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.

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

  1. Divide the decimal number by 2 and store remainders in array.
  2. Divide the quotient by 2.
  3. Repeat step 2 until we get the quotient equal to zero.
  4. Equivalent binary number would be reverse of all remainders of step 1.

B) Convert the fractional part of decimal to binary equivalent

  1. Multiply the fractional decimal number by 2.
  2. Integral part of resultant decimal number will be first digit of fraction binary number.
  3. 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 5 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 bianry 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

C++ Program to demonstrate above steps:

// 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;
}
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

This article is contributed by Shubham Bansal. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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