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
We strongly recommend that you click here and practice it, before moving on to the solution.
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++ 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 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 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# 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
<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>
<?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.