"How Much Information is in DNA?"
(Science Week, day 2!)
Despite its layperson-defying depth and incricacy, and its attribution only to "Dynomight" who partway through claims not even to be a biologist, I've chosen this longer article for today's post for its thoughtfulness. And because, even if you don't read it carefully, the most wondrous element of it, a simple calculation, is found only two paragraphs in.
This calculation is the simplest attempt to answer the question. If you consider "information" to be data measured in computer bits, all you have to do is combine basic arithmetic with basic knowledge of DNA, and the author does that in plain sight, later comparing it to what a DVD can store.
The remaining purpose of the article seems to be the author's dissatisfaction with that definition of "information." I'll invoke a metaphor they didn't: you might consider one page from an encyclopedia to have less information than the whole encyclopedia. But if you then discovered that every page of the full encyclopedia was identical to the single page, one might concede the full encyclopedia actually contained the same amount. DNA isn't so redundant, but does contains material that doesn't seem to matter in the generation of an organism. That category of arguably "non-informational" DNA is apparently divisible into a bunch of actually meaningful subcategories which do have effects that still don't seem to affect the organism, and, in its quest to answer the question in a way that better satisfies the author, those categories are recounted and explained in some detail, along with the encompassing process of replicating DNA and winding up with proteins. I find that exploration, enabling me to vaguely visualize what happens within all of us at that unfamiliar scale, much more interesting than the framed question.
To step back and reword the question: what the author is reallyu trying to answer turns out to be pretty close to "how small could the DNA theoretically be and still result in the same organism?". That's an interesting question too, and they do ultimately propose a clear way to figure it.