Not really a book, but check out James Burkes Connections series. Other shows he's worked on have to do with the history of science/technology as well.
The episode pertaining to the birth of the computer is here: http://www.youtube.com/watch?v=ORY-mXXgJg4&feature=PlayL...
That's worth checking out first, to give you an idea of what it's like. The rest of his stuff is here: http://www.youtube.com/profile?user=JamesBurkeWeb#g/p