Why is number of bits always(?) a power of two?

Question

We have 8-bit, 16-bit, 32-bit and 64-bit hardware architectures and operating systems. But not, say, 42-bit or 69-bit ones.

Why? Is it something fundamental that makes 2

Answer 1

That's mostly a matter of tradition. It is not even always true. For example, floating-point units in processors (even contemporary ones) have 80-bits registers. And there's nothing that would force us to have 8-bit bytes instead of 13-bit bytes.

Sometimes this has mathematical reasoning. For example, if you decide to have an N bits byte and want to do integer multiplication you need exactly 2N bits to store the results. Then you also want to add/subtract/multiply those 2N-bits integers and now you need 2N-bits general-purpose registers for storing the addition/subtraction results and 4N-bits registers for storing the multiplication results.