C++ Program to Convert Binary Number to Decimal

Introduction

The problems related to converting a number in one number system to another are very common in programming. They are asked from university exams to even in the coding rounds of various companies.

The key to easily solving such problems is to understand the number system in which the number is represented. In this article, we are going to discuss the conversion from binary to decimal. We would be given a number in the binary system, and we would be required to convert it into a decimal. For example, 101 in binary corresponds to 5 in decimal.

Let's quickly recap what a binary number and a decimal number are.

What is Binary Number?

The binary number system is made up of two different numerals, zero and one. All numbers can be represented using 0 and 1. In fact, our computer only understands binary numbers. They have a base of 2. We will see what this base means later on in the article.

This article assumes that the readers are aware of what a binary number is. We shall see how to convert it to a decimal number.

What is Decimal numbers?

These are the numbers which we generally use, like 6, 9875, 123, etc. They have a base of 10. The decimal numbers consist of numerals from 0 to 9.

The logic for Converting Binary Numbers to Decimal

Before we move on to discuss the code implementation of converting a binary number into a decimal number, let us first discuss the logic that we shall use in the code while converting binary to decimal.

We start from the least significant bit (LSB), i.e., from the right-hand side of the binary number, and travel towards the most significant bit (MSB), i.e., towards the left.
The position of the rightmost bit is considered zero, and every time we move towards the left, the position is increased by 1.
For every bit (the value is either 0 or 1), we multiply that bit with 2 raised to the power of the position of that bit and add it to the result.
We multiply it with the power of 2 because the base of the binary number is 2.

Consider the below image to understand it in a better way.

We have a binary number 101001. In order to convert it into decimal, we start with the rightmost bit. Here the rightmost bit is 1 at position 0. Therefore the result at this level is 1 X 2⁰ = 1. For the second bit, the result is 0. We simply have to sum up the result at every step. The sum gives us the decimal number.

C++ Program to Convert Binary Number to Decimal

Input: A binary number consisting of only 0s and 1s.

Expected output: The decimal form of the binary number provided in the input.

Code

// C++ program to convert binary number to Decimal


#include <iostream>
#include<cmath>
using namespace std;


// this function receives a number in binary form 
// and returns the corresponding value in decimal form


int binaryToDecimal(int num){
    
    int temp= num;
    
    // position variable to keep track of the position of the bits
    // from right to left, position increases from 0, 1, 2,...,n
    int position=0;
    
    // result variable stores the sum after every bit is multiplied
    // by the 2 raised to the power of the position of the corresponding bit
    int result=0;
    
    while(temp>0){
        
        // this will give the rightmost digit
        // e.g. 36748%10 will give 8.
        int rightMostBit = temp%10;
        
        
        result += rightMostBit * pow(2, position);
        
        // increment position as we travel from right to left
        position++;
        
        // this will remove the rightmost digit
        // e.g. 36748/10 = 3674
        temp= temp/10;
    }
    
    // return the calculated result
    return result;
}


// main function where the code is tested
int main()
{
    int num;
    cout<<"Enter the Binary Number.\n";
    cin>>num;
    
    
    int temp= binaryToDecimal(num);
    
    cout<<"The Decimal form of the given binary number is : "<< temp;


    return 0;
}

You can also try this code with Online C++ Compiler

Run Code

Input

101001

Output

Enter the Binary Number.

101001

The Decimal form of the given binary number is : 41

You can also practice with the help of Online C++ Compiler

Time Complexity

The time complexity of the above code is O(n), where n is the number of digits in the input binary number. This is because the loop runs for n times, for every digit of the binary number given.

Space Complexity

The space complexity of the above code is O(1) because there is no extra space used in the code.

If The Input is In The Form of String

Since the value passed in the binaryToDecimal() function is an integer we cannot provide a very large value of the binary number to the function. Consider an example where we have, say, 25 bits in a binary number. An integer type variable cannot store it. The best way is to take such a number in string format as input and do computation and accordingly convert it to decimal.

Code

// C++ program to convert binary string to Decimal
#include <iostream>
#include <string>
#include <cmath>
using namespace std;


// this function receives a string in binary form 
// and returns the corresponding integer value in decimal form
int binaryToDecimal(string binNum){
    string num = binNum;
    
    // position variable to keep track of the position of the bits
    // from right to left, position increases from 0, 1, 2,...,n
    int position = 0;
    
    int result=0;
    
    // length() determines the length of the given string
    int len = num.length();
    for(int i= len-1; i>=0;i--){
        // whenever we encounter 1, we can simply add power of 2 raised to the position 
        // for 0 the multiplication with power of 2 will be zero
        if(num[i]=='1'){
            result+= pow(2,position);
        }
        
        // increment the position variable
        position++;
    }
    
    // return the result
    return result;
}


int main() {
    
    string binaryNum;
    cout<<"Enter the binary number.\n";
    cin>>binaryNum;
    
    int decimal = binaryToDecimal(binaryNum);
    
    cout<<"The decimal form is : "<<decimal;
    
    return 0;
}

You can also try this code with Online C++ Compiler

Run Code

Input

101001

Output

Enter the binary number.

101001

The decimal form is : 41

Time Complexity

The time complexity of the above code is O(n), where n is the number of characters in the input string of the binary number. It is because the for-loop runs for the number of times equal to the number of characters in the input string.

Space Complexity

The space complexity of the above code is O(1) because there is no extra space used in the code.

Alternate Way to convert Binary to decimal in C++

Instead of using pow(2, position), we can use a base variable that will be multiplied by 2 after every iteration.

Code

// C++ program to convert binary string to Decimal 
// without using pow() function
#include <iostream>
#include <string>
using namespace std;


// this function receives a string in binary form 
// and returns the corresponding integer value in decimal form
int binaryToDecimal(string binNum){
    string num = binNum;
    
    // this represents the rightmost position.
    // observe that we have assigned base=1 and not 0
    // because at position =0 
    // pow(2,0)=1
    int base= 1;
    
    int result=0;
    
    // length() determines the length of the given string
    int len = num.length();
    for(int i= len-1; i>=0;i--){
        // whenever we encounter 1, we can simply the value of base variable
        if(num[i]=='1'){
            result+= base;
        }
        
        // multiply base by 2 after every iteration
        base= base *2;
    }
    
    // return the result
    return result;
}


int main() {
    
    string binaryNum;
    cout<<"Enter the binary number.\n";
    cin>>binaryNum;
    
    int decimal = binaryToDecimal(binaryNum);
    
    cout<<"The decimal form is : "<<decimal;
    
    return 0;
}

You can also try this code with Online C++ Compiler

Run Code

Input

111100010100000011111

Output

Enter the binary number.

111100010100000011111

The decimal form is : 1976351

Time Complexity

Space Complexity

The space complexity of the above code is O(1) because there is no extra space used in the code.

Also check out this article - Pair in C++

Using Predefined Function

We can use the stoi() function in C++ to convert a binary number given as a string into a decimal number.

Code

// using stoi() in C++ to convert binary to decimal
#include <iostream>
using namespace std;


int main() {
    
    string binNum;
    cout<<"Enter a binary number.\n";
    cin>> binNum;
    
    // C++ stoi() convert binary string to decimal  
    int decimal = stoi(binNum, 0, 2);
    
    cout<<"The decimal form is : "<<decimal;
    
    return 0;
}

You can also try this code with Online C++ Compiler

Run Code

Input

1001001110

Output

Enter a binary number.

1001001110

The decimal form is : 590

Time Complexity

The time complexity of the stoi() function is O(n), where n is the number of characters in the input string of the binary number.

Space Complexity

The space complexity of the above code is O(1) because there is no extra space used in the code.

Must read decimal to binary c++ and Application of Oops

Frequently Asked Questions

What is a binary number?

The binary number system is made up of two different numerals, zero and one. All numbers can be represented using 0 and 1.

What is the base of binary numbers?

The base of binary numbers is 2.

What is a decimal number?

These are the numbers which we generally use like 6, 9875, 123, etc. They have a base of 10. The decimal numbers consist of numerals from 0 to 9.

What will be the value of 1101101010 in the decimal system?

874

Conclusion

In this article, we have discussed what binary numbers are and the C++ program to convert binary numbers to decimal numbers. You should definitely read this blog to get a more clear understanding of number systems.

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