You may skip Sections 4 (Digital Computers) and 5 (Universality of Digital Computers), pp. 4-8, of the paper in your reading; however, resume with the last two paragraphs of Section 5, on p.9. The first section explains how a digital computer works, the second that any one computer can mimic any other (so that one need not worry about focussing on a particular computer, because they are all equivalent in some sense).
In Section 7, p.22: "10^10 to 10^15 binary digits" -- Today we would say 1GB (Gigabyte) to 10 TB (Terabytes).