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Find total Number of bits required to represent a number in binary in C++

Here, we will learn to find the number of required bits to represent a number using C++ program.
Submitted by Hritik Raj, on June 24, 2018 [Last updated : February 28, 2023]

Problem statement

Find total Number of bits required to represent a number in binary

Example 1:

    input : 10
    output: 4

Example 2:

    input  : 32
    output : 6

Explanation:

input       Binary representation          count of bits
10               1010                        4
32              100000                       6

Finding the total Number of bits required to represent a number in binary

We can count required number of bits to represent a number using many ways; here we are using Bit manipulation technique to do the same.

We will right shift ( >> ) a number by one place in each iteration until we get zero as result. And, total count of right shift ( >> ) operation will be our result.

Example

Let Number = 45 ( 101101 in binary)

shifting 45 to right by 1 place
45 >> 1 = ( 101101 ) >> 1 = ( 10110 ) =  22 in decimal

so n= 22  ( 10110 in binary )
Again shifting 22 to right by 1 place
22 >> 1 = ( 10110 ) >> 1 = ( 1011 ) =  11  in decimal

now n= 11
Again shifting 11 to right by 1 place
11 >> 1 = ( 1011 ) >> 1 = ( 101 ) = 5 in decimal

now n= 5
Again shifting 5 to right by 1 place
5 >> 1 = ( 101 ) >> 1 = ( 10 ) = 2 in decimal

now n=2
Again shifting 2 to right by 1 place
2 >> 1 = ( 10 ) >> 1 = ( 1 ) = 1 in decimal

now n=1
Again shifting 1 to right by 1 place
1 >> 1 = ( 1 ) >> 1 = ( 0 )= 0 in decimal

Here we got n=0
So we will stop.

As u can see we have used total 6 right shift operation ( >> ) to get 0, so 6 will be required number of minimum bits to represent a number in binary.

C++ code to find total Number of bits required to represent a number in binary

#include<bits/stdc++.h>
using namespace std;

int countBits(int n)
{
	int count=0;
	// While loop will run until we get n = 0
	while(n)
	{
		count++;
		// We are shifting n to right by 1 
		// place as explained above
		n=n>>1;
	}
	return count;
}


int main()
{
	int n;
	cout << "Enter any Number\n";
	cin >> n;
	int count=countBits(n);
	cout << "Number of bits : " << count ;
	return 0;
}

Output

Enter any Number
45
Number of bits : 6
Process returned 0 (0x0)   execution time : 1.721 s
Press any key to continue.