First define all the basic operation you can apply on two numbers.

Binary operation : +, -, *, /, %, optional(&(and), |(or), ^(xor))
Unary operation : !, ~, -
Comparison : <, > ==, !=

Define all these operation.

Most simplest one can be,
class BIG_INT {
   private string val;
   //Define constructor
   private BIG_INT(){}
   public BIG_INT(int x) {
       this.val = x.toString();
   }
   public BIG_INT(long x) {
       this.val = x.toString();
   }
   public BIG_INT(string x) {
       this.val = x;
   }
   public BIG_INT add(BIG_INT x);
   public BIG_INT add(int x);
   public BIG_INT add(long x);

  similarly write methods for other operation also;

  }

If this question asked for only design testing purpose only all method
declaration will be sufficient.

-- 
Anshuman Mishra | Software Development Engineer | Amazon

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