Convert Binary fraction to Decimal

Given an string of binary number n. Convert binary fractional n into it's decimal equivalent.

Examples:

Input: n = 110.101
Output: 6.625
Explanation: Integer part (110 = 6) and fractional part (.101 = 0.625) -> total = 6.625

Input: n = 101.1101
Output: 5.8125
Explanation: Integer part (101 = 5) and fractional part (.1101 = 0.8125) -> total = 5.8125

Following are the steps of converting binary fractional to decimal.

1) Convert the integral part of binary to decimal equivalent

1. Multiply each digit separately from left side of radix point till the first digit by 2⁰, 2¹, 2²,... respectively.
2. Add all the result coming from step 1.
3. Equivalent integral decimal number would be the result obtained in step 2.

2) Convert the fractional part of binary to decimal equivalent

1. Divide each digit from right side of radix point till the end by 2¹, 2², 2³, ... respectively.
2. Add all the result coming from step 1.
3. Equivalent fractional decimal number would be the result obtained in step 2.

3) Add both integral and fractional part of decimal number.

Let's take an example for n = 110.101 ,

Step 1: Conversion of 110 to decimal => 110₂ = (1*2²) + (1*2¹) + (0*2⁰) => 110₂ = 4 + 2 + 0 => 110₂ = 6 So equivalent decimal of binary integral is 6.
Step 2: Conversion of .101 to decimal => 0.101₂ = (1*1/2) + (0*1/2²) + (1*1/2³) => 0.101₂ = 1*0.5 + 0*0.25 + 1*0.125 => 0.101₂ = 0.625 So equivalent decimal of binary fractional is 0.625
Step 3: Add result of step 1 and 2. => 6 + 0.625 = 6.625

// C++ program to demonstrate above steps of
// binary fractional to decimal conversion
#include<bits/stdc++.h>
using namespace std;

// Function to convert binary fractional to
// decimal
long double convertToDecimal(const string &n) {
    
    int pos = n.length();
    
    // Find the position of '.'
    for(int i = 0; i < n.length(); i++)
    {
        if(n[i] == '.')
        {
            pos = i;
            break;
        }
    }
    
    long double intDecimal = 0.0, fracDecimal = 0.0, twos = 1.0;

    // Convert integral part
    for (int i = pos - 1; i >= 0; --i)
    {
        intDecimal += (n[i] - '0') * twos;
        twos *= 2.0;
    }

    // Convert fractional part
    twos = 2.0;
    for (int i = pos + 1; i < n.length(); ++i)
    {
        fracDecimal += (n[i] - '0') / twos;
        twos *= 2.0;
    }
    
    return intDecimal + fracDecimal;
}

// Driver code
int main()
{
    string n = "110.101";
    cout << convertToDecimal(n) << "\n";

    n = "101.1101";
    cout << convertToDecimal(n);

    return 0;
}

#include <stdio.h>
#include <string.h>
#include <math.h>

// Function to convert binary fractional to
// decimal
long double convertToDecimal(const char *n) {
    int pos = strlen(n);

    // Find the position of '.'
    for(int i = 0; i < strlen(n); i++)
    {
        if(n[i] == '.')
        {
            pos = i;
            break;
        }
    }

    long double intDecimal = 0.0, fracDecimal = 0.0, twos = 1.0;

    // Convert integral part
    for (int i = pos - 1; i >= 0; --i)
    {
        intDecimal += (n[i] - '0') * twos;
        twos *= 2.0;
    }

    // Convert fractional part
    twos = 2.0;
    for (int i = pos + 1; i < strlen(n); ++i)
    {
        fracDecimal += (n[i] - '0') / twos;
        twos *= 2.0;
    }

    return intDecimal + fracDecimal;
}

// Driver code
int main() {
    char n[] = "110.101";
    printf("%Lf\n", convertToDecimal(n));

    strcpy(n, "101.1101");
    printf("%Lf", convertToDecimal(n));
    return 0;
}

import java.util.*;

// Function to convert binary fractional to
// decimal
public class Main {
    public static double convertToDecimal(String n) {
        int pos = n.length();

        // Find the position of '.'
        for(int i = 0; i < n.length(); i++)
        {
            if(n.charAt(i) == '.')
            {
                pos = i;
                break;
            }
        }

        double intDecimal = 0.0, fracDecimal = 0.0, twos = 1.0;

        // Convert integral part
        for (int i = pos - 1; i >= 0; --i)
        {
            intDecimal += (n.charAt(i) - '0') * twos;
            twos *= 2.0;
        }

        // Convert fractional part
        twos = 2.0;
        for (int i = pos + 1; i < n.length(); ++i)
        {
            fracDecimal += (n.charAt(i) - '0') / twos;
            twos *= 2.0;
        }

        return intDecimal + fracDecimal;
    }

    // Driver code
    public static void main(String[] args) {
        String n = "110.101";
        System.out.println(convertToDecimal(n));

        n = "101.1101";
        System.out.println(convertToDecimal(n));
    }
}

# Python3 program to convert binary fractional to decimal

# Function to convert binary fractional to decimal
def convertToDecimal(n):
    
    pos = len(n)
    
    # Find the position of '.'
    for i in range(len(n)):
        if n[i] == '.':
            pos = i
            break
    
    intDecimal = 0.0
    fracDecimal = 0.0
    twos = 1.0
    
    # Convert integral part
    for i in range(pos - 1, -1, -1):
        intDecimal += (ord(n[i]) - ord('0')) * twos
        twos *= 2.0
    
    # Convert fractional part
    twos = 2.0
    for i in range(pos + 1, len(n)):
        fracDecimal += (ord(n[i]) - ord('0')) / twos
        twos *= 2.0
    
    return intDecimal + fracDecimal

# Driver code
n = "110.101"
print(convertToDecimal(n))

n = "101.1101"
print(convertToDecimal(n))

// C# program to convert binary fractional to decimal
using System;

public class GfG
{
    // Function to convert binary fractional to decimal
    public static double ConvertToDecimal(string n)
    {
        int pos = n.Length;

        // Find the position of '.'
        for (int i = 0; i < n.Length; i++)
        {
            if (n[i] == '.')
            {
                pos = i;
                break;
            }
        }

        double intDecimal = 0.0, fracDecimal = 0.0, twos = 1.0;

        // Convert integral part
        for (int i = pos - 1; i >= 0; --i)
        {
            intDecimal += (n[i] - '0') * twos;
            twos *= 2.0;
        }

        // Convert fractional part
        twos = 2.0;
        for (int i = pos + 1; i < n.Length; ++i)
        {
            fracDecimal += (n[i] - '0') / twos;
            twos *= 2.0;
        }

        return intDecimal + fracDecimal;
    }

    // Driver code
    public static void Main()
    {
        string n = "110.101";
        Console.WriteLine(ConvertToDecimal(n));

        n = "101.1101";
        Console.WriteLine(ConvertToDecimal(n));
    }
}

// JavaScript program to demonstrate above steps of
// binary fractional to decimal conversion

// Function to convert binary fractional to
// decimal
function convertToDecimal(n) {
    
    let pos = n.length;
    
    // Find the position of '.'
    for(let i = 0; i < n.length; i++)
    {
        if(n[i] === '.')
        {
            pos = i;
            break;
        }
    }
    
    let intDecimal = 0.0, fracDecimal = 0.0, twos = 1.0;
    
    // Convert integral part
    for (let i = pos - 1; i >= 0; --i)
    {
        intDecimal += (n[i].charCodeAt(0) - '0'.charCodeAt(0)) * twos;
        twos *= 2.0;
    }
    
    // Convert fractional part
    twos = 2.0;
    for (let i = pos + 1; i < n.length; ++i)
    {
        fracDecimal += (n[i].charCodeAt(0) - '0'.charCodeAt(0)) / twos;
        twos *= 2.0;
    }
    
    return intDecimal + fracDecimal;
}

// Driver code
let n = "110.101";
console.log(convertToDecimal(n) + "\n");

n = "101.1101";
console.log(convertToDecimal(n));

6.625
5.8125

Time complexity: O(len(n)) 
Auxiliary space: O(len(n)) 

Where len is the total digits contain in binary number of n.

See this: Convert decimal fraction to binary number.