The size of a message containing 2048 characters was 2/512 part of a MB. Determine the cardinality of the alphabet.

The formula for determining the amount of information: N = 2i,

where N is the cardinality of the alphabet (number of characters),

i is the number of bits (informational weight of the character).

Let’s express 1 MB in bytes: 1 MB = 1024 KB, in turn 1 KB = 1024 bytes. Therefore: 1 MB = 1024 * 1024 = 1048576 bytes.

Considering that 1 byte = 8 bits, let’s determine the message size in bits:

2/512 * 1048576 * 8 = 32768 bits

Next, we determine how many bits one character takes:

32768/2048 = 16 bits

The power of the alphabet is N = 2 ^ 16 = 65536.