This is an interesting and challenging experiment. Challenging because I sometimes have problems getting from schematics to breadboards, and I always have in the back of my mind that I may have cooked a chip. No cooking this time, just stupid wiring tricks. But, I got it to work.
We started with a 555 timer to send pulses to the a 74LS92 counter chip and 3 LEDs to count from 0-5 in binary, Note that the LSs are TTL chips as opposed to the HC CMOS chips we've been using.
Since the idea is to emulate dice, we need 7 LEDs, one for each dot on a die. We did that by adding a 74LS27 quad-gate triple input NOR chip, along with 4 diodes too protect inputs from flowing back into outputs. In this version we had low-current LEDs tied to GND through 4.7KOhm resistors. This LEDs were not too bright (like me). By connecting the middle dot, to one output. each of the to diagonal pairs to 2 more outputs, and the two middle side LEDs to another, we were able to produce 7 combinations from the 4 outputs by connecting thim. The middle lights on 1, 3, and 5. The middle sides light on 6 only. One diagonal lights on 2, 3. 4, 5, and 6, and the other lights on 4, 5, and 6.
Next step was to add an inverter. In the previous set up, the NOR chip needed to power the LEDs, What we want is for it to sink power, but to do that we needed to reverse the logic. We used normal LEDs connected to power through 100Ohm resistors, and connected the inverter outputs to the negative side if the LEDs. This was much better, because the LEDs are much brighter.
Making the right connections from the NOR to the inverter to the LEDs turned out to be a challenge, but I stuck with it.
Finally, I replaced the 10uf capacitor between pins 7 and 8 of the timer with a .01uf, making the lights flash 1000 times faster and the change not visible (to me, at least).
So, you hold down the pushbutton and all LEDs appear to be lit. Release the button, and you have a roll of the die. Nice dice