How many bits are needed to represent 1024 gray shades?

How many bits are needed to represent 1024 gray shades?

• A. 8
• B. 3
• C. 1024
• D. 10

Answer: (D)

To encode a set number of grayscale levels, you need enough bits so that 2^n covers that many distinct shades. Each bit doubles how many different values you can represent. For 1024 shades, solve 2^n = 1024. Since 1024 equals 2^10, you need 10 bits. (8 bits give 256 shades, 3 bits give 8 shades, so 10 is the minimum to reach 1024.)

To encode a set number of grayscale levels, you need enough bits so that 2^n covers that many distinct shades. Each bit doubles how many different values you can represent. For 1024 shades, solve 2^n = 1024. Since 1024 equals 2^10, you need 10 bits. (8 bits give 256 shades, 3 bits give 8 shades, so 10 is the minimum to reach 1024.)