Reddit mentions of When Computers Were Human

The man who loved only numbers (on Erdos)

The imitation game Alan Turing: The Enigma (on Turing, much more in depth (and accurate) than the movie on both the life and mathematics).

And not a biography per say, When Computers Were Human, but there is a lot of focus on the people involved.

Not just banks, but all kinds of computations. Probably the first examples of organized computation dealt with astronomical data, such as computing the orbit of Halley's Comet or creating tables for navigational almanacs.

I just finished this book on the subject, and found it absolutely fascinating. Highly recommended if you're interested in historical/scientific stuff.

Actually, go ahead and take a look at this one too. Computers were mostly given one set of instructions to compute at a time and the big picture was left to the few people in charge. This book offers great account of the origins of our modern scientific method (in the same time period as some of the first book), and of course a look at a very different part of the scientific world of the day.