Given a 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
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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 ?> |
Javascript
<script> // JavaScript 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) { let binary = ""; // Fetch the integral part of decimal number let Integral = parseInt(num, 10); // Fetch the fractional part decimal number let fractional = num - Integral; // Conversion of integral part to // binary equivalent while (Integral > 0) { let rem = Integral % 2; // Append 0 in binary binary += (String.fromCharCode(rem + '0'.charCodeAt())); Integral = parseInt(Integral / 2, 10); } // 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; let fract_bit = parseInt(fractional, 10); if (fract_bit == 1) { fractional -= fract_bit; binary += String.fromCharCode(1 + '0'.charCodeAt()); } else { binary += String.fromCharCode(0 + '0'.charCodeAt()); } } return binary; } function reverse(input) { let temparray = input.split(''); let left, right = 0; right = temparray.length - 1; for (left = 0; left < right; left++, right--) { // Swap values of left and right let temp = temparray[left]; temparray[left] = temparray[right]; temparray[right] = temp; } return temparray.join(""); } let n = 4.47; let k = 3; document.write(decimalToBinary(n, k) + "</br>"); n = 6.986; k = 5; document.write(decimalToBinary(n, k)); </script> |
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
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