Real number to Binary conversion

The number system conversion is carried out for a real number to binary number bits. The input real number consists of integer and fraction values separated by a decimal point. The integer value and fractional value are converted into binary separately and then combined to print binary bits as a result of the real number.

The fractional decimal number are converted into binary numbers by successive multiplication of the fraction by 2 and resulting string of integer digits is the converted binary numbers.

Real number to Binary Conversion - Manual Calculation

       Given input real number= 14.125, convert it into binary numbers

       real   = integer . fraction  

       separate real into integer and fractional part   

       decimal  = 14
       fraction = .125

     Decimal value (integer) into Binary conversion 

       2 | 14  | 0
       -----------
       2 | 7   | 1 
       -----------
       2 | 3   | 1 
       -----------
          1   

    decimal value (base 10) 14 =  1110   (binary base 2)

  Fractional value into Binary conversion  
    
 The fraction value is multiplied by 2  and
          result has a integer (1 or 0) and fraction value.
     the integer as a binary bit and the faction value used for next iteration.
     The process repeated until the fraction value reached to 0.   
 
     fraction = .125

              = .125 x 2    
              = 0.250 x 2
              = 0.50  x 2
              = 1.0
     
     fraction = 0.125 = 100           
   
 combined results  
    given real value (base 10)= 14.125  
    into binary bits (base 2)    = 1110.100
  

Real number to Binary Conversion - Java program

 
import java.util.Scanner;
public class FractionDecimal {
  
 public static String dec2bin(int decval)
 {  
  StringBuffer sbuf =new StringBuffer();  
  while(decval>1) 
  {
   sbuf.append( decval % 2 ) ;
   decval = decval /2;      
  }    
  if (decval==1)
   sbuf.append(1);
  
  return sbuf.reverse().toString();
 }
 
 public static String frac2bin(double fval)
 {  
  StringBuffer sbuf =new StringBuffer();  
  while(fval != 0) 
  {
   fval = fval * 2;
   sbuf.append(Math.floor(fval)) ;
   fval = (fval>=1) ? fval-1 : fval;      
  }    
    
  return sbuf.reverse().toString();
 }

 public static void main(String[] args) {
  
    Scanner sc=new Scanner(System.in);
    System.out.println("Fractional decimal to Binary Conversion");
  
  System.out.println("Enter double value");  
  double val=sc.nextDouble();
  sc.close();
  
  
  int  decpart = (int) val;
  double fracpart = (val - decpart);
  
  StringBuffer bits = new StringBuffer();
  String ibits =  FractionDecimal.dec2bin(decpart);
  String fbits =  FractionDecimal.frac2bin(fracpart);

  bits.append(ibits);bits.append('.');
  bits.append(fbits);
  
  
  System.out.println("\nDecimal value :" + decpart);
  System.out.println("Binary :" + ibits);
  
  System.out.println("\nFractional value :" + fracpart);
  System.out.println("Binary :" + fbits);
  
  System.out.println("\nDecimal with Fraction number :" + val);
  System.out.println("Binary :" + bits);  
 }
}

Real number to Binary Conversion - Java program Output

Fractional decimal to Binary Conversion
Enter double value
13.625

Decimal value :13
Binary :1101

Fractional value :0.625
Binary :101

Decimal with Fraction number :13.625
Binary :1101.101