Question

To encode 70 different characters in binary form, what's the minimal number of total bits required? with your answer, when all 70 characters are encoded, how many more could be encoded if we want to maximize this encoding capacity?

Answer 1

To encode 70 different characters in binary form, we need to determine the minimal number of total bits required. We can calculate this by finding the smallest power of 2 that is greater than or equal to 70.

The smallest power of 2 that is greater than or equal to 70 is 2^7, which equals 128. Therefore, we need 7 bits to encode 70 different characters.

Now, let's calculate the additional number of characters that could be encoded if we want to maximize the encoding capacity:

The maximum number of characters that can be encoded with 7 bits is 2^7, which equals 128. However, since we have already used 70 characters, we can encode an additional number of characters equal to 128 - 70 = 58.

Therefore, if we want to maximize the encoding capacity, we could encode 58 more characters using the remaining bits.