To represent 16 shades of grey with minimum bits, how many bits are needed?

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Multiple Choice

To represent 16 shades of grey with minimum bits, how many bits are needed?

Explanation:
Representing grayscale levels efficiently depends on how many distinct values you can encode with a given number of bits. Each bit doubles the number of representable levels, so with n bits you can encode 2^n different gray values. To cover 16 shades, you need 2^n to be at least 16. The smallest n that works is four, since 2^4 equals 16. Therefore, four bits are required to represent sixteen shades. Using fewer bits would yield only four or eight levels, which isn’t enough, while more bits would exceed the minimum needed.

Representing grayscale levels efficiently depends on how many distinct values you can encode with a given number of bits. Each bit doubles the number of representable levels, so with n bits you can encode 2^n different gray values. To cover 16 shades, you need 2^n to be at least 16. The smallest n that works is four, since 2^4 equals 16. Therefore, four bits are required to represent sixteen shades. Using fewer bits would yield only four or eight levels, which isn’t enough, while more bits would exceed the minimum needed.

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