I would say one of the versions of the Menabrea paper, written in 1842 by Luigi F. Menabrea.

Ada Lovelace became involved in computing when she was asked to translate this paper from Italian to French. She did so, and unlike many translators, was knowledgeable enough about the subject matter that rather than introducing errors into the translation, she actually corrected quite a few errors. In addition, she expanded the paper, adding a great deal of explanation not only about the machine itself, but about how it would be used to solve real problems.

Babbage saw her translation in 1843, and was happy enough with it that he asked her to expand further. She added footnotes and more explanation--in fact, what she added was about twice the length of the original paper.

The original was short enough that it might be open to argument whether it qualified as a book, but at least in my opinion, her edited version clearly did qualify.

And yes, in case there should be any question, Babbage's analytical engines were digital computers, not analog. There were decimal, not binary, but still digital. Many early computers were analog in nature (e.g., slide rules of various sorts) but Babbage's was a mechanical, digital computer.