All currently functioning computers rely on such gates. Most likely, millions and millions of them are in your cellphone.
If you're at least a little familiar with formal logic, more specifically logical connections such as "and", "or", "nor", "xor" (="exclusive or") and so on, the way these circuits work will probably make sense to you very quickly.
I've written a few posts recently about a logic gate simulator I am writing in Python, pyGates. I won't say I finished it, because there are still a few bugs that come up every now and then, but it's far enough along for others to use. Here's a screenshot of what it currently looks like:
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You can create new gates by simply dragging them from the left side of the screen, and destroy them by simply dragging them back there. This is actually the only part where I still get bugs every now and then, sometimes cables don't get destroyed properly, but I'll work on fixing this. For now, you can usually work around that by manually deleting the cable - detaching it from the other gate it is connected to, and clicking into empty space.
The website for the project, a zip file with everything you need and the raw source code is located at my website here: http://home.in.tum.de/~dowling/pyGates/.
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