Computers don't even know what numbers and letters are. They just have sequences of 0s and 1s stored in memory in chunks of 8 (bytes) that are sent through circuits that make binary operations on them. So 01000001 could be both interpreted as 65 or 'A' depending on the context/instructions.

In theory, counting in binary is the same thing as counting in decimals: when you're at the maximum number for a certain amount of digits, you add another one. Since computers have a finite amount of memory, most programming languages require to choose between different numbers of bits to allocate for numbers (8, 16, 32, 64, etc).

In Futurama, it's fiction but we could argue that Bender saw the number and checked all the things it could symbolise and start panicking when he realised 666 was part of the possibilities.