Why are 8 and 256 such important numbers in computer sciences?

Question

I don\'t know very well about RAM and HDD architecture, or how electronics deals with chunks of memory, but this always triggered my curiosity: Why did we choose to stop at 8 bi

Answer 1

Since computers work with binary numbers, all powers of two are important.

8bit numbers are able to represent 256 (2^8) distinct values, enough for all characters of English and quite a few extra ones. That made the numbers 8 and 256 quite important.
The fact that many CPUs (used to and still do) process data in 8bit helped a lot.

Other important powers of two you might have heard about are 1024 (2^10=1k) and 65536 (2^16=65k).