Relays alone are used for the logic. Some designs employ resistors. I wanted to see what I can do without them. Here, resistors are used for current limiting for the display, but not for the logic.
A total of 123 NAIS (Matsushita / Panasonic) TX2-5V DPDT relays are used. Its footprint is 0.3 in by 0.6 in. I happened to find a dealer on Taobao that sold used ones for ¥0.6. I tested each of the 132 that I ordered, and 3 turned out not working. Those that I soldered on to the board have all worked properly till now.
ICs are used to generate a 1/2 Hz signal driving the first bit's relays. And all bits after that are generated with relay counters.
For the counters, 4 relays are used for most bits, and 3 for those that only go from 1 to 0 when the whole digit wraps over. In some other designs, resistors are used to make some relays slower than the rest. My design does not depend on the relays' timings relative to each other. However, it does require that the 2 poles of a relay should both open before one makes contact with the other contact when switching.
The display is driven with lookup tables built with relays. At most 12 relays are used to drive a digit (not including maybe spare pole from the counters). Power for the display and for the logic are separated, which is a feature I did not eventually need. Also the display inputs are connected to ground when off, again which I did not need. Some relays can be saved here.
The whole thing measures 10 cm by 13 cm by 4 cm. I estimated how much space the relays could take and chose an extruded aluminum enclosure of that size at a local electronics market. It allows me to use 2 PCBs to hold the relays. I left 0.3 in for the display, just enough for the thickness of a segment display and a PCB. It is held in place by the components on the top and bottom PCBs and some Styrofoam padding. Since I wanted to use thru-hole components only, I had to put the current-limiting resistors on the back of the main PCBs. I did not notice the width of the connectors. I laid some of the pins were too close to relays, and I had to file the connectors on the ribbon cable.
The relays have a rated power dissipation of 140mW. During operation, the inside of the device reaches about 70 °C.
The pinout of the connectors to the display goes like this. Odd-numbered pins of the 32-pin connector connect to the top row of the 4 leftmost digits. Even-numbered pins connect to the bottom row of those digits along with power to the colons and ground. Even-numbered pins of the 16-pin connector connect to the top row of the 2 rightmost digits. Odd-numbered pins connect to the bottom row, along with power and ground.
I put the 32-pin connector on to the PCB, and then learned that they do not have 32-pin connectors of this type, so I used a 34-pin one.
A video of it working.