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permits some additional features of RT-level design to emerge that remain hidden if a fixed set of primitives is taken. It also reflects the fact that most RT-level design is still done ad hoc, without a set of primitives in mind. Chapter 9 is on the problem of debugging a system, designing systems for testability, and testing (verifying) that the individual modules carry out their required function. To a very real extent we have completely overlooked the constraint in all problems that these designs have to be tested. We hope to be forgiven for this, for we do not approve of such design. Our only excuse is that the testing constraint might obscure the problem. For the student who builds actual systems, testing will be a very important problem, after he builds his first system.

Various supporting and reference materials are gathered into Tables at the end of the book.

Ideally all of the example problems would have been verified by either construction or simulation. This is not the case. Only a few of the designs have been wired; these include sum-of-integers, multiplication, Teletrola (by Michael Knudsen), several of the computers, and various arithmetic algorithms. Simulation has also been used on the CMU RTM simulator, but is generally top costly. Also, some of the designs are pedagodical in nature, and presented only to show tradeoffs. Therefore, the reader will no doubt find a number of errors. We hope these will be fed back to us so that we may correct subsequent versions.

The list of acknowledgements with regards to the modules is long and we will attempt to be as complete as our memories allow. It would be difficult to acknowledge all the representational work which permits the simple description of these structures, because its origin is with the state machine and flowchart. Clark's Macromodules (with engineering care and assistance of Charles Molnar), provided the main impetus to the idea that fairly large modules could exist to build digital systems, these being smaller than computer components (i.e., Processor, Memory, Switches), but still much larger than gates and flip flops packaged into Integrated Circuits. Much of the work on expressing and implementing control was taken from the PDP-6 and PDP-1O -- especially the ideas of parallel and serial branches and subroutines.

Research on basic . ideas underlying hardware modularity together with various applications, studies was supported by Advanced Research Projects Agency of the Office of the Secretary of Defense (F 44620-67-C-0058) and is monitored by the Air Force Office of Scientific Research.

The whole management group at DEC who, in fact, are on the line for deciding to produce such a collection of modules, are perhaps the only real pioneers that have anything to lose by building them. These include Kenneth Olsen, Stanley Olsen, Al Devault, and Fred Gould. Robert Pouliot and Bill Hogan finally decided to produce and distribute the textbook -- they also being responsible for module sales. This group is responsible for allowing us to experiment with the production of textbooks. The engineering group led by John Eggert, with the assistance of Peter Williams and Robert Van Naarden are to be commended for carrying basic ideas and specifications to a workable engineering solution.

Professor E. M. (Rod) Williams, former Head of Electrical Engineering at CMU, was a key factor in PDP-16's existence, since they came about through his

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