Fundamentals of Modern Digital Systems

To express any body of ideas in a meaningful form, some sort of logical framework is required. This book is concerned with digital systems, and the framework used is that based on a mathematical logic developed largely by the English mathematician George Boole. Boole published the basic axioms and rules for a two-valued algebra in 1854, but for the rest of the nineteenth century his work remained firmly in the province of mathematics (see Boole, 1953). Huntington (1904) published a set of postulates for a two-state algebra which forms the basis of our modern approach to boolean algebra. However, it was not until 1938 that this algebra was shown to be a useful tool for the engineer. Shannon (1938) introduced a switching algebra, adapting boolean algebra for use in the analysis of relay switching networks used in telephone systems. The development of digital systems since the 1940s, initially restricted to the digital computer, now extends over a seemingly unlimited range of applications. A grasp of the structure of Boole’s two-state logic is essential to the understanding of switching theory, which is itself fundamental to the design of all digital systems.

Numeracy is a relative latecomer in man’s intellectual development. The Greek and Roman civilisations had no need for anything other than a primitive numbering system and it was not until the twelfth century that the Arabic concepts of zero and positional notation were accepted. It is generally accepted that the decimal system became universally popular because man has ten readily available digits, but any other relatively small number would have served as well, if not better; twelve, for example, has more factors and would probably have been more useful.

We have seen previously how logical functions, developed from the basic equations or problem definitions, can be implemented using NAND/NOR elements and techniques for reducing the number of gates demanded by a function were also described. The introduction of devices such as the multiplexer and the read-only memory over the last decade has produced a change of emphasis in logic circuit synthesis. These complex LSI circuits make possible the realization of logic functions directly from their primitive canonical form, whilst still keeping the package count down to a minimum. Techniques for using such devices will be introduced in this chapter. However, the designer may be faced with the need to realize a logic function which he knows can be synthesized using only a few NAND/NOR gates, perhaps those contained in only one or two packages. In such cases LSI may not be the best approach and other techniques are more appropriate.

The counters and registers we considered in the previous chapter are standard sequential circuits, but many applications require other specially designed circuits, and we must now look to the general theory behind all sequential circuits in order to formulate design methods which are broadly applicable.

All organizations require some means of retaining information for later reference, and digital systems are no exception.

The invention of the transistor was announced in 1948 and the first commercial equipment using transistors was available in the early 1950s. Development of improved production techniques, especially the planar process, led to the first tentative integration of circuits about a decade later, and after small scale and medium scale integration, large scale integration was introduced in hand-held calculators and similar equipment in the late 1960s. The first microprocessor, announced in 1971, was a ‘spin-off’ from the calculator work and since then there has been a rapid development in these very large scale integrated circuits.