10. First Draft of a Report on the EDVAC
The three specific parts CA, CC (together C) and M correspond to the associative neurons in the human nervous system. It remains to discuss the equivalents of the sensory or afferent and the motor or efferent neurons. These are the input and the output organs of the device, and we shall now consider them briefly.
Apparently von Neumann had an unfinished book/lecture called The Computer and the Brain. This language was dropped from the second draft according to the editor. A good chunk held up apparently, but a lot has changed. The book was cited in this article that I saved for later.
A consistent use of the binary system is also likely to simplify the operations of multiplication and division considerably. Specifically it does away with the decimal multiplication table, or with the alternative double procedure of building up the multiples of each multiplier or quotient digit by additions first, and then combining these (according to positional value) by a second sequence of additions or subtractions. In other words: Binary arithmetics has a simpler and more one-piece logical structure than any other, particularly than the decimal one.
Decomposing the architecture into different specific purposes allows for things such as this. Binary simplifies the calculation and is more native to the C/M. Von Neumann notes after this that this requires conversion for input and output layers, between human readable and non-readable text.
There are certain trade offs you get overall for being in binary vs decimal. For example, using 27 bits he says, multiplication gives you 27^2 operations, and collecting/combining gives you around 1000-1500 steps, he says. In decimal this would be about 100, but he says that this is worth it in the grand scheme as a trade off for avoiding decimal math such as multiplication tables.
Even this large number can be optimized he says, by telescoping operations, which means doing them in parallel. Like all engineering problems, there are trade offs. To do double addition at the same time, your architecture needs "double adding equipment".
Von Neumann estimates that an "all-purpose automatic digital computing system" built this way would need some 10,000 plus elements. Even back in the early days of computer science, the computer was already a massive system in itself and one of the great feats of humankind.
Author: John von Neumann
Original date: 1945