# Check whether all the bits are unset in the given range

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. The bits are numbered from right to left, i.e., the least significant bit is considered to be at first position.
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 = 39, l = 4, r = 6
Output : No
(39)10 = (100111)2
The bits in the range 4 to 6 are all not unset.
```

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 ` `bool` `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 could only have one or more ` `    ``// set bits in the range l to r and nowhere else ` `    ``int` `new_num = n & num; ` ` `  `    ``// if true, then all bits are unset ` `    ``// in the given range ` `    ``if` `(new_num == 0) ` `        ``return` `true``; ` ` `  `    ``// else all bits are not unset ` `    ``// in the given range ` `    ``return` `false``; ` `} ` ` `  `// Driver program to test above ` `int` `main() ` `{ ` `    ``unsigned ``int` `n = 17; ` `    ``unsigned ``int` `l = 2, r = 4; ` `    ``if` `(allBitsSetInTheGivenRange(n, l, r)) ` `        ``cout << ``"Yes"``; ` `    ``else` `        ``cout << ``"No"``; ` `    ``return` `0; ` `} `

## Java

 `// Java implementation to check  ` `// whether all the bits are  ` `// unset in the given range or not ` `class` `GFG ` `{ ` `     `  `// function to check whether  ` `// all the bits are unset in ` `// the given range or not ` `static` `boolean` `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 could only  ` `    ``// have one or more set bits in ` `    ``// the range l to r and nowhere else ` `    ``int` `new_num = n & num; ` ` `  `    ``// if true, then all bits are  ` `    ``// unset in the given range ` `    ``if` `(new_num == ``0``) ` `        ``return` `true``; ` ` `  `    ``// else all bits are not  ` `    ``// unset in the given range ` `    ``return` `false``; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `main(String[] args) ` `{ ` `    ``int` `n = ``17``; ` `    ``int` `l = ``2``, r = ``4``; ` `    ``if` `(allBitsSetInTheGivenRange(n, l, r)) ` `        ``System.out.println(``"Yes"``); ` `    ``else` `        ``System.out.println(``"No"``); ` `} ` `} ` ` `  `// This code is contributed ` `// by Smitha `

## Python3

 `# Python3 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 could only  ` `    ``# have one or more set bits in  ` `    ``# the range l to r and nowhere else ` `    ``new_num ``=` `n & num ` ` `  `    ``# if true, then all bits are  ` `    ``# unset in the given range ` `    ``if` `(new_num ``=``=` `0``): ` `        ``return` `True` ` `  `    ``# else all bits are not  ` `    ``# unset in the given range ` `    ``return` `false ` ` `  `# Driver Code ` `n ``=` `17` `l ``=` `2` `r ``=` `4` `if` `(allBitsSetInTheGivenRange(n, l, r)): ` `    ``print``(``"Yes"``) ` `else``: ` `    ``print``(``"No"``) ` ` `  `# This code is contributed  ` `# by Smitha `

## C#

 `// C# implementation to check  ` `// whether all the bits are  ` `// unset in the given range or not ` `using` `System; ` ` `  `class` `GFG ` `{ ` `     `  `// function to check whether  ` `// all the bits are unset in ` `// the given range or not ` `static` `bool` `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 could   ` `    ``// only have one or more  ` `    ``// set bits in the range  ` `    ``// l to r and nowhere else ` `    ``int` `new_num = n & num; ` ` `  `    ``// if true, then all  ` `    ``// bits are unset ` `    ``// in the given range ` `    ``if` `(new_num == 0) ` `        ``return` `true``; ` ` `  `    ``// else all bits are not  ` `    ``// unset in the given range ` `    ``return` `false``; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main() ` `{ ` `    ``int` `n = 17; ` `    ``int` `l = 2, r = 4; ` `    ``if` `(allBitsSetInTheGivenRange(n, l, r)) ` `        ``Console.Write(``"Yes"``); ` `    ``else` `        ``Console.Write(``"No"``); ` `} ` `} ` ` `  `// This code is contributed  ` `// by Smitha `

## PHP

 ` `

Output:

```Yes
```

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