How many bits are needed to represent 16 shades of grey?

How many bits are needed to represent 16 shades of grey?

• A. 2
• B. 3
• C. 4
• D. 5

Answer: (C)

To capture 16 different shades, you need enough binary combinations to encode 16 distinct values. Each bit doubles the number of possible values, so with n bits you can represent 2^n different levels. You need 2^n to be at least 16, and the smallest n that satisfies this is 4 because 2^4 equals 16. With four bits you can code 16 distinct levels (often 0 to 15). Using fewer bits would miss some shades, while more bits would exceed what’s necessary. So the number of bits required is four.

To capture 16 different shades, you need enough binary combinations to encode 16 distinct values. Each bit doubles the number of possible values, so with n bits you can represent 2^n different levels. You need 2^n to be at least 16, and the smallest n that satisfies this is 4 because 2^4 equals 16. With four bits you can code 16 distinct levels (often 0 to 15). Using fewer bits would miss some shades, while more bits would exceed what’s necessary. So the number of bits required is four.