Note that a "pure" 8 bit processor, one with 8 bit data and 8 bit addresses, can't do much either. That is why there were so few of them (like the Kenbak-1) and

Note that a "pure" 8 bit processor, one with 8 bit data and 8 bit addresses, can't do much either. That is why there were so few of them (like the Kenbak-1) and most 8 bit processor were a hybrid design with a wider address like 16 or (very rarely) 24 bits. You could have a hybrid 4 bit processor too. In fact, unless just 16 nibbles gets the job done you pretty much have to use a larger address. Applications where binary coded decimal math is more interesting than regular binary, such as calculators, can be a good use for a 4 bit processor. This was the original application of the 4004, for example. And Intel ads always talked about fuel pumps.