What is an N-bit machine?

In early computer designs, arithmetic registers were much longer than
addresses, the classic examples being machines with 36-bit words and 15-
to 18-bit addresses.

Large logical address spaces started with the IBM 360, which had 32-bit
arithmetic registers and 32-bit address registers. You couldn't put
32-bits worth of physical memory in a machine for over a decade after it
appeared, but it was allowed for in the architecture.

Nowadays, the bit-ness of a machine seems to be the *smaller* of the
arithmetic registers and the address space. This became true in the early
1970s, as far as I can see, and the terminology became confused around
then. A few examples from that period:

Classic "8-bit" microprocessors, such as the 8080 or 6800 have 8-bit
arithmetic and 16-bit addressing.

The PDP-11 has 16-bit arithmetic and 16-bit addressing, plus
bank-switching.

The original 8086 has 16-bit arithmetic and a strange 20-bit addressing
scheme.

Modern architectures have arithmetic and address registers that are the
same size.

John