I happened to google that the other day and found a 2015 Scientific American article that did a pretty good job of working through this thought experiment.
To answer that question, let us consider the work of Martin Hilbert and Priscilla López. In 2011 Hilbert and López, then at the University of Southern California and the Open University of Catalonia in Spain, respectively, published an estimate of the cultural information stored in our planet’s texts, pictures and videos. They concluded that as of 2007, humans had stored 2 × 1021 bits, or two trillion gigabits. But there is much more information in our planet than what is contained in cultural artifacts. Information is also embodied in human-designed objects, such as your car and your shoes, and in biological systems, such as your ribosomes, mitochondria and DNA. Indeed, it turns out that most of the information contained in Earth is stored in the form of biomass. Based on Lloyd’s formula, I estimate that Earth contains roughly 1044 bits. That figure might sound like a lot, but it is only a small fraction of the globe’s capacity. If humans continued to generate 1021 bits every year, it would still take much more than a trillion ages of the universe to fill our planetary hard drive.
What these calculations tell us is that although Earth has an enormous capacity to store information, order is still rare. That insight, in turn, tells us a lot about how information is created and processed by the planet and the hurdles that could limit its growth in the future.