A text-editing application uses binary sequences to represent each of 200 different characters. What is the minimum number of bits needed to assign a unique bit sequence to each of the possible characters?

To find the minimum number of bits needed to represent 200 different characters, we need to find the smallest power of 2 that is greater than or equal to 200.

Here are the steps:

1. Start with 2^0 = 1. This is less than 200.
2. Move to 2^1 = 2. This is still less than 200.
3. Continue this process until you reach a power of 2 that is greater than or equal to 200.

Following these steps:

2^0 = 1 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 16 2^5 = 32 2^6 = 64 2^7 = 128 2^8 = 256

So, 2^8 = 256 is the smallest power of 2 that is greater than or equal to 200. Therefore, the minimum number of bits needed to represent 200 different characters is 8.