Given an integer x, write a function that multiplies x with 3.5 and returns the integer result. You are not allowed to use %, /, *.

**Examples :** Input: 2 Output: 7 Input: 5 Output: 17 (Ignore the digits after decimal point)

Solution:

**1.** We can get x*3.5 by adding 2*x, x and x/2. To calculate 2*x, left shift x by 1 and to calculate x/2, right shift x by 2. 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.

Below is the implementation of the above approach:

`// C++ program to multiply`

`// a number with 3.5`

`#include <bits/stdc++.h>`

`int`

`multiplyWith3Point5(`

`int`

`x)`

`{`

` `

`return`

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

`}`

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

`int`

`main()`

`{`

` `

`int`

`x = 4;`

` `

`printf`

`(`

`"%d"`

`, multiplyWith3Point5(x));`

` `

`getchar`

`();`

` `

`return`

`0;`

`}`

**Output**

14

**2.** Another way of doing this could be (8*x – x)/2 (See below code).

- C

`#include <stdio.h>`

`int`

`multiplyWith3Point5(`

`int`

`x)`

`{`

` `

`return`

`((x<<3) - x)>>1;`

`} `