# Check whether all the bits are unset in the given range or not

Given a non-negative number n and two values l and r. The problem is to check whether all the bits are unset or not in the range l to r in the binary representation of n.
Constraint: 1 <= l <= r <= number of bits in the binary representation of n.

Examples:

```Input : n = 17, l = 2, r = 4
Output : Yes
(17)10 = (10001)2
The bits in the range 2 to 4 are all unset.

Input : n = 36, l = 3, r = 5
Output : No
(36)10 = (100100)2
The bits in the range 3 to 5 are all not unset.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: Following are the steps:

1. Calculate num = ((1 << r) – 1) ^ ((1 << (l-1)) – 1). This will produce a number num having r number of bits and bits in the range l to r are the only set bits.
2. Calculate new_num = n & num.
3. If new_num == 0, return “Yes” (all bits are unset in the given range).
4. Else return “No” (all bits are not unset in the given range).

## C++

 `// C++ implementation to check whether all  ` `// the bits are unset in the given range  ` `// or not ` `#include ` `using` `namespace` `std; ` ` `  `// function to check whether all the bits ` `// are unset in the given range or not ` `string allBitsSetInTheGivenRange(unsigned ``int` `n, ` `                                ``unsigned ``int` `l,  ` `                                ``unsigned ``int` `r) ` `{ ` `    ``// calculating a number 'num' having 'r' ` `    ``// number of bits and bits in the range l ` `    ``// to r are the only set bits ` `    ``int` `num = ((1 << r) - 1) ^  ` `            ``((1 << (l - 1)) - 1); ` `     `  `    ``// new number which will only have  ` `    ``// one or more set bits in the range ` `    ``// l to r and nowhere else ` `    ``int` `new_num = n & num; ` `     `  `    ``// if new num is 0, then all bits  ` `    ``// are unset in the given range ` `    ``if` `(new_num == 0) ` `        ``return` `"Yes"``; ` `         `  `    ``// else all bits are not unset  ` `    ``return` `"No"``;  ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``unsigned ``int` `n = 17; ` `    ``unsigned ``int` `l = 2, r = 4; ` `    ``cout << allBitsSetInTheGivenRange(n, l, r); ` `    ``return` `0; ` `}  `

## Java

 `// Java implementation to  ` `// check whether all the ` `// bits are unset in the  ` `// given range or not ` `import` `java.io.*; ` ` `  `class` `GFG  ` `{ ` `     `  `// function to check whether  ` `// all the bits are unset in ` `// the given range or not ` `static` `String allBitsSetInTheGivenRange(``int` `n, ` `                                        ``int` `l,  ` `                                        ``int` `r) ` `{ ` `    ``// calculating a number 'num'  ` `    ``// having 'r' number of bits  ` `    ``// and bits in the range l to ` `    ``// r are the only set bits ` `    ``int` `num = ((``1` `<< r) - ``1``) ^  ` `              ``((``1` `<< (l - ``1``)) - ``1``); ` `     `  `    ``// new number which will  ` `    ``// only have one or more ` `    ``// set bits in the range ` `    ``// l to r and nowhere else ` `    ``int` `new_num = n & num; ` `     `  `    ``// if new num is 0, then  ` `    ``// all bits are unset in ` `    ``// the given range ` `    ``if``(new_num == ``0``) ` `        ``return` `"Yes"``; ` `         `  `    ``// else all bits ` `    ``// are not unset  ` `    ``return` `"No"``;  ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main (String[] args) ` `{ ` `    ``int` `n = ``17``; ` `    ``int` `l = ``2``; ` `    ``int` `r = ``4``; ` `    ``System.out.println( ` `           ``allBitsSetInTheGivenRange(n, l, r)); ` `} ` `} ` ` `  `// This code is contributed by akt_mit `

## Python 3

 `# Python 3 implementation to check whether   ` `# all the bits are unset in the given range  ` `# or not ` ` `  `# function to check whether all the bits ` `# are unset in the given range or not ` `def` `allBitsSetInTheGivenRange(n, l, r): ` ` `  `    ``# calculating a number 'num' having 'r' ` `    ``# number of bits and bits in the range l ` `    ``# to r are the only set bits ` `    ``num ``=` `((``1` `<< r) ``-` `1``) ^ ((``1` `<< (l ``-` `1``)) ``-` `1``) ` `     `  `    ``# new number which will only have  ` `    ``# one or more set bits in the  ` `    ``# range l to r and nowhere else ` `    ``new_num ``=` `n & num ` `     `  `    ``# if new num is 0, then all bits  ` `    ``# are unset in the given range ` `    ``if` `(new_num ``=``=` `0``): ` `        ``return` `"Yes"` `         `  `    ``# else all bits are not unset  ` `    ``return` `"No"` ` `  `# Driver Code ` `if` `__name__ ``=``=` `"__main__"``: ` `     `  `    ``n ``=` `17` `    ``l ``=` `2` `    ``r ``=` `4` `    ``print``(allBitsSetInTheGivenRange(n, l, r)) ` ` `  `# This code is contributed by ita_c `

## C#

 `// C#  implementation to  ` `// check whether all the  ` `// bits are unset in the  ` `// given range or not  ` `using` `System; ` ` `  `public` `class` `GFG{ ` `             `  `// function to check whether  ` `// all the bits are unset in  ` `// the given range or not  ` `static` `String allBitsSetInTheGivenRange(``int` `n,  ` `                                        ``int` `l,  ` `                                        ``int` `r)  ` `{  ` `    ``// calculating a number 'num'  ` `    ``// having 'r' number of bits  ` `    ``// and bits in the range l to  ` `    ``// r are the only set bits  ` `    ``int` `num = ((1 << r) - 1) ^  ` `            ``((1 << (l - 1)) - 1);  ` `     `  `    ``// new number which will  ` `    ``// only have one or more  ` `    ``// set bits in the range  ` `    ``// l to r and nowhere else  ` `    ``int` `new_num = n & num;  ` `     `  `    ``// if new num is 0, then  ` `    ``// all bits are unset in  ` `    ``// the given range  ` `    ``if``(new_num == 0)  ` `        ``return` `"Yes"``;  ` `         `  `    ``// else all bits  ` `    ``// are not unset  ` `    ``return` `"No"``;  ` `}  ` ` `  `// Driver Code  ` `    ``static` `public` `void` `Main (){ ` `        ``int` `n = 17;  ` `        ``int` `l = 2;  ` `        ``int` `r = 4;  ` `        ``Console.WriteLine(  ` `            ``allBitsSetInTheGivenRange(n, l, r));  ` `    ``}  ` `}  ` ` `  `// This code is contributed by k_mit `

## PHP

 ` `

Output:

```Yes
```

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Improved By : jit_t, Sach_Code, chitranayal

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