I know he explained it in that early scene.. but when he got in the tesseract what was happening was not very clear due to a strange lack of closeups of the relevant details. It would be like Picard pointing to something on the science station monitor and the director never cuts to show it
.... I don't know what more you wanted. We were TOLD in that earlier scene what was happening and how the information was coded. We then see in the tesseract it was Coop relaying the information by manipulating gravity (pushing the books out of the bookcase, blocking the fall of the sand, etc.) So.... what else do we need?
Did you want us to spend five minutes with Coop there going, "Let's see... Okay, the first number is a 5, in binary that's 00000101, so I need a thin line here..."
Anyone paying attention knew what was going on, the movie gave us all of the information we needed:
1. Someone/thing was leaving coded messages using the books and sand in the room.
2. The coded messages were either based on the titles of the books (Murph's theory) in Morse Code (another theory that was floated) or in Binary (what Coop revealed to be the case.)
3. Thin lines/gaps represented one value, wide ones represented the other value.
4. The coded messages were the word "STAY" and the coordinates to the NORAD/NASA base. (As well as the message being left on the watch for the solution to the gravity equation.)
5. Inside the tesseract the "ghost" was really Coop manipulating gravity in order to leave the messages for Murph to use to a)get him to not go on the mission b)find the NORAD/NASA base c)the solution to the gravity equation.
So. I'm not really sure what more we needed. It's like in, let's pick an episode almost at random...
"The Ensigns of Command"!
In the episode Picard is battling with aliens who find human language to be imprecise and a complicated legal document was drafted to precisely lay out the terms of a precarious "peace" treaty between the Federation and these aliens.
We see a couple scenes of the crew's view of the monitor as they go over the document but finally we focus on Picard as he says, "There it is!" and walks off to talk with the aliens to use a legal loop-hole to save a planet of colonists from invasion by these aliens. We're not shown from Picard's perspective what the text is that motivated Picard to make this discovery. In fact when he talks with the aliens he calls out the the numerical location of the clause (page, section, paragraph, sub-sections/paragraphs) but never outright speaks the legal mumbo-jumbo that makes this clause noteworthy.
He simply summarizes it as he explains the loophole to the aliens (and us) and how it allows him to save the colonists!
Infuriating! They gave us all of the information we needed to know how Picard saves the day but they didn't precisely tell us what this information was! I wanted to read several paragraphs of complicated legal text to know precisely how Picard exploited this loophole and discovered it!
Just like you, apparently, wanted to see Coop standing there for 20 minutes doing the math in converting decimal numbers into binary ones and then making the appropriate lines in the sand (no pun intended?) to relay the information to past Murph.