Digital Principles and Logic Design Techniques

The field of electronics can be broadly classified into two groups, viz. analog electronics and digital electronics. Analog electronics deals with matters which are continuous in nature and digital electronics deals with systems which are discrete in nature. But they are much inter-linked. For example, if we consider a bucket of water then it is analog in terms of the content i.e., water but it is discrete in terms of the container, i.e., bucket. Now though in nature most of the things are analog, still we very often require digital concepts. It is because it has some specific advantages over analog, which we will discuss in due course of time.

CODES AND THEIR CONVERSIONS

Binary logic deals with variables that have two discrete values—1 for TRUE and 0 for FALSE. A simple switching circuit containing active elements such as diode and transistor can demonstrate the binary logic, which can either be ON (switch closed) or OFF (switch open). Electrical signals such as voltage and current exist in the digital system in either one of the two recognized values, except during transition.

The complexity of digital logic gates to implement a Boolean function is directly related to the complexity of algebraic expression. Also increase in number of variables results in increase of complexity. Although the truth table representation of a Boolean function is unique, its algebraic expression may be of many different forms. Boolean functions may be simplified or minimized by algebraic means as described in chapter 3. However, this minimization procedure is not unique because it lacks specific rules to predict succeeding step in the manipulative process. The map method, first proposed by Veitch and slightly improvised by Karnaugh provides a simple straightforward procedure for simplification of Boolean functions. The method is called Veitch Diagram or Karnaugh Map, which may be regarded either as a pictorial representation of a truth table or as an extension of the Venn diagram.

A combinational circuit consists of logic gates, where outputs at any instant are determined only by the present combination of inputs without regard of previous inputs or previous state of outputs. A combinational circuit performs a specific information-processing operation assigned logically by a set of Boolean functions. Sequential circuits contain logic gates as well as memory cells. Their outputs depend on the present inputs and also on the states of memory elements. Since the outputs of sequential circuits depend not only on the present inputs but also on past inputs, the circuit behavior must be specified by a time sequences of inputs and memory states. The sequential circuits will be discussed in later chapter.

In chapter 5, we have discussed on various combinational circuits that are commercially available in IC package. We have also seen how other combinational circuits and Boolean functions are realized with the help of these commercially available IC packages. With the advent of large-scale integration technology, it has become feasible to fabricate large circuits within a single chip. One such consequence of this technology are the Programmable Logic Devices or in short PLDs.

So far all logic circuits we have studied were basically based on the analysis and design of combinational digital circuits. Though these type of circuits are very important, but these constitute only a part of digital systems. The other major aspect of digital system is the analysis and design of sequential digital circuits. However, sequential circuit design depends, greatly, on the combinational circuit design.

A register is a group of binary storage cells capable of holding binary information. A group of flip-flops constitutes a register, since each flip-flop can work as a binary cell. A n-bit register, has n flip-flops and is capable of holding n-bit of information. In addition to flipflops a register can have a combinational part that performs data processing tasks.

Counters are one of the simplest types of sequential networks. A counter is usually constructed from one or more flip-flops which change state in a prescribed sequence when input pulses are received. A counter driven by a clock can be used to count the number of clock cycles. Since the clock pulses occur at known intervals, the counter can be used as an instrument for measuring time and therefore period of frequency. Counters can be broadly classified into three categories:

There are numerous advantages of processing signals using digital systems and because of these advantages digital systems are widely used for control, communication, computers, instrumentation etc. In many such applications of digital systems, the signals are not available in the digital form. Therefore, to process these analog signals using digital hardware, they have to be converted into digital form. The process of conversion of analog signal to digital signal is referred to as analog to digital conversion. The system that realizes the conversion is referred to as analog to digital converter or A/D Converter or ADC.

Logic gates and memory devices are fabricated as integrated circuits (ICs) because the components used such as resistors, diodes, bipolar junction transistors and the insulated gate or metal-oxide semiconductor field-effect transistors are the integral parts of the chip. The various components are interconnected within the chip to form an electronic circuit during assembly. The chip is mounted on a metal or plastic package, and connections are welded to the external pins to form an IC. The ICs result in an increase in reliability and reduction in weight and size.

Memory is an indispensable part of computer and microprocessor based system. The information consisting of instructions for execution of program or the processing steps coded in binary form, data to be processed, intermediate and final results are required to be stored. Storing device that is a subsystem of the digital system is referred as memory. In the early era of digital system used magnetic type of memory which required large, bulky circuit boards stored in large cabinets. With unprecedented advances in semiconductor technology, it has become possible to make semiconductor memories of various types and sizes. These memory devices are very popular due to their small size, low cost, high speed and ease of expansion in memory size.