Tip: Claude Shannon's new biography [https://www.amazon.com/Mind-Play-Shannon-Invented-Informatio...]
is an enjoyable read.
If you want a little bit of both, I highly recommend Seife's Decoding the Universe: How the New Science of Information Is Explaining Everything in the Cosmos, from Our Brains to Black Holes or Gleick's The Information: A History, A Theory, A Flood.