Schazamp tried to read an I2C temperature sensor using only logic chips. It isn’t working yet, but the writeup is impressively detailed:
My project is to use logic devices to read a TC74 temperature sensor. The general idea is to have some kind of master clock (from 3 of the 74HC04’s 6 inverters), manipulate the clock to drive the SDA and SCL lines, and then clock data from a sequence of PISO shift registers (75HC165) to drive the I2C bus commands (start, device ID, write, set read address, start, device ID, read) and then, based on a series of counters, clock the response from the device off the I2C bus into a SIPO register (74HC595), and use that to drive some 74HC4511s and 7-segment displays.
Via the forum.