To code a signal with 16 levels, you would need a 4-bit coder.
Each bit in a binary number can represent two levels (0 or 1). Therefore, with a 4-bit coder, you can represent 2^4 = 16 different levels, which matches the requirement for coding a signal with 16 levels. The other options, 8-bit, 2-bit, 16-bit, and 1-bit coders, would not be suitable for precisely representing 16 levels.
I hope this helped!
~~~Harsha~~~