I think several points I made in my answer to your previous question are valid here, too.

Their computer is 15 quadrillion floating points operations per second^2 (the PS in FLOPS stands for per second)! It's accelerating!

Note that Humanity itself has had 16 PFLOPS computers for a few years now, and our current record holder is over 33 PFLOPS. EFLOPS (ExaFLOPS) computers are currently thought to be possible in 2018. 15 PFLOPS is a massive number for 1960, but for 2060, it might be more on the scale of a really beefy gaming rig, if that.

@DanielM. evolving biological computers, i say!

So by the time it gets here, it will have a speed of 4.731x10^25 FLOPS

There are historical artifacts we still cant explain, and its here on earth. Add a cultural abyss between two species. Just the fact that they are aliens is enough to justify not understanding. Make a leap, forgetting the hoax thing, and think "decode crop circles"...

What's the difference between this and your other question?

@ArtOfCode because in previous setting you can easily blame low signal and not enough of it. Here we have setting where there is plenty of signal

Have you read "Blindsight" by Peter Watts? It describes a similar encounter, where the specifics of alien intelligence make our messages completely meaningless to them. Not sure if spoilers are allowed here, though...

PFLOPS is not so much (it is in the order of magnitude of what we have on earth, and much much much less than your watch will have, by the time the alien get here)

Why would they have the ability to build a generation ship but not have more advanced computers and full AI in particular? Note that Watson is shown at 80 Tflops with 2880 cores. But a $300 GPU board can do 4 Tflops, so raw floating-point performance doesn't give the full story. Can it do thousands of completely independent calculations at once, or only huge arrays of one calculation repeated?

Related: gutenberg.org/files/19445/19445-h/19445-h.htm

We cracked the Enigma with a computer that had vacuum tubes in it. I have a problem with this being a problem, with any intelligible signal.

Solaris discusses the problems with trying to communicate with a truly alien intelligence. If the aliens are nothing at all like us, we're going to have severe difficulties communicating anything meaningful with any amount of processing power. We could transmit a series of prime numbers, but that doesn't say anything--it just looks deliberate, so it will pique the aliens' interest. In fact, the challenges in communication are so severe that I would turn the question around and ask what could cause them to understand us at all.

You don't think "alien" enough. The mere statement that "they" "have" "computers" manipulating "floating-point numbers" whose "performance" is "measured" in "FLOPs" presumes an alien civilization with far more in common with us than is reasonable to assume. Maybe "they" are not individual solids like persons, but "it" is a single gaseous cloud or liquid pool, have no concept of property, ownership or measurements, calculate in their minds à la Dune (Mentats) using analog, and have never needed any notion of performance because the thought of intra-species competition is alien to them?

I don't think there is much hope of them understanding us. Just before they get here they will intercept broadcasts of the Donald Trump and Hilary Clinton presidential campaigns. They will turn around and go home.

Don't they arrive in 2060 though? When Batman will be running for president and not Trump?

"As they are closing by, the Earth's signal is getting stronger, and stronger (obviously)." Is that due to greater proximity, or is it due to Earth getting more technologically active, and therefore sending stronger signals? (Both may be a possibility; which has more impact? That probably depends on which signal.) I would assume the ship would also carry more sensors, possibly some that get created/re-configured during trip, to look more additional signals as they get physically closer (able to sense more) and as their arrival time simultaneously approaches.

Numberphiles did a great video on the problems with aliens potentially understanding any of our languages, and vice versa: youtube.com/watch?time_continue=2&v=l4bmZ1gRqCc This would be worth considering.

Well, you're really probably imagining "alien" as in "Mexican to a Statesian", rather than "non-human-like-intelligence". After all, you're trying to write something that makes sense to humans, and we're very inclined to think everything in the universe is "human-like". However, even for relatively non-alien aliens that humans can understand, real communication can be tricky - lesswrong.com/lw/y4/three_worlds_collide_08 is quite a nice take on the problem :) Note that they immediately skip the language barrier, and it's still absurdly hard to deal together.

This short story illustrates some of the above points (and below answers) nicely: They're Made of Meat