How to Write an Emulator?

If you own the original software, it's okay that you have a copy of it on your own computer. But if I go and don't have the original cartridge and I just download Super Mario Bros. that's illegal. So in essence, it's pretty impractical unless you're going to go and actually download the software. However, there is a kind of a loophole here. The reverse engineering is legal, but copying the software is the illegal part. And what uses the emulator without any software? So why would you even want to have the emulators if you don’t have the original games to run on them? It's really the- what are you doing with the software?