Convert decimal fraction to binary number
Given an fraction decimal number n and integer k, convert decimal number n into equivalent binary number up-to k precision after decimal point.
Examples:
Input: n = 2.47, k = 5 Output: 10.01111 Input: n = 6.986 k = 8 Output: 110.11111100
A) Convert the integral part of decimal to binary equivalent
- Divide the decimal number by 2 and store remainders in array.
- Divide the quotient by 2.
- Repeat step 2 until we get the quotient equal to zero.
- Equivalent binary number would be reverse of all remainders of step 1.
B) Convert the fractional part of decimal to binary equivalent
- Multiply the fractional decimal number by 2.
- Integral part of resultant decimal number will be first digit of fraction binary number.
- Repeat step 1 using only fractional part of decimal number and then step 2.
C) Combine both integral and fractional part of binary number.
Illustration
Let's take an example for n = 4.47 k = 3 Step 1: Conversion of 4 to binary 1. 4/2 : Remainder = 0 : Quotient = 2 2. 2/2 : Remainder = 0 : Quotient = 1 3. 1/2 : Remainder = 1 : Quotient = 0 So equivalent binary of integral part of decimal is 100. Step 2: Conversion of .47 to binary 1. 0.47 * 2 = 0.94, Integral part: 0 2. 0.94 * 2 = 1.88, Integral part: 1 3. 0.88 * 2 = 1.76, Integral part: 1 So equivalent binary of fractional part of decimal is .011 Step 3: Combined the result of step 1 and 2. Final answer can be written as: 100 + .011 = 100.011
Program to demonstrate above steps:
C++
// C++ program to convert fractional decimal // to binary number #include<bits/stdc++.h> using namespace std; // Function to convert decimal to binary upto // k-precision after decimal point string decimalToBinary( double num, int k_prec) { string binary = "" ; // Fetch the integral part of decimal number int Integral = num; // Fetch the fractional part decimal number double fractional = num - Integral; // Conversion of integral part to // binary equivalent while (Integral) { int rem = Integral % 2; // Append 0 in binary binary.push_back(rem + '0' ); Integral /= 2; } // Reverse string to get original binary // equivalent reverse(binary.begin(),binary.end()); // Append point before conversion of // fractional part binary.push_back( '.' ); // Conversion of fractional part to // binary equivalent while (k_prec--) { // Find next bit in fraction fractional *= 2; int fract_bit = fractional; if (fract_bit == 1) { fractional -= fract_bit; binary.push_back(1 + '0' ); } else binary.push_back(0 + '0' ); } return binary; } // Driver code int main() { double n = 4.47; int k = 3; cout << decimalToBinary(n, k) << "\n" ; n = 6.986 , k = 5; cout << decimalToBinary(n, k); return 0; } |
Java
// Java program to convert fractional decimal // to binary number import java.util.*; class GFG { // Function to convert decimal to binary upto // k-precision after decimal point static String decimalToBinary( double num, int k_prec) { String binary = "" ; // Fetch the integral part of decimal number int Integral = ( int ) num; // Fetch the fractional part decimal number double fractional = num - Integral; // Conversion of integral part to // binary equivalent while (Integral > 0 ) { int rem = Integral % 2 ; // Append 0 in binary binary += (( char )(rem + '0' )); Integral /= 2 ; } // Reverse string to get original binary // equivalent binary = reverse(binary); // Append point before conversion of // fractional part binary += ( '.' ); // Conversion of fractional part to // binary equivalent while (k_prec-- > 0 ) { // Find next bit in fraction fractional *= 2 ; int fract_bit = ( int ) fractional; if (fract_bit == 1 ) { fractional -= fract_bit; binary += ( char )( 1 + '0' ); } else { binary += ( char )( 0 + '0' ); } } return binary; } static String reverse(String input) { char [] temparray = input.toCharArray(); int left, right = 0 ; right = temparray.length - 1 ; for (left = 0 ; left < right; left++, right--) { // Swap values of left and right char temp = temparray[left]; temparray[left] = temparray[right]; temparray[right] = temp; } return String.valueOf(temparray); } // Driver code public static void main(String[] args) { double n = 4.47 ; int k = 3 ; System.out.println(decimalToBinary(n, k)); n = 6.986 ; k = 5 ; System.out.println(decimalToBinary(n, k)); } } // This code contributed by Rajput-Ji |
Python3
# Python3 program to convert fractional # decimal to binary number # Function to convert decimal to binary # upto k-precision after decimal point def decimalToBinary(num, k_prec) : binary = "" # Fetch the integral part of # decimal number Integral = int (num) # Fetch the fractional part # decimal number fractional = num - Integral # Conversion of integral part to # binary equivalent while (Integral) : rem = Integral % 2 # Append 0 in binary binary + = str (rem); Integral / / = 2 # Reverse string to get original # binary equivalent binary = binary[ : : - 1 ] # Append point before conversion # of fractional part binary + = '.' # Conversion of fractional part # to binary equivalent while (k_prec) : # Find next bit in fraction fractional * = 2 fract_bit = int (fractional) if (fract_bit = = 1 ) : fractional - = fract_bit binary + = '1' else : binary + = '0' k_prec - = 1 return binary # Driver code if __name__ = = "__main__" : n = 4.47 k = 3 print (decimalToBinary(n, k)) n = 6.986 k = 5 print (decimalToBinary(n, k)) # This code is contributed by Ryuga |
C#
// C# program to convert fractional decimal // to binary number using System; class GFG { // Function to convert decimal to binary upto // k-precision after decimal point static String decimalToBinary( double num, int k_prec) { String binary = "" ; // Fetch the integral part of decimal number int Integral = ( int ) num; // Fetch the fractional part decimal number double fractional = num - Integral; // Conversion of integral part to // binary equivalent while (Integral > 0) { int rem = Integral % 2; // Append 0 in binary binary += (( char )(rem + '0' )); Integral /= 2; } // Reverse string to get original binary // equivalent binary = reverse(binary); // Append point before conversion of // fractional part binary += ( '.' ); // Conversion of fractional part to // binary equivalent while (k_prec-- > 0) { // Find next bit in fraction fractional *= 2; int fract_bit = ( int ) fractional; if (fract_bit == 1) { fractional -= fract_bit; binary += ( char )(1 + '0' ); } else { binary += ( char )(0 + '0' ); } } return binary; } static String reverse(String input) { char [] temparray = input.ToCharArray(); int left, right = 0; right = temparray.Length - 1; for (left = 0; left < right; left++, right--) { // Swap values of left and right char temp = temparray[left]; temparray[left] = temparray[right]; temparray[right] = temp; } return String.Join( "" ,temparray); } // Driver code public static void Main(String[] args) { double n = 4.47; int k = 3; Console.WriteLine(decimalToBinary(n, k)); n = 6.986; k = 5; Console.WriteLine(decimalToBinary(n, k)); } } // This code has been contributed by 29AjayKumar |
PHP
<?php // PHP program to convert fractional decimal // to binary number // Function to convert decimal to binary upto // k-precision after decimal point function decimalToBinary( $num , $k_prec ) { $binary = "" ; // Fetch the integral part of decimal number $Integral = (int)( $num ); // Fetch the fractional part decimal number $fractional = $num - $Integral ; // Conversion of integral part to // binary equivalent while ( $Integral ) { $rem = $Integral % 2; // Append 0 in binary $binary .= chr ( $rem + 48 ); $Integral = (int)( $Integral /2); } // Reverse string to get original binary // equivalent $binary = strrev ( $binary ); // Append point before conversion of // fractional part $binary .= '.' ; // Conversion of fractional part to // binary equivalent while ( $k_prec --) { // Find next bit in fraction $fractional *= 2; $fract_bit = (int) $fractional ; if ( $fract_bit == 1) { $fractional -= $fract_bit ; $binary .= chr (1 + 48 ); } else $binary .= chr (0 + 48 ); } return $binary ; } // Driver code $n = 4.47; $k = 3; echo decimalToBinary( $n , $k ). "\n" ; $n = 6.986; $k = 5; echo decimalToBinary( $n , $k ); // This code is contributed by mits ?> |
Output:
100.011 110.11111
Time complexity: O(len(n))
Auxiliary space: O(len(n))
where len() is the total digits contain in number n.
Convert Binary fraction to Decimal
Reference:
http://cs.furman.edu/digitaldomain/more/ch6/dec_frac_to_bin.htm
http://www.cquestions.com/2011/07/c-program-for-fractional-decimal-to.html
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