# Python program to subtract two numbers without using arithmetic operators

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 implementation based on above equations.

`def` `subtract(x, y):`

` ` `# Iterate till there`

` ` `# is no carry`

` ` `while` `(y !` `=` `0` `):`

` `

` ` `# borrow contains common`

` ` `# set bits of y and unset`

` ` `# bits of x`

` ` `borrow ` `=` `(~x) & y`

` `

` ` `# Subtraction of bits of x`

` ` `# and y where at least one`

` ` `# of the bits is not set`

` ` `x ` `=` `x ^ y`

` ` `# Borrow is shifted by one`

` ` `# so that subtracting it from`

` ` `# x gives the required sum`

` ` `y ` `=` `borrow << ` `1`

` `

` ` `return` `x`

`# Driver Code`

`x ` `=` `29`

`y ` `=` `13`

`print` `(` `"x - y is"` `,subtract(x, y))`

Output :

x - y is 16