将小数转换成二进制数-yiteyi-C++库

给定小数n和整数k，将小数n转换为小数点后精度达到k的等价二进制数。 例如：

null

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

我们强烈建议您在继续解决方案之前单击此处并进行练习。

A）将十进制数的整数部分转换为等价的二进制数

将十进制数除以2，并将余数存储在数组中。
把商除以2。
重复步骤2，直到商等于零。
等价的二进制数与第一步的所有余数相反。

B）将小数的小数部分转换为等价的二进制

将小数乘以2。
结果十进制数的整数部分将是分数二进制数的第一位。
只使用小数的小数部分重复步骤1，然后重复步骤2。

C）将二进制数的整数部分和小数部分结合起来。 插图

Let's take an example for n = 4.47 k = 3Step 1: Conversion of 4 to binary1. 4/2 : Remainder = 0 : Quotient = 22. 2/2 : Remainder = 0 : Quotient = 13. 1/2 : Remainder = 1 : Quotient = 0So equivalent binary of integral part of decimal is 100.Step 2: Conversion of .47 to binary1. 0.47 * 2 = 0.94, Integral part: 02. 0.94 * 2 = 1.88, Integral part: 13. 0.88 * 2 = 1.76, Integral part: 1So equivalent binary of fractional part of decimal is .011Step 3: Combined the result of step 1 and 2.Final answer can be written as:100 + .011 = 100.011

演示上述步骤的程序：

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 = 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                                     = 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>                       

输出：

100.011110.11111

时间复杂性： O（len（n）） 辅助空间： O（len（n））其中len（）是数字n中包含的总位数。将二进制分数转换成十进制 参考： 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 本文由 Shubham Bansal .如果你喜欢GeekSforgek，并想贡献自己的力量，你也可以使用写极客。组织或者把你的文章寄到contribute@geeksforgeeks.org.看到你的文章出现在Geeksforgeks主页上，并帮助其他极客。如果您发现任何不正确的地方，或者您想分享有关上述主题的更多信息，请写下评论。

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