Yes, but those 1's and 0's represent the physical area they came from... they contain the light/data from that original area, and that light/data will be used to recreate the same physical area in the image.
I think you are getting stuck on the dpi/ppi with inkjet printing. Instead consider sending a digital file to have a photographic print made... that system will use LED lasers with lenses to project the image onto the photographic paper. Or consider using a digital projector to display the image, also using an optical system to reproduce the image. Both are very much like the film enlarger, and the original sensor size has the same impact/relevance. You can consider the size and spacing of the pixels as being equivalent to the size/spacing of halide crystals in the film negative (just much more regular). A digital file is still very much a "digital negative."
I think you do get it... there's just one small part that isn't clicking.
If you take the same 24mp low light image with a 4/3 camera and a FF camera (same settings, different FL); and you then display them both at 100% on your monitor, the m4/3 image will look worse; noisier because it got less light (the lack of equivalence). Right?
But how can you make the 4/3 image look better on your monitor? By displaying it smaller, right? And when it reaches the 4/3 relative size (25% magnification) the relative quality of the two images will be equal (i.e. noise), just at different sizes... because they originated from different sizes. Or similarly, print it at a smaller size.
There are ceratinly other things that can play into it... different lenses between the systems, AA filter or not, etc. But the primary factor is the sensor size, and larger wins because it actually gets more light. And when you record the same image/composition the details are also projected larger onto the larger sensor, which makes them easier for the sensor to resolve.