Givet en brøk decimaltal n og heltal k, konverter decimaltal n til ækvivalent binært tal op til k præcision efter decimalkomma.

Eksempler:

Input: n = 2.47, k = 5 Output: 10.01111 Input: n = 6.986 k = 8 Output: 110.11111100 

Vi anbefaler stærkt, at du klikker her og øver dig på det, inden du går videre til løsningen.

A) Konverter den integrerede del af decimal til binær ækvivalent

1. Divider decimaltallet med 2 og gem resterne i array.
2. Divider kvotienten med 2.
3. Gentag trin 2, indtil vi får kvotienten lig med nul.
4. Ækvivalent binært tal ville være omvendt af alle rester af trin 1.

B) Konverter brøkdelen af ​​decimal til binær ækvivalent

1. Multiplicer brøkdecimaltallet med 2.
2. Integral del af det resulterende decimaltal vil være det første ciffer i brøkens binære tal.
3. Gentag trin 1 med kun en brøkdel af decimaltal og derefter trin 2.

C) Kombiner både integral og brøkdel af binært tal.

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 til at demonstrere ovenstående trin:

C++

// C++ program to convert fractional decimal> // to binary number> #include> 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 = 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 { // 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 { // 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 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 = 6.986; $k = 5; echo decimalToBinary($n, $k); // This code is contributed by mits ?>>

Javascript

> > > // 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 { // 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) + ''); n = 6.986; k = 5; document.write(decimalToBinary(n, k));>

Produktion

100.011 110.11111 

Tidskompleksitet: O(len(n))
Hjælperum: O(len(n))

hvor len() er det samlede antal cifre, der indeholder i nummer n.
Konverter binær brøk til decimal