Logic Circuits - Binary divisible by 16 I have a question

  Given a 16-bit register A holding a number in 2’s complement form, use a 
   single gate (e.g., AND, OR,
  XOR, NAND, NOR, NOT) with an arbitrary number of inputs to implement a 
  circuit that produces an
  output 1 if the number is divisible by 16, and an output 0 otherwise. The 
 bits are labelled A15, A14, ..., A0.


I'm confused at how this answer is expected because the question is only 2 marks my answer was that it would be a single XOR gate with inputs a0-a15 - would this be correct and why?
A decimal number is divisible by 100 if it ends with two zeroes. The same thing happens in your case, and leads to a solution using a single NOR gate.