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

Input: n = 101.1101
Output: 5.8125

We strongly recommend that you click here and practice it, before moving on to the solution.

Following are the steps of converting binary fractional to decimal.

A) 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.

B) 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.

C) Add both integral and fractional part of decimal number.
Illustration

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

Implementation:

C++

// 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
double binaryToDecimal(string binary, int len)
{
    // Fetch the radix point
    size_t point = binary.find('.');

    // Update point if not found
    if (point == string::npos)
        point = len;

    double intDecimal = 0, fracDecimal = 0, twos = 1;

    // Convert integral part of binary to decimal
    // equivalent
    for (int i = point-1; i>=0; --i)
    {
        // Subtract '0' to convert character
        // into integer
        intDecimal += (binary[i] - '0') * twos;
        twos *= 2;
    }

    // Convert fractional part of binary to
    // decimal equivalent
    twos = 2;
    for (int i = point+1; i < len; ++i)
    {
        fracDecimal += (binary[i] - '0') / twos;
        twos *= 2.0;
    }

    // Add both integral and fractional part
    return intDecimal + fracDecimal;
}

// Driver code
int main()
{
    string n = "110.101";
    cout << binaryToDecimal(n, n.length()) << "\n";

    n = "101.1101";
    cout << binaryToDecimal(n, n.length());

    return 0;
}

Java

// Java program to demonstrate above steps of
// binary fractional to decimal conversion
import java.io.*;

class GFG{

// Function to convert binary fractional to
// decimal
static double binaryToDecimal(String binary,
                              int len)
{

    // Fetch the radix point
    int point = binary.indexOf('.');

    // Update point if not found
    if (point == -1)
        point = len;

    double intDecimal = 0,
           fracDecimal = 0,
           twos = 1;

    // Convert integral part of binary to decimal
    // equivalent
    for(int i = point - 1; i >= 0; i--)
    {
        intDecimal += (binary.charAt(i) - '0') * twos;
        twos *= 2;
    }

    // Convert fractional part of binary to
    // decimal equivalent
    twos = 2;
    for(int i = point + 1; i < len; i++)
    {
        fracDecimal += (binary.charAt(i) - '0') / twos;
        twos *= 2.0;
    }

    // Add both integral and fractional part
    return intDecimal + fracDecimal;
}

// Driver Code
public static void main(String[] args)
{
    String n = "110.101";
    System.out.println(
        binaryToDecimal(n, n.length()));

    n = "101.1101";
    System.out.println(
        binaryToDecimal(n, n.length()));
}
}

// This code is contributed by dheeraj_2801

Python3

# Python3 program to demonstrate above steps
# of binary fractional to decimal conversion

# Function to convert binary fractional
# to decimal
def binaryToDecimal(binary, length) :

    # Fetch the radix point
    point = binary.find('.')

    # Update point if not found
    if (point == -1) :
        point = length

    intDecimal = 0
    fracDecimal = 0
    twos = 1

    # Convert integral part of binary
    # to decimal equivalent
    for i in range(point-1, -1, -1) :

        # Subtract '0' to convert
        # character into integer
        intDecimal += ((ord(binary[i]) -
                        ord('0')) * twos)
        twos *= 2

    # Convert fractional part of binary
    # to decimal equivalent
    twos = 2

    for i in range(point + 1, length):

        fracDecimal += ((ord(binary[i]) -
                         ord('0')) / twos);
        twos *= 2.0

    # Add both integral and fractional part
    ans = intDecimal + fracDecimal

    return ans

# Driver code :
if __name__ == "__main__" :
    n = "110.101"
    print(binaryToDecimal(n, len(n)))

    n = "101.1101"
    print(binaryToDecimal(n, len(n)))

# This code is contributed
# by aishwarya.27

C#

// C# program to demonstrate above steps of
// binary fractional to decimal conversion
using System;

class GFG{

// Function to convert binary fractional to
// decimal
static double binaryToDecimal(string binary,
                              int len)
{

    // Fetch the radix point
    int point = binary.IndexOf('.');

    // Update point if not found
    if (point == -1)
        point = len;

    double intDecimal = 0,
           fracDecimal = 0,
           twos = 1;

    // Convert integral part of binary to decimal
    // equivalent
    for(int i = point - 1; i >= 0; i--)
    {
        intDecimal += (binary[i] - '0') * twos;
        twos *= 2;
    }

    // Convert fractional part of binary to
    // decimal equivalent
    twos = 2;
    for(int i = point + 1; i < len; i++)
    {
        fracDecimal += (binary[i] - '0') / twos;
        twos *= 2.0;
    }

    // Add both integral and fractional part
    return intDecimal + fracDecimal;
}

// Driver Code
public static void Main(string[] args)
{
    string n = "110.101";
    Console.Write(
        binaryToDecimal(n, n.Length) + "\n");

    n = "101.1101";
    Console.Write(
        binaryToDecimal(n, n.Length));
}
}

// This code is contributed by rutvik_56

Javascript

<script>
      // JavaScript program to demonstrate above steps of
      // binary fractional to decimal conversion
      // Function to convert binary fractional to
      // decimal
      function binaryToDecimal(binary, len) {
        // Fetch the radix point
        var point = binary.indexOf(".");

        // Update point if not found
        if (point === -1) point = len;

        var intDecimal = 0,
          fracDecimal = 0,
          twos = 1;

        // Convert integral part of binary to decimal
        // equivalent
        for (var i = point - 1; i >= 0; i--) {
          intDecimal += (binary[i] - "0") * twos;
          twos *= 2;
        }

        // Convert fractional part of binary to
        // decimal equivalent
        twos = 2;
        for (var i = point + 1; i < len; i++) {
          fracDecimal += (binary[i] - "0") / twos;
          twos *= 2.0;
        }

        // Add both integral and fractional part
        return intDecimal + fracDecimal;
      }

      // Driver Code
      var n = "110.101";
      document.write(binaryToDecimal(n, n.length) + "<br>");

      n = "101.1101";
      document.write(binaryToDecimal(n, n.length));
    </script>

Output

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.
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