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I'm having the same problem. Maybe I don't understand what you mean by the word "save." When I start this program on my Windows 10 (by double-clicking on the Digital Logic Sim.exe file, since there doesn't seem to be an installer for this program), I see a dialog box with options that include creating a new project or opening an existing project. When I start a new project by giving it a name like "A New Hope," I see your screen where I can put inputs, chips, and wires. After I do some work there and I want to save the project, I get a dialog box that tells me to save it as a chip, not a project. I see the new chip. If I close the program again and reload "A New Hope," I don't see the work I was doing there. I do see the chip that was saved as "A New Hope," but that's not a project. It's a chip, and I can't continue the work I was doing in it. What am I doing wrong?
When you load an existing project (e.g. "A New Hope"), it will open on a blank editor where you can start making a new chip. From what I understand, you want to continue editing the chip you were working on before closing. To do this, once you have loaded the project, go to Menu > Library. From the library, you can select the chip you were working on, and then press the Edit button to open it.
Maybe it would be a better default behaviour to open the chip you were working on last, I'll think about changing it. I hope that helps for now!
What you're describing is not like the program I downloaded. After I load a project and open the Library, I don't see the chips that I made. I only see the ones that came with the program, and there's no Edit button to edit the chip. I was hoping that I could work on circuits without having to save every circuit as a chip, but this program doesn't work that way.