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Chapter 3

PMS Notation

At the PMS level, a system is described as an interconnected set of components, or individual devices, associated with a set of operations that work on a medium of information measured in bits (or some other base). Such a description is complicated by the amount of detail involved. It takes a whole manual, for instance, to describe the operations of a major computer, such as the IBM System/370. Thus the descriptive system must permit very compressed descriptions. It must also permit description of only those aspects of the components that are of interest, ignoring the rest. And what is of interest at the PMS level? Besides a description of the gross structure of a computer system, it is primarily the analysis of the amounts of information held in various components, the flows of information between components, and the distribution of the control that accomplishes these flows.

Thus a PMS-level description is analogous to the chemical engineer's diagram of a refinery in which the interest is in various kinds of liquid and gas flow. The engineer has to account for matter and energy loss with the system at various stages involving the transduction of materials from one form to another. A specific chemical plant's external performance is measured in terms of its production flow rate for a given cost. With computers, external performance is concerned with the economical accomplishment of discrete tasks, but at the PMS level this translates into operation rates and cost of operations.

For the PMS level we ignore all the fine structure of information processing and consider a system consisting of components that work on a homogeneous medium called information. Information comes in packets, called "i-units" (for information units), and is measured in bits (or equivalent units, such as characters). I-units have the sort of hierarchical structure indicated by the statement, A record consists of 300 words; a word consists of 4 bytes; a byte consists of 8 bits. A record, then, contains 300 ´ 4 ´ 8 = 9,600 bits. Each of these numbers-300, 4, 8-is called a length, since one often thinks of an i-unit as a spatial sequence of the next lower i-units of which it is composed. For example, one speaks of "word length," and of a record as "300 words long."

Other than being decomposable into a hierarchy of factors, i-units have no other structure at the PMS level. They do have a referent, i.e., a meaning. Thus it is possible to say of an i-unit that it refers to an employer's payroll, to the pressure of a boiler, or to a prime number satisfying certain conditions. To do so, of course, the i-units encode the information necessary to make the reference. At the PMS level we are not concerned with what is referred to, but only with the fact that certain components transform i-units but do not modify their meaning. In fact, these meaning-preserving operations are the most basic information- processing operations of all, and they provide the basic classification of computer components.


PMS Primitives

In PMS there are seven basic component types, each distinguished by the kinds of operations it performs:

Memory, M. A component that holds or stores information (i.e., i-units) over time. Its operations are reading i-units out of the memory and writing i-units into the memory. Each memory that holds more than a single i-unit has associated with it an addressing system by means of which particular i-units can be designated or selected. A memory can also be considered as a switch to a number of submemories. The i-units are not changed in any way by being stored in a memory.

Link, L. A component that transfers information (i.e., i-units) from one place to another in a computer system. It has fixed ports. The operation is that of transmitting an i-unit (or a sequence of them) from the component at one port to the component at the other. Again, except for the change in spatial position, there is no change of any sort in the i-units.

Control, K A component that evokes the operations of other components in the system. All other components are taken to consist of a set of discrete operations, each of which, when evoked, accomplishes some discrete transformation of state. With the exception of a processor, P, all other components are essentially passive and require some other active agent (a K) to set them into small episodes of activity.

Switch, S. A component that constructs a link between other components. Each switch has associated with it a set of possible links, and its operations consist of setting some of these links and breaking others.

Transducer, T. A component that changes the i-unit used to encode a given meaning (i.e., a given referent). The change may involve the medium used to encode the basic bits (e.g., voltage levels to magnetic flux, or voltage levels to holes in a paper card), or it may involve the structure of the i-unit (e.g., bit-serial to bit-parallel). Note that T's are meaning-preserving but not necessarily information-preserving (in number of bits), since the encodings of the (invariant) meaning need not be equally optimal.

Data-operation, D. A component that produces i-units with new meanings. It is this component that accomplishes all the data-operations, e.g., arithmetic, logic, and shifting.

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