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
Following are the steps of converting binary fractional to decimal.
A) Convert the integral part of binary to decimal equivalent
- Multiply each digit separately from left side of radix point till the first digit by 20, 21, 22,… respectively.
- Add all the result coming from step 1.
- Equivalent integral decimal number would be the result obtained in step 2.
B) Convert the fractional part of binary to decimal equivalent
- Divide each digit from right side of radix point till the end by 21, 22, 23, … respectively.
- Add all the result coming from step 1.
- 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> |
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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