ISC Practical Program – ISC 2004

Number have different representations depending on the bases on which they are expressed. For example in base 3, the number 12 is written as 110 , but in base 8 it is written as

Consider, for example, the integers 12 and 5. Certainly these ar 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 was 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 calculated 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. The uppercase alphabetic characters A through J represent digits 10 through 19 respectively.

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

INPUT :
X = 12, Y = 5
OUTPUT:
	12(base 3) = 5(base 6)
INPUT :
X = 10, Y = A
OUTPUT:
	10(base 10) = A(base 11)
INPUT :
X = 123, Y = 456
OUTPUT:
	123 is not equal to 456 in any base between 2 to 20
INPUT :
X = 42, Y = 36
OUTPUT:
	42(base 7) = 36(base 8)

import java.util.*;
public class Base_Equality
{
    String dg = "0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ";
    int base2dec(String n, int b)
    {
        int i, l = n.length(), d=0, x, c=0;
        for(i = l-1; i>=0; i--)
        {                   //Converting the number to decimal from base b
            x = dg.indexOf(n.charAt(i));
            if(b<=x)        //If any digit is greater than or equal to the base then the number cannot be from that base
                return -1;
            d = d + x*(int)Math.pow(b, c);
            c++;
        }
        return d;
    }

    void check(String a, String b)
    {
        int i, j, m, n;
        for(i=2;i<=20;i++)
        {
            m = base2dec(a, i);
            if(m==-1)       //Skipping the loop
            continue;
            for(j=2;j<=20;j++)
            {
                n = base2dec(b, j);
                if(n==-1)   //Skipping the loop
                continue;
                if(m == n)
                {
                    System.out.println(a+" in base "+i+" and "+b+" in base "+j+" are equal");
                    System.exit(0);
                }
            }
        }
        System.out.println(a+" is not equal to "+b+" in any base between 2 to 20");
    }
    
    public static void main()
    {
        Scanner sc = new Scanner(System.in);
        String a, b;
        Base_Equality ob = new Base_Equality();
        System.out.println("Enter 2 numbers: ");
        a = sc.nextLine();      //Taking input
        b = sc.nextLine();
        ob.check(a, b);      //Calling the function
    }
}

Output 1

Output 2