Has there ever been a version of an arcade-perfect Donkey Kong made for a home system?

Hey everyone- I'm looking to introduce my five-year-old to Donkey Kong, the original one that appeared as a coin-operated machine in 1981. So, to my question: Is there a home-port copy of the EXACT SAME ARCADE GAME I played back then, anywhere?

Again, to be clear: I'm looking to play the original Donkey Kong at home somehow- can it be done? Because to my knowledge, every play-at-home version is missing something- be it a level (like the Cement Factory), or the way the game is played, or graphically...something is always "missing." Indeed, I have yet to come across the exact same game I used to play- in its entirety- for the home. What I don't get is: it seems like a relatively easy port- I mean, the graphics- while awesome for 1981- are certainly not difficult to replicate on a home system today. Hell, I should be able to play an arcade-perfect version on my iPhone! Why didn't Nintendo ever just do a straight-up Donkey Kong port for, say, the N64 or whatever? There were always "versions" of DK, but they were never like-for-like...

How best to show my son this game- every note, every level, etc.- without buying a coin-op machine an lugging it into my basement?