> The part I'm struggling with here is what is meant by whole-value computation, 

It means digital numeric system using integers, instead of analog or digital/analog systems. The D17 used 24 bit integer for all calculation.

> and why was it a problem for real-time systems?

It needs a lot of operations to do the job, thus considerable time and all done in a single computer (to reduce weight *1), while previous designs used two analog operating systems.

A digital system has to go through the whole calculation for a new result, while an analog's reaction time is tied to the input difference, thus fast, practically instant, on small chances - which are the usual case - while also offering in-between correction.

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## Background

The Minuteman is somewhat of a turning point in US rocket development as it's the first major design that's no longer a variation of German WW2 technology (*2). This is not only due the use of solid fuel for a large scale guided missile, but also the guidance systems. The guidance systems until that point where derived from the basic designs as used in V1/V2 guidance. While much improved, these still consisted of separate modules of an autopilot 'planning' the route to follow and a correction unit comparing this with the flight data delivered by an inertial platform, with the result sent to motor/control surfaces.

While developments previous to the D17 were greatly improved, in parts even digitalized, it was the D17 that replaced it by an integrated, all digital system. The digital nature made it possible to reduce the system in size and weight and also greatly reduce the setup time, as setting a new destination was now merely transferring a new data set onto the hard disk, which could be done in minutes instead of hours (*3)


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*1 - Weight was a major design goal for the Minuteman, beside short reaction time. It grossed only about 1/6th of the competing Soviet designs. Just by sheer size the Soviets hat the luxury to load a full-blown tube computer onto a [R-7][1] - which BTW was effectively the first iteration of today's Soyuz design.

*2 - In contrast the mentioned, in parallel developed Navaho missile is still a direct descendant of the V1 Buzz-Bomb, based on recommendations already made by German scientists during the war for future vehicles. Now beefed up in size and with improved engines and guidance systems, partly digital but still split in two.

*3 - Using air-cushioned gyroscopes further made it possible so save on spin-up time making all the other improvements count, but that's a different story.

  [1]: https://en.wikipedia.org/wiki/R-7_Semyorka