# Check if a number N starts with 1 in b-base

Given a number N and base b if N in base b representation starts with 1 print Yes else print No
Examples :

```Input : n = 6, b = 4
Output : Yes
6 can be written as in base 4
so answer is Yes as it starts with 1

Input : n = 24, b = 2
Output : Yes
24 can be written as in base 2
so answer is Yes as it starts with 1

Input :  n = 24, b = 7
Output : No
24 can be written as in base 7
so answer is No as it starts with 3
```

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

When a number N is represented in base ‘b’ it gets converted to m+1 length sequence  ….. which implies * + * …..+ * = N
The smallest number in base b and starting with ‘1’ i.e. 100..00 and m+1 digits in base is and largest number is 2* -1.So N should lie in this range. <= N <= 2* -1
Now another thing to notice is that m cannot exceed floor( (N)) because when we represent any number in base-2 it gets converted into a sequence of only 1s and 0s so the length of this sequence will always be greater than any other base representation and its length will be equal to floor( (N))+1.
So to check for a given base 'b' if N starts with 1 or not we will traverse from m = 1 to m = floor( (N)) and check if for any m N lies in the range <= N <= 2* -1 or not and accordingly print "Yes" or "No".

## C++

 `// C++ program to check if number starts with ` `// one in base b representation ` `#include ` `using` `namespace` `std; ` ` `  `// Returns true if n starts with  1 in ` `// base b represenation ` `bool` `CheckIfstartsWithOne(``int` `n, ``int` `b) ` `{ ` `    ``// highest m can be log2(n) ` `    ``int` `m = log2(n); ` `    ``for` `(``int` `i = 1; i <= m; i++) { ` `        ``// if b^m <= N <= 2*b^m - 1, ` `        ``// return true ` `        ``if` `(n >= ``pow``(b, i) && n <= 2 * ``pow``(b, i) - 1) ` `            ``return` `true``; ` `    ``} ` `    ``return` `false``; ` `} ` ` `  `// printing yes or no ` `void` `printYesORno(``int` `n, ``int` `b) ` `{ ` `    ``if` `(CheckIfstartsWithOne(n, b) == ``true``) ` `        ``cout << ``"Yes"` `<< endl; ` `    ``else` `if` `(CheckIfstartsWithOne(n, b) == ``false``) ` `        ``cout << ``"No"` `<< endl; ` `} ` ` `  `// driver function ` `int` `main() ` `{ ` `    ``printYesORno(6, 4); ` `    ``printYesORno(24, 2); ` `    ``printYesORno(24, 7); ` `    ``printYesORno(24, 15); ` `} `

## Java

 `// Java program to check if number starts with ` `// one in base b representation ` ` `  `class` `GFG { ` `     `  `    ``// Returns true if n starts with 1 in ` `    ``// base b represenation ` `    ``static` `boolean` `CheckIfstartsWithOne(``int` `n, ``int` `b) ` `    ``{ ` `         `  `        ``// highest m can be log2(n) ` `        ``int` `m = (``int``)(Math.log10(n) / Math.log10(``2``)); ` `        ``for` `(``int` `i = ``1``; i <= m; i++) { ` `             `  `            ``// if b^m <= N <= 2*b^m - 1, ` `            ``// return true ` `            ``if` `(n >= (``int``)Math.pow(b, i) && ` `                ``n <= ``2` `* (``int``)Math.pow(b, i) - ``1``) ` `                ``return` `true``; ` `        ``} ` `         `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Driver method ` `    ``public` `static` `void` `main(String args[]) ` `    ``{ ` `        ``System.out.println( ` `           ``CheckIfstartsWithOne(``6``, ``4``) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``System.out.println( ` `           ``CheckIfstartsWithOne(``24``, ``2``) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``System.out.println( ` `           ``CheckIfstartsWithOne(``24``, ``7``) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``System.out.println( ` `           ``CheckIfstartsWithOne(``24``, ``15``) ? ``"Yes"` `: ``"No"``); ` `    ``} ` `} `

## Python3

 `# Python3 program to check  ` `# if number starts with one ` `# in base b representation ` `import` `math ` ` `  `# Returns true if n  ` `# starts with 1 in  ` `# base b represenation ` `def` `CheckIfstartsWithOne(n, b): ` `     `  `    ``# highest m can be log2(n) ` `    ``m ``=` `(``int``)(math.log2(n)); ` `    ``for` `i ``in` `range` `(``1``, m ``+` `1``): ` `         `  `        ``# if b^m <= N <= 2*b^m - 1, ` `        ``#return true ` `        ``x ``=` `(``int``)(math.``pow``(b, i)); ` `        ``if` `n >``=` `x ``and` `n <``=` `2` `*` `x ``-` `1``: ` `            ``return` `1``; ` `    ``return` `0``; ` ` `  `# printing yes or no ` `def` `printYesORno(n, b): ` `    ``if` `CheckIfstartsWithOne(n, b) ``=``=` `1``: ` `        ``print``(``"Yes"``); ` `    ``if` `CheckIfstartsWithOne(n, b) ``=``=` `0``: ` `        ``print``(``"No"``); ` `         `  `# Driver Code ` `printYesORno(``6``, ``4``); ` `printYesORno(``24``, ``2``); ` `printYesORno(``24``, ``7``); ` `printYesORno(``24``, ``15``); ` ` `  `# This code is contributed by mits. `

## C#

 `// C# program to check if number starts ` `// with one in base b representation ` `using` `System; ` ` `  `public` `class` `GFG { ` `     `  `    ``// Returns true if n starts with ` `    ``// 1 in base b represenation ` `    ``static` `bool` `CheckIfstartsWithOne(``int` `n, ``int` `b) ` `    ``{ ` `         `  `        ``// highest m can be log2(n) ` `        ``int` `m = (``int``)(Math.Log10(n) / Math.Log10(2)); ` `         `  `        ``for` `(``int` `i = 1; i <= m; i++) ` `        ``{ ` `             `  `            ``// if b^m <= N <= 2*b^m - 1, ` `            ``// return true ` `            ``if` `(n >= (``int``)Math.Pow(b, i) &&  ` `                   ``n <= 2 * (``int``)Math.Pow(b, i) - 1) ` `                ``return` `true``; ` `        ``} ` `         `  `        ``return` `false``; ` `    ``} ` ` `  `    ``// Driver method ` `    ``public` `static` `void` `Main() ` `    ``{ ` `        ``Console.WriteLine( ` `           ``CheckIfstartsWithOne(6, 4) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``Console.WriteLine( ` `           ``CheckIfstartsWithOne(24, 2) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``Console.WriteLine( ` `           ``CheckIfstartsWithOne(24, 7) ? ``"Yes"` `: ``"No"``); ` `            `  `        ``Console.WriteLine( ` `           ``CheckIfstartsWithOne(24, 15) ? ``"Yes"` `: ``"No"``); ` `    ``} ` `} ` ` `  `// This code is contributed by Sam007. `

## PHP

 `= pow(``\$b``, ``\$i``) &&  ` `                ``\$n` `<= 2 * pow(``\$b``, ``\$i``) - 1) ` `            ``return` `true; ` `    ``} ` `    ``return` `false; ` `} ` ` `  `// printing yes or no ` `function` `printYesORno(``\$n``, ``\$b``) ` `{ ` `    ``if` `(CheckIfstartsWithOne(``\$n``, ``\$b``) == true) ` `        ``echo` `"Yes"` `,``"\n"``; ` `    ``else` `if` `(CheckIfstartsWithOne(``\$n``, ``\$b``) == false) ` `        ``echo` `"No"` `,``"\n"``; ` `} ` ` `  `// Driver Code ` `printYesORno(6, 4); ` `printYesORno(24, 2); ` `printYesORno(24, 7); ` `printYesORno(24, 15); ` ` `  `// This code is contributed by ajit  ` `?> `

Output :

```Yes
Yes
No
Yes
```

This article is contributed by Ayush Jha. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up

Improved By : Sam007, jit_t, Mithun Kumar

Article Tags :
Practice Tags :

Be the First to upvote.

Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.