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I was taught that it was based on the data bus width. At that time we did not have a lot of memory cashing and the external data bus matched the width of the internal buses and registers. It seems that is dated.
Recently scientists have been talking about the non linearity of time. Not so much about how Einstein's relativity relates to time but rather our perception.
As we age each year passes more quickly. We all get old much sooner then we expected too. Don't blink.
I am going to be contrary and point out that byte addressing in a CPU, greater then 8 bits, does not tend to make it an 8 bit machine.It's not that simple anymore and it wasn't simple with the PDP-11. Words were 16 bits, but the system was addressed as byte locations. It was considered a 16 bit processor. One way that might work is what's the largest integer that can be represented.
It is amazing to recall that these multi million beasties (IBM 360/40 etc) had 16MB of memory. Amazing because it was so little and amazing because it was core. That is a lot of little magnets. The memory cycle time for this machine was 2.5 ms. Register to register operations were much faster at 625ns.Through the 1970's and 1980's, the machines got bigger and faster, and multi-processor systems became common, but the basic architecture did not change. Around 1982, addresses were extended from 24 bits to 31 bits (370-XA),
I've always said, the older you get, the faster time seems to pass.