How many data bits are needed to represent 46 gray shades?

How many data bits are needed to represent 46 gray shades?

• A. 46
• B. 6
• C. 5
• D. 8

Answer: (C)

To encode a certain number of distinct shades, you need enough codes to cover that many values. The number of distinct codes you can represent with n bits is 2^n. So for 46 gray shades, you look for the smallest n such that 2^n ≥ 46. Five bits give 2^5 = 32 possibilities, which isn’t enough. Six bits give 2^6 = 64 possibilities, which does cover 46 shades. Therefore, six data bits are needed. Using Gray coding doesn’t change the bit count; it just changes the pattern of bit transitions between adjacent shades.

To encode a certain number of distinct shades, you need enough codes to cover that many values. The number of distinct codes you can represent with n bits is 2^n. So for 46 gray shades, you look for the smallest n such that 2^n ≥ 46. Five bits give 2^5 = 32 possibilities, which isn’t enough. Six bits give 2^6 = 64 possibilities, which does cover 46 shades. Therefore, six data bits are needed. Using Gray coding doesn’t change the bit count; it just changes the pattern of bit transitions between adjacent shades.