Keeping things simple, firmware is identical in all four of the PIC16F1509s. When power is first applied to the system, controllers wake up, "sniff" the slots (specified using pull-up/pull-down resistors on two of their pins), then set their I2C addresses accordingly.
Of particular interest is the way in which the Microchip engineers used tools like Excel to determine the X-Y coordinates for the Nixie Tube lead holes, and for the orientations and locations of the surface-mount drive transistors (one for each cathode). The PCB was created using CadSoft EAGLE PCB Design Software and fabricated through ValueProto for $25 each, which is a really good deal for a small hobbyist prototyping run.
The Nixie Tube clock circuit board.
The video below shows the clock displaying time, followed by a random sequence, then temperature.
Day and Cappy also will discuss future enhancements, including the
addition of a pressure transducer, a humidity sensor and Wi-Fi
capability. They alos will introduce a variety of Nixie Tube resources,
including alternative Nixie Tube Clock implementations.