Actually dialup didn't terminate at the exchange. The signals were digitised and then sent along ISDN, potentially in bigger pipes still, to wherever they needed to go to reach the ISP's racks.
My employer purchased FRIACO from BT: calls to the FRIACO numbers were routed to us digitally where they were then demultiplexed back into individual calls, converted back to analogue and demodulated.
Yes - your digital data on dialup left your machine via DAC, digital to analogue, then ADC at the exchange, multiplexing onto a primary rate ISDN circuit for delivery to the ISP where it was demultiplexed, put through DAC, then ADC for the ones and zeroes to be fed to ongoing kit.
Same happened for non-FRIACO calls except that rather than the ISP buying the entire 32 channel primary rate ISDN bearer they went as normal calls so were billed per minute.