Find most significant bit of a number X in base Y

20 Apr, 2021
Given two positive integers X and Y, the task is to find the MSB of X, in the given base Y.Examples:
Input: X = 55, Y = 3 Output: 2 Explanation: 55 is 2001 in base 3 with first digit as 2.Input: X = 123, Y = 10 Output: 1 Explanation: 123 is 123 in base 10 with first digit 1. 
Approach: Let the task to find 1st digit of X = 1234 in base Y = 10, So to get First digit = 1:  
Divide 1234 by 1000 = X / 103 = X / 10Number of Digits in X – 1 = X / 10log(X) / log(10) (which is for base 10)  
For any other base, we can replace 10 with Y. Therefore, we can calculate the first digit of a number X in base Y by using the formula:
X / Y(log(X)/log(Y))
Below is the implementation of the above approach:  
C++
Java
Python3
C#
Javascript
// C++ Program to find the// first digit of X in base Y #include <bits/stdc++.h>using namespace std; // Function to find the first// digit of X in base Yvoid first_digit(int x, int y){    // calculating number of digits of    // x in base y    int length = log(x) / log(y) + 1;     // finding first digit of x in base y    int first_digit = x / pow(y, length - 1);     cout << first_digit;} // Driver codeint main(){    int X = 55, Y = 3;     first_digit(X, Y);     return 0;}
// Java Program to find the// first digit of X in base Yimport java.util.*;class GFG{ // Function to find the first// digit of X in base Ystatic void first_digit(int x, int y){    // calculating number of digits of    // x in base y    int length = (int)(Math.log(x) /                       Math.log(y) + 1);     // finding first digit of x in base y    int first_digit = (int)(x / Math.pow(y,                                length - 1));     System.out.println(first_digit);} // Driver codepublic static void main(String args[]){    int X = 55, Y = 3;     first_digit(X, Y);}} // This code is contributed by AbhiThakur
# Python3 program to find the# first digit of X in base Yimport math # Function to find the first# digit of X in base Ydef first_digit(x, y):         # Calculating number of digits of    # x in base y    length = int (math.log(x) /                  math.log(y) + 1)         # Finding first digit of x in base y    first_digit = x / math.pow(y, length - 1)     print(int(first_digit))     # Driver codeX = 55Y = 3 first_digit(X, Y) # This code is contributed by ishayadav181
// C# Program to find the// first digit of X in base Yusing System;class GFG{ // Function to find the first// digit of X in base Ystatic void first_digit(int x, int y){    // calculating number of digits of    // x in base y    int length = (int)(Math.Log(x) /                       Math.Log(y) + 1);     // finding first digit of x in base y    int first_digit = (int)(x / Math.Pow(y,                                length - 1));     Console.Write(first_digit);} // Driver codepublic static void Main(){    int X = 55, Y = 3;     first_digit(X, Y);}} // This code is contributed by Akanksha_Rai
<script> // Javascript Program to find the// first digit of X in base Y // Function to find the first// digit of X in base Yfunction first_digit(x, y){    // calculating number of digits of    // x in base y    var length = parseInt(Math.log(x) / Math.log(y)) + 1;     // finding first digit of x in base y    var first_digit = parseInt(x / Math.pow(y, length - 1));     document.write( first_digit);} // Driver codevar X = 55, Y = 3;first_digit(X, Y); </script>
2
 
Time Complexity: O(1)
Auxiliary Space: O(1)
ishayadav181
abhaysingh290895
Akanksha_Rai
rishavmahato348
rrrtnx
base-conversion
maths-log
maths-power
Mathematical
Mathematical
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