"` `, subtract(x, y));`

` ` `return` `0;`

`}`

Output :

x - y is 16