Between 1945 and 1947 John von Neumann produced a significant body of writing on computer design and programming. Some of this material is well known and widely available, but much is still only available in archives. Here is a broadly chronological description of von Neumann’s texts, with links to online copies where available.
January 30, 1945 : Memorandum on Mechanical Computing Devices
Von Neumann had consulted at the US Army Ordnance Department’s Ballistic Research Laboratory (BRL) since 1937. In January 1945, at the request of the Director, Col. Leslie Simon, who was concerned about “the growing seriousness of the computing problem that confronts the Laboratory”, von Neumann wrote a memo on “Mechanical Computing Devices” for a meeting of BRL’s Scientific Advisory Committee. The memo includes von Neumann’s account of the rationale for the EDVC [sic] and the advantages it would offer over other machines, including the BRL’s own ENIAC. A rough transcription of the memo and related correspondence is here.
March/April 1945 : the original text of the First Draft
At the end of April, 1945, von Neumann sent Herman Goldstine a long manuscript describing his perspective on the design of the EDVAC. Goldstine immediately had it typed up. The manuscript has not been traced, but the typescript is preserved in Goldstine’s archive at the American Philosophical Society. Michael D. Godfrey’s transcription of this text is available at https://archive.org/details/vnedvac.
May 8, 1945 : von Neumann letter to Goldstine
On May 8, von Neumann wrote a 28-page letter to Goldstine containing much new material which he intended to add to the manuscript. The autograph copy of this letter is in Valentine Bargmann’s papers, but as far as I know it has not been published anywhere.
June 30, 1945 : First Draft of a Report on the EDVAC
In June, 1945, Goldstine (controversially, as it turned out) had most of von Neumann’s original manuscript typed, duplicated, and circulated to project members and managers and a relatively restricted circle of well-connected outsiders. A copy of this text can be read here: https://archive.org/details/firstdraftofrepo00vonn.
1945 : Revised EDVAC design and sorting routine
In this same period, von Neumann worked on what he referred to in the May 8 letter to Goldstine as “sorting questions”. This resulted in what Donald Knuth described in a 1970 paper as “Von Neumann’s First Computer Program“. As I explain in my book Routines of Substitution, in the course of this work von Neumann significantly changed his ideas about the EDVAC’s architecture and order code, and wrote a complete “meshing routine” (to merge two sequences of numbers) using the new code. Transcripts of a little-known document describing the new code and the manuscript of the meshing routine are available here.