The text containing 16 384 characters occupies 22 Kbytes in the computer memory.

The text containing 16 384 characters occupies 22 Kbytes in the computer memory. Determine how many bits are allocated for each character. How many different characters can you use with this encoding?

22 kB = 22 * 1024 * 8 bits = 2 * 2 ^ 10 * 2 ^ 3 * 11 bits = 2 ^ (10 + 3 + 1) * 11 bits = 2 ^ 14 * 11 bits.

i (weight of one character) = 2 ^ 14 * 11 bits / 16 384 = 2 ^ 14 * 11 bits / 2 ^ 14 = 11 bits.

N = 2 ^ i, where N is the cardinality of the alphabet.

N = 2 ^ 11 bits.

N = 2048 bits = 2048/8 bytes = 256 bytes. 2048 different characters can be encoded.

Answer: 11 bits are allocated for each character; 2048 characters can be encoded.