ISC COMPUTER SCIENCE PRACTICAL 2004 SOLVED QUESTION 2 : BASE EQUALITY

 Numbers have different representations depending on the bases on which they are expressed. For example in base 3, the number 12 is written as 110 (1 x 3² + 1 x 3¹ + 0 x 3⁰), but in base 8 it is written as 14(1 x 8¹ + 4 x 8⁰).

Consider, for example, the integers 12 and 5. Certainly these are not equal if base 10 is used for each. But suppose 12 was a base 3 number and 5 was a base 6 number then what happens, 12 base 3 = 1 x 3¹ + 2 x 3⁰, or 5 base 6 or 5 base 10 (5 in any base is equal to 5 base 10). So 12 and 5 can be equal if you select the right bases for each of them.

Write a program to input two integers, X and Y, and calculate the smallest base for X and smallest base for Y (likely different from X) so that X and Y represent the same value. The base associated with X and Y will be between 1 and 20 (both inclusive). In representing these numbers the digits 0 to 9 have their usual decimal interpretations.

Test your program for the following data and some random data:

The logic is quite simple just imput two integers, starting from base 1 find its value and compare it

with the value of the second number from bases 1 to 20 (minus the base of first number). 

Look for equality and print!

import java.util.*;

public class ISC2004Q2 {

       public static void main(String[] args) {

       int X,Y;

       Scanner in = new Scanner(System.in);

       System.out.println("Enter the value of X:");

       X = in.nextInt();

       System.out.println("Enter the value of Y:");

       Y = in.nextInt();

       Base obj = new Base(X,Y);

       obj.display();

       in.close();

       }

}

class Base {

       public void display() {

             for(int i=1;i<=20;i++) {

                    for(int j=1;j<=20;j++) {

                           if(baseRepresentation(X,i)==baseRepresentation(Y,j) && i!=j) {

                                 flag=true;

                                 System.out.println(X+" in base "+i+" equals "+Y+" in base "+j);

                                 break;

                          }

                          if(flag==true)

                                 break;

                    }

             }

             if(!flag)

                    System.out.println("NEVER EQUAL IN ANY BASE LESS THAN 20");

       }

       private int baseRepresentation(int numb,int b) {

             int tmp=0,j=0,N=numb;

             do {

                    tmp=tmp+(N%10)*(int)Math.pow(b, j);

                    j++;

                    N /=10;

                    }while(N>=1);

             return tmp;

       }

       Base(int X,int Y){

             this.X=X;

             this.Y=Y;

             flag=false;

       }

       private boolean flag;

       private int X;

       private int Y;

}