How many bits are needed to represent 32 gray shades?

How many bits are needed to represent 32 gray shades?

• A. 4
• B. 6
• C. 5
• D. 7

Answer: (C)

Bits determine how many distinct gray levels you can encode: each additional bit doubles the number of possibilities. With n bits you can represent up to 2^n different gray shades. To get 32 distinct shades, you need n such that 2^n = 32. The smallest n that works is 5, since 2^5 equals 32. Four bits would only provide 2^4 = 16 shades, which is not enough, while six bits would give 2^6 = 64 shades, more than needed. So five bits are required to represent 32 gray shades.

Bits determine how many distinct gray levels you can encode: each additional bit doubles the number of possibilities. With n bits you can represent up to 2^n different gray shades. To get 32 distinct shades, you need n such that 2^n = 32. The smallest n that works is 5, since 2^5 equals 32. Four bits would only provide 2^4 = 16 shades, which is not enough, while six bits would give 2^6 = 64 shades, more than needed. So five bits are required to represent 32 gray shades.