Problem

Given a binary number as input, we need to write a program to convert the given binary number into equivalent decimal number.

Examples :

Input : 111
Output : 7

Input : 1010
Output : 10

Input: 100001
Output: 33

Solution

The idea is to extract the digits of given binary number starting from right most digit and keep a variable dec_value. At the time of extracting digits from the binary number, multiply the digit with the proper base (Power of 2) and add it to the variable dec_value. At the end, the variable dec_value will store the required decimal number.

For Example:
If the binary number is 111.
dec_value = 1*(2^2) + 1*(2^1) + 1*(2^0) = 7

Below diagram explains how to convert ( 1010 ) to equivalent decimal value:
binary2decimal

Approach:

public int binaryToDecimal(int n) {
        int num = n; 
        int dec_value = 0; 
  
        // Initializing base 
        // value to 1, i.e 2^0 
        int base = 1; 
  
        int temp = num; 
        while (temp > 0) { 
            int last_digit = temp % 10; 
            temp = temp / 10; 
  
            dec_value += last_digit * base; 
  
            base = base * 2; 
        } 
        return dec_value; 
}

Note: The program works only with binary numbers in the range of integers. In case you want to work with long binary numbers like 20 bits or 30 bit, you can use string variable to store the binary numbers.

Below is a similar program which uses string variable instead of integers to store binary value:

Approach:

public int binaryToDecimal(String n) { 
        String num = n; 
        int dec_value = 0; 
  
        // Initializing base value to 1, 
        // i.e 2^0 
        int base = 1; 
  
        int len = num.length(); 
        for (int i = len - 1; i >= 0; i--) { 
            if (num.charAt(i) == '1') 
                dec_value += base; 
            base = base * 2; 
        } 
        return dec_value; 
}

References