The first computer design is widely accepted to that of Charles Babbage, and the first computer program is widely recognized to be that written by Ada Lovelace for it. Babbage's design wasn't made until 1991.
There's a lot of popular disinformation about her:
The person you're thinking of wasn't called Ada Lovelace. "Lovelace" was part of the title she acquired when her husband inherited a title. It wasn't part of her name. Augusta Ada, Countess of Lovelace. The Honourable Augusta Ada Byron before she was married. Which was also, obviously, a title and not a name so "Ada Byron" (another common mistake nowadays) is also wrong. Off the top of my head, I don't know what her title would have been after her marriage and before her husband inherited his title. Her name would have been Augusta Ada Gordon before she married but that would never have been used because the title would have overwritten it and she was born into that title. Likewise for her married name after she gained the more senior title. Off the top of my head, I don't know what would have been correct for the time between her marriage and her becoming Countess of Lovelace.
It might be "widely recognised" as the first computer program, but it's not true. The claim is made on the basis of a program (more accurately, an algorithm) she wrote that did something (I forget what) with Bernoulli numbers. Not only was it not the first program written (that one was written by, unsurprisingly, Babbage), it wasn't even the first program she wrote. Not only was it not even the first program she wrote, it wasn't even the first version of that particular program. Not only was it not even the first version of that particular program, she didn't write most of it (Babbage did). It is the first known example of one programmer fixing a mistake in another programmer's work. Babbage got part of the maths wrong. Ada, Countess of Lovelace was a much better mathematician than Babbage and noticed the mistake very quickly.
It's a shame because the simplistic (and false) claim of FIRST! overshadows what she actually did, which was more impressive. She thoroughly understood the concept of a general purpose computer. Might not sound like much nowadays, but at the time if there had been a meeting of everyone who thoroughly understood the idea that meeting could probably have been held in a lift. Her letters are often rather weird (she was hitting the drugs pretty hard) but her understanding of the concept is clear, to the extent that she was able to correctly speculate about possible future uses of a general purpose computer.
Also, Babbage's
computer has never been built. His
calculator was first built long after his death. 1991 sounds right for that, although I don't know off the top of my head. At least some parts of the calculator were built in his lifetime, as was a scale model. He kept changing it before it was finished, though, because he kept thinking of ways to make it better. Brilliant inventor, rubbish businessman. The computer was, of course, far larger and far more complicated and he'd have had a very hard time getting that built even if it did finalise the design and say "that's good enough, build it to that design". There's an ongoing attempt to build his computer for the first time but it's proving very slow going because there's a mass of drawings from numerous different (and often incompatible) versions of it. Maybe if he could have stuck with one version long enough to get it built he could have gone on to make improved versions, but he didn't work that way.