To solve this, we will add the two binary numbers directly and take into account that these are 16-bit, 2's complement numbers.

Step-by-step solution:

1. Write the numbers in binary:

   • $0101\ 0101\ 0101\ 0101_2$
   • $0011\ 1001\ 1100\ 1111_2$

2. Add the two binary numbers:

  0101 0101 0101 0101
+ 0011 1001 1100 1111
----------------------
  1000 1111 0001 0100

3. Check for overflow: Since both operands are positive (their most significant bits, MSB, are 0), and the result's MSB is 1, this suggests an overflow has occurred. In a 16-bit 2's complement system, the result would actually represent a negative number.

4. Interpret the result: The binary result is $1000\ 1111\ 0001\ 0100_2$.

   To interpret this in 2's complement, we need to find its decimal value:

   • The MSB is 1, so it's a negative number.

   • To find the magnitude, take the 2's complement (invert all bits and add 1):

     Invert: 0111 0000 1110 1011
     Add 1:  0111 0000 1110 1100
     

     $0111\ 0000\ 1110\ 1100_2$ is $28908_{10}$.

   • Since the original number was negative, the final answer is $-28908$.

Final Answer:

The sum of the two 16-bit 2's complement numbers is $-28908$.

Would you like more details or explanations on any step?

Here are 5 related questions you might find interesting:

1. How do you detect overflow in binary addition?
2. What are the advantages of 2's complement over 1's complement?
3. How does a 16-bit machine handle overflow?
4. How would you subtract binary numbers using 2's complement?
5. How would the addition differ if the numbers were unsigned?

Tip: When adding 2's complement numbers, always check the sign bits before and after the addition to detect overflow.