This is the second of four papers in a series containing THE FIRST THEORETICAL DISCUSSION OF PROGRAMMING, and the first use of "flow diagram" as a logical tool used to express mathematical problems, EVENTUALLY FORMING THE BASIS FOR ALL COMPUTER PROGRAMMING. As the authors state in the preface, "[this report] is essentially the second paper referred to in the Preface of the earlier report entitled, "Preliminary Discussion of the Logical Design of an Electronic Computing Instrument [by Burks, Goldstine and von Neumann]... dated, 28 June 1946)"

Von Neumann and Goldstine worked closely and collaborated together at the Institute for Advanced Study based mostly at Princeton University. In 1945 they initiated a new project to create an electronic computing instrument. Frank Aydelotte, director of the IAS, introduced the project to the board by saying: “I think it is soberly true to say that the existence of such a computer would open up to mathematicians, physicists, and other scholars area of knowledge in the same remarkable way that the two-hundred-inch telescope promises to bring under observation universes which at the present moment are entirely outside the range of any instrument now existing.” Von Neumann predicted that the device would be at the very least 10,000 times faster than the human and computer machine collaborations currently in use.

While a team was assembled, von Neumann and Goldstine began to work on a tentative aid to programming the machine. This second paper in the series provided the foundation for computer programming techniques internationally, and introduced the "flow diagram" as a logically complete and precise notation for expressing a mathematical problem.

The team at the Institute began to see the finish line of their project within five years. Julian Bigelow, an engineer, summed up the excitement: “It was happening here … and we were lucky to be in on it… A tidal wave of computational power was about to break and inundate everything in science and much elsewhere, and things would never be the same afterwards.” When testing the arithmetic unit of the machine, the team set von Neumann up to compete against the computer. When von Neumann’s calculations began to fail first they were satisfied. By the summer of 1951 the unit was functional. Its main use was to produce calculations for the hydrogen bomb. The machine ran until 1958.

Two years after the publication of this document, and four years into the project von Neumann declared: “It would appear that we have reached the limits of what is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in five years.”