How many bits are needed to encode 27 characters, including the 26 letters of the alphabet and a space?

To determine how many bits are needed to encode 27 characters, we must consider how many unique combinations can be formed with a certain number of bits. Each bit can represent two states: 0 or 1. Therefore, the number of unique combinations that can be represented with (n) bits is calculated using the formula (2^n).

For encoding 27 unique characters, we need to find the smallest (n) such that (2^n \geq 27).

• With 2 bits, the maximum combinations are (2^2 = 4).

• With 3 bits, the maximum combinations are (2^3 = 8).

• With 4 bits, the maximum combinations are (2^4 = 16).

• With 5 bits, the maximum combinations are (2^5 = 32).

Since 32 (which is achievable with 5 bits) is the first power of 2 that is greater than or equal to 27, 5 bits are sufficient to encode the 27 characters.

The correct answer provides a bit count that allows for the representation of all the required characters with some capacity to spare, demonstrating an understanding of