Binary to Real number conversion

The number system conversion is carried out for a binary numbers (base-2) into real number (base 10). The input binary bit sequence consists of integer and fraction binary bits separated by a decimal point. The integer bits and fractional bits are converted into decimal value separately and then combined to print real value as a result of given binary bit sequence.

The fractional part of binary bits are converted into decimal fraction value by multiplication of the bits by 2 power of negative positional value of the bits.

Binary to Real number Conversion - Manual Calculation

       Given input binary numbers = 1110.1001, converts it into a real number.      

       separate binary bits into integer binary bits and fractional binary bits   
                by a delimiter . (point)
       binary bits (integer part)   = 1110
       binary bits (fraction part)  = 1001

      Binary bits (integer part) into decimal conversion 
             binary bits (integer part)   = 1110
             1 x 2^3  + 1 x 2^2 + 1 x 2^1 + 0 x 2^0
             1 x 8     +  1 x 4 + 1 x 2   + 0  x 1
                8       +  4          +  2  + 0

          1110 (base 2)   = 14  (base 10)            
 
 Binary bits into Decimal fraction conversion  
 The fraction binary bits is multiplied by 2 power of negative bit position value. 
    The position value order starts from right to left

  Binary bits(fractional part)  = 1001
                                = 1x 2^(-4) + 0x 2^(-3) + 0x 2^(-2)  +1 x 2^(-1)    
                                = 1 x 0.0625  + 0 x 0.125  + 0x 0.25 +1 x 0.5          
                                =0.5625          
   
 combined results  
    Given binary bits (base 2)    = 1110.1001  
                real value (base 10)= 14.5625 
  

Binary to Real number conversion - Java program

The Java param converts a binary bit sequence read from user into a real value consists of decimal value (integer) and fractional value.

 
import java.util.Scanner;
public class Binary2FDecimal {

 public static int bin2dec(String bits) {
  
    int decval=0;
    int len = bits.length();
    for(int n=0; n<len; n++ ) 
     {      
       if ( bits.charAt(n) == '1' )         
        decval += Math.pow(2,len-n-1);             
                      
    }
    return decval;
 }
 
 public static double bin2frac(String bits) {
  
    double fval=0;
    int len = bits.length();
    for(int n=0; n<len; n++ ) 
     {     
         int bval = Integer.parseInt(bits.charAt(n)+"");                
         fval += bval *  1.0/Math.pow(2,n+1);             
                      
    }
    return fval;
  
 }
 
 public static void main(String[] args) {
  
    Scanner sc=new Scanner(System.in);
    System.out.println("Binary to Fractional decimal Conversion");
  
  System.out.println("Enter binary bits with a decimal point");  
  String bits=sc.nextLine();
  sc.close();

  String parts[]=bits.split("\\.");
  
  System.out.println("\nBinary decimal part : " + parts[0]);
  int decval = Binary2FDecimal.bin2dec(parts[0]) ;
  System.out.println("Decimal value : " + decval);
  
  System.out.println("\nBinary fractional part : " + parts[1]);
  double fval = Binary2FDecimal.bin2frac(parts[1]);
  System.out.println("Fractional value : " + fval);
  
  
  double dval  = fval+decval;
  System.out.println("Combined Double value : " + dval);      
 }
}

Binary to Real number conversion - Java code output

 Binary to Fractional decimal Conversion
Enter binary bits with a decimal point
11010.11010

Binary decimal part : 11010
Decimal value : 26

Binary fractional part : 11010
Fractional value : 0.8125
Combined Double value : 26.8125