# Round to next smaller multiple of 8

Given an unsigned integer x. Round it down to the next smaller multiple of 8 using bitwise operations only.

**Examples:**

Input : 35 Output : 32 Input : 40 Output : 40 As 40 is already a multiple of 8. So, no modification is done.

**Solution 1:** A naive approach to solve this problem using arithmetic operators is :

Let x be the number then,

x = x – (x % 8)

This will round down x to the next smaller multiple of 8. But we are not allowed to use arithmetic operators.

**Solution 2:** An efficient approach to solve this problem using bitwise AND operation is: x = x & (-8)

This will round down x to the next smaller multiple of 8. The idea is based on the fact that last three bits in a multiple of 8 must be 0,

Below is the implementation of above idea:

## C++

`// CPP program to find next smaller ` `// multiple of 8. ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `int` `RoundDown(` `int` `& a) ` `{ ` ` ` `return` `a & (-8); ` `} ` ` ` `int` `main() ` `{ ` ` ` `int` `x = 39; ` ` ` `cout << RoundDown(x); ` ` ` `return` `0; ` `} ` |

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## Java

`//Java program to find next smaller ` `// multiple of 8. ` ` ` `import` `java.io.*; ` ` ` `class` `GFG { ` `static` `int` `RoundDown(` `int` `a) ` `{ ` ` ` `return` `a & (-` `8` `); ` `} ` ` ` ` ` `public` `static` `void` `main (String[] args) { ` ` ` ` ` `int` `x = ` `39` `; ` ` ` `System.out.println (RoundDown(x)); ` ` ` `} ` `} ` `//This Code is Contributed by ajit ` |

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## Python3

# Python 3 program to find next

# smaller multiple of 8.

def RoundDown(a):

return a & (-8)

# Driver Code

if __name__ == ‘__main__’:

x = 39

print(RoundDown(x))

# This code is contributed

# by Surendra_Gangwar

## C#

`// C# program to find next smaller ` `// multiple of 8. ` `using` `System; ` ` ` `class` `GFG ` `{ ` `static` `int` `RoundDown(` `int` `a) ` `{ ` ` ` `return` `a & (-8); ` `} ` ` ` `public` `static` `void` `Main() ` `{ ` ` ` `int` `x = 39; ` ` ` `Console.Write(RoundDown(x)); ` `} ` `} ` ` ` `// This code is contributed ` `// by Akanksha Rai ` |

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## PHP

`<?php ` `// PHP program to find next smaller ` `// multiple of 8. ` ` ` `function` `RoundDown(` `$a` `) ` `{ ` ` ` `return` `(` `$a` `& (-8)); ` `} ` ` ` `// Driver Code ` `$x` `= 39; ` `echo` `RoundDown(` `$x` `); ` ` ` `// This code is contributed by jit_t ` `?> ` |

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**Output:**

32

**Time Complexity:** The time complexity of this approach is O(1)

**Space Complexity:** The space complexity of this approach is O(1)

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