Dané zlomkové desetinné číslo n a celé číslo k převeďte desetinné číslo n na ekvivalentní binární číslo s přesností na k za desetinnou čárkou.
Příklady:
Input: n = 2.47, k = 5 Output: 10.01111 Input: n = 6.986 k = 8 Output: 110.11111100>Důrazně doporučujeme, abyste klikli sem a procvičili si to, než přejdete k řešení.
A) Převeďte integrální část desítkové soustavy na binární ekvivalent
- Desetinné číslo vydělte 2 a uložte zbytky do pole.
- Vydělte podíl 2.
- Opakujte krok 2, dokud nedostaneme podíl rovný nule.
- Ekvivalentní binární číslo by bylo opačné než všechny zbytky kroku 1.
B) Převeďte zlomkovou část desítkové soustavy na binární ekvivalent
- Vynásobte zlomkové desetinné číslo 2.
- Nedílnou součástí výsledného desetinného čísla bude první číslice zlomkového binárního čísla.
- Opakujte krok 1 s použitím pouze zlomkové části desetinného čísla a poté krok 2.
C) Spojte integrální i zlomkovou část binárního čísla.
Ilustrace :
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 pro demonstraci výše uvedených kroků:
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;> }> |
>
>
Jáva
// 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> |
>
markdown obrázky
>
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)); > |
>
>Výstup
100.011 110.11111>
Časová složitost: O(délka(n))
Pomocný prostor: O(délka(n))
kde len() je celkový počet číslic v čísle n.
Převést binární zlomek na desítkové