Decimal to binary and Binary to decimal

The number system conversion process is carried out between base 10 and base 2 number system. The base 10 number system has 10 distinct numbers from 0 to 9 is called decimal number system and the base 2 number system has 2 distinct numbers 0 and 1 is binary number system.

Decimal to binary (base 10 to base 2) conversion - algorithm

Given a decimal value, decval and converts it into binary bits

1. modulus decval by 2, it returns a reminder ( 0 or 1)
2. divide decval by 2, it returns a quotient
3. the quotient becomes the decval
4. and repeat step 1 to 3 until decval becomes 0
5. the reminders on each iteration is results of binary bits

Decimal to binary (base 10 to base 2) conversion - Example

 
      Given decimal value = 47 ,convert it into binary bits         
         divide the decimal value by 2 returns a quotient and reminder, 
         the returned quotient becomes decimal value for next division by 2

      divider | quotient | reminder 

         2 | 47  
         -----------    
         2 | 23   | 1
         -----------    
         2 | 11   | 1
         -----------    
         2 | 5    | 1
         -----------    
         2 | 2    | 1
         -----------    
         2 | 1    | 0

     decimal value (base 10) 47 =  binary bits (base 2) 101111. 
   

Binary to Decimal conversion - algorithm

Given binary bits, converts it into a decimal value

1. set decval==0
2. Read a LSB bit from binary-bits
3.    decval + LSB x 2 power of the LSB position value
4. Next LSB
5. print decval

binary to decimal value conversion - Example

 
      Given binary bits = 10111 ,convert it into a decimal value. 
       A bit position value(0 to n-1 bits) starts right to left on the binary bits.   
         
           = 1 x 24 + 0 x 23 + 1 x 22 + 1x 21  + 1 x 20   
           =  1x16      + 0x8   + 1x4     + 1x2     + 1x1
           =   16  +  0  + 4  + 2 + 1              
     decimal value  = 23
     binary bits (base 2)  10111 = 23 decimal value (base 10). 
   

Number System Conversion - Java Programming Code

The Java program converts a decimal number to binary numbers and binary bit sequence to a decimal value.

 
import java.util.Scanner;
public class Conversion {

 
    public static String dec2bin(int decval) {
  
  StringBuffer bits=new StringBuffer();
  while ( decval>1 ) 
  {
   bits.append( decval % 2 );
   decval  = decval/2;
  }
  
  if ( decval ==1)
    bits.append( decval );
  
  return bits.reverse().toString();
 }
 
   public static int bin2dec(String bits) {
  
    int decval =0;
    StringBuffer sbits =new StringBuffer(bits);
    sbits.reverse();
    
    for(int n=0;n<sbits.length();n++) 
    {      
     if ( sbits.charAt(n)=='1')
    decval = decval +(int)Math.pow(2, n);  
    }     
   return decval; 
 }
 
 public static void main(String[] args) {
  
       int decval=0; String bstr=""; 
       System.out.println("nt Number System Conversion ");
       System.out.println("Decimal to Binary / Binary to Decimal");       
       System.out.println("\n Select Choice \t 1 - Binary2Decimal \t 
                                                    2- Decimal2Binary \n ");
         
       Scanner sc=new Scanner(System.in);      
       int choice =sc.nextInt();
       
       switch ( choice ) {
          
         case 1:
          System.out.println("Enter Binary bits");
          bstr= sc.next();
          decval = Conversion.bin2dec(bstr);
          System.out.println("nDecimal value :" + decval);
          break; 
         case 2:
          System.out.println("Enter positive Decimal value ");
          decval = sc.nextInt();
          bstr = Conversion.dec2bin(decval);
          System.out.println("nBinary bits :" + bstr);
          break;          
         }
      
         sc.close();

 }

}


 

Number System Conversion - Java program output

Number System Conversion 
Decimal to Binary / Binary to Decimal

 Select Choice 
  1 - Binary2Decimal 
  2- Decimal2Binary 
 
2
Enter positive Decimal value 
527

Binary bits :1000001111


Number System Conversion 
Decimal to Binary / Binary to Decimal

 Select Choice 
  1 - Binary2Decimal 
  2- Decimal2Binary 
 
1
Enter Binary bits
110000111

Decimal value :391