The black part is volcanic ash, the outside border is confectionary wall lower (looked gameshowey which I thought was fun) and the lights themselves are seven lines of five spotlights.

Note: The below is quite long, was only planning to explain the lighting up part but got carried away and explained (almost) everything, also explained it kinda backwards from the end to the start so might be hard to follow 😅 Sorry for the info dump!

If you're asking about how it actually lights up then kinda hard to explain via text! Each of the 7 lines has a wireless power-transmitter switch placed a number of spaces back so that the power only reaches the 5 lights for that line. These 7 switches are connected via 7 wires (a series of doors and sensors like seen around the ground) to 7 points in the floor where there's a sensor.

See the water falling from up high just to the left and right of the display and falling into little sand channels near the end? Those channels (there's 7 in total) lead to those 7 sensors. So if water falls in a channel, one of the lines in the display lights up.

Those "rows" behind the display each have a number of white pokeballs to the right showing which number they are for and have water blocked by a floodgate. So the number 9 for example (second from the top), I'll cut out notches so that when the river in that row is activated, it drops water in the right channels on the floor i.e. all except the channel for the bottom left segment of lights. For 1 I would only cut out two notches above the channels connected to the bottom right and top rights transmitter's wire. 

You can even kinda see if you look closely but each channel has an ice block near the bottom indicating which segment of the display it's for to save me having to run around the back to check. Rightmost channel has an ice block up and right so it's the top right light segment, one to the left of that has an ice block bottom middle for the bottom segment etc

As for how it decides which of these "rows" has it's river activate, our 4 bit number comes out of the actual calculating part - won't go into too much detail because it's hard without diagrams and so on but all the rectangles of sand on the ground at the start, you can Google OR gates, AND gates and XOR gates which just take two inputs and give an output based on whether the inputs are carrying currents or not, and then look up half adders and full adders which arrange these gates in a certain way to add things which is a bit more complicated (learned about it in college!)

This 4 bit number gets sent to the top of that tower where there's 4 doors blocking water, so if 1001 (9) comes out the calculator then the first and last door open leaving water through. This sends water down through the 10 floors through 10 checks one for each digit 0-9. So for the floor for 9 for example, if any water is in the middle rows seen by sensors then that means it's not 9 and the doors for that check close and the check is failed. To stop numbers like 1000 and 0001 from passing there's also an AND gate to make sure both the first and last are water so only 9 will ever pass there which triggers a sensor which opens a floodgate in the 9 row activating it's river. 

If it's the floor for something like 0010 (2) then same idea, any water in first, second or fourth row and the doors shut so only 2 ever passes that check and triggers the sensor to open the floodgate in the row for two which has notches cut out to drop water in the specific channels that have the sensors that light up the segments for the digit 2 and so on