Are there such encodings in which each byte (each byte out of 256 possible) encodes an ordered pair of keyboard characters?

Question

Character encoding

Are there such encodings in which each byte (each byte out of 256 possible) encodes an ordered pair of keyboard characters?

Answer 1

For keyboards with eight or fewer keys, ASCII. With more keys, one byte is not enough.
To encode ordered pairs of a standard 113-key keyboard, you need ⎡log ₂ (113*113)⎤ = 14 bits.

Answer 2

How do you even imagine it?
Let's say that if each character of a pair is encoded with one nibble, then it will be 256 pairs of two sets of 16 characters each. 16 characters is not enough for the alphabet, only enough for numbers and arithmetic signs.
If you divide a byte into 5 and 3 bits, there will be 32 characters and 8. This, with reservations, is enough for Latin consonants and vowels, that is, for syllables, but this will turn out to be a rather useless and inconvenient way to encode. Perhaps this design is suitable for storing compound characters (like Korean or Japanese syllabic characters), but it's still somehow through the ass.