Question: 1111111111111111 = FFFF
Each F in this scenario is clearly only representing 4 bits.

Would 1 F not suffice in this situation?

Forgive me if this is a bit of a simpleton question, but it is just really bothering me. Thank you!

Answer: 
`F` = 15, `FF` = 255.

It's like asking "if 1 = one, why do we need 11 to mean *eleven*?"
F (in hexa) equal to 15 (and not 16).
FF (in hexa) equal to 255.

BTW, 16 in decimal is 10 in hexa.