It doesn’t really “know” anything. It’s just a machine doing a job. I’m going to oversimplify, not all monitors work like this but it’s a good description of the important parts.
Part of that job is “listening” to the signal coming down the cable. The machine that does this job has a “clock” signal it uses. Signals computers send are often like music, they have a “rhythm” and the things that listen for signals only read the “note” in between beats. The “note” in this case will be a signal that is either high voltage (“on” or “1”) or low voltage (“off” or “0”). There is a complex code based on series of those signals sort of like Morse code that is how the computer communicates with the monitor.
So the monitor, after startup, starts reading the “notes” on the cable and waits until it sees a certain pattern. That pattern means “this is the start of a frame”.
So when the monitor gets that signal, another part of it starts to work. This is a tiny computer responsible for changing the colors of the pixels. It doesn’t really remember what color any of them are, it’s not that sophisticated.
Now the “signal reader” expects the next few signals to represent the color of a pixel. There’s a special code for how the high and low voltages correspond to a color. Once it reads enough signals, it tells the “pixel changer” to change the “first” pixel to the color it just read. Then it listens to the signal for more patterns and tells the “pixel changer” what color the “second” pixel should be. This happens once for every pixel, so at the end every pixel has been told what color to be. If it didn’t change, it just gets told to “change” to the same color.
How does the “pixel changer” actually pull this off? Well, it’s kind of the same. It has a special circuit that works kind of like a switch to connect itself to any pixel it wants. Once it’s connected to a pixel, it can control how much red, green, or blue that pixel is going to display. So it uses the signal it gets from the “signal reader”, coverts that to the appropriate amounts of red/green/blue, then outputs a signal to the pixel that means “change to these amounts of red/green/blue”.
(It’s kind of more complicated than that. There’s not really “a pixel” in modern displays. It’s really just a tiny area that happens to have a lot of little different-colored lights. Making “a pixel” be a certain color involves controlling how bright each light is in a specific area. That makes a the area on the screen that counts as “a pixel” look like the correct color.)
A lot of this is more complex in reality, but we can imagine it as those three little systems talking to each other using a special code. The “signal reader” listens for signals from your computer that tell it the color for each pixel. It tells the “pixel changer” what color each pixel should be. The “pixel changer” does the work to adjust the actual pixels so they display the right color.
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