Introduction to Digital Electronics

The quantities that are to be measured, monitored, recorded, processed and controlled are analog and digital, depending on the type of system used. It is important when dealing with various quantities that we be able to represent their values efficiently and accurately. There are basically two ways of representing the numerical value of quantities: analog and digital.

Systems which are capable of processing a continuous range of values varying with respect to time are called analog systems. In analog representation a quantity is represented by a voltage, current, or meter movement that is proportional to the value of that quantity. Analog quantities such as those cited above have an important characteristic: they can vary over a continuous range of values.

The Systems which process discrete values are called digital systems. In digital representation the quantities are represented not by proportional quantities but by symbols called digits. As an example, consider the digital watch, which provides the time of the day in the form of decimal digits representing hours and minutes (and sometimes seconds). As we know, time of day changes continuously, but the digital watch reading does not change continuously; rather, it changes in steps of one per minute (or per second). In other words, time of day digital representation changes in discrete steps, as compared to the representation of time provided by an analog watch, where the dial reading changes continuously.

Below is a diagram of digital voltage vs time: here input voltage changes from +4 Volts to -4 Volts; it can be converted to digital form by Analog to Digital converters (ADC). An ADC converts continuous signals into samples per second. Well, this is an entirely different theory.

The major difference between analog and digital quantities, then, can be stated simply as follows:

• Analog = continuous
• Digital = discrete (step by step)

Advantages of Digital Techniques

• Easier to design. Exact values of voltage or current are not important, only the range (HIGH or LOW) in which they fall.
• Information storage is easy.
• Accuracy and precision are greater.
• Operations can be programmed. Analog systems can also be programmed, but the available operations variety and complexity is severely limited.
• Digital circuits are less affected by noise, as long as the noise is not large enough to prevent us from distinguishing HIGH from LOW (we discuss this in detail in an advanced digital tutorial section).
• More digital circuitry can be fabricated on IC chips.

Limitations of Digital Techniques

Most physical quantities in real world are analog in nature, and these quantities are often the inputs and outputs that are being monitored, operated on, and controlled by a system. Thus conversion to digital format and re-conversion to analog format is needed.

Numbering System

Many number systems are in use in digital technology. The most common are the decimal, binary, octal, and hexadecimal systems. The decimal system is clearly the most familiar to us because it is a tool that we use every day. Examining some of its characteristics will help us to better understand the other systems. In the next few pages we shall introduce four numerical representation systems that are used in the digital system. There are other systems, which we will look at briefly.

• Decimal
• Binary
• Octal
• Hexadecimal

Decimal System
The decimal system is composed of 10 numerals or symbols. These 10 symbols are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. Using these symbols as digits of a number, we can express any quantity. The decimal system is also called the base-10 system because it has 10 digits.

103	102	101	100		10-1	10-2	10-3
=1000	=100	=10	=1	.	=0.1	=0.01	=0.001
Most Significant Digit				Decimal point			Least Significant Digit

Even though the decimal system has only 10 symbols, any number of any magnitude can be expressed by using our system of positional weighting.

Decimal Examples

• 3.14₁₀
• 52₁₀
• 1024₁₀
• 64000₁₀

Binary System

In the binary system, there are only two symbols or possible digit values, 0 and 1. This base-2 system can be used to represent any quantity that can be represented in decimal or other base system.

23	22	21	20		2-1	2-2	2-3
=8	=4	=2	=1	.	=0.5	=0.25	=0.125
Most Significant Digit				Binary point			Least Significant Digit

Binary Counting

The Binary counting sequence is shown in the table:

23	22	21	20	Decimal
0	0	0	0	0
0	0	0	1	1
0	0	1	0	2
0	0	1	1	3
0	1	0	0	4
0	1	0	1	5
0	1	1	0	6
0	1	1	1	7
1	0	0	0	8
1	0	0	1	9
1	0	1	0	10
1	0	1	1	11
1	1	0	0	12
1	1	0	1	13
1	1	1	0	14
1	1	1	1	15

Representing Binary Quantities
In digital systems the information that is being processed is usually presented in binary form. Binary quantities can be represented by any device that has only two operating states or possible conditions. E.g.. a switch is only open or closed. We arbitrarily (as we define them) let an open switch represent binary 0 and a closed switch represent binary 1. Thus we can represent any binary number by using series of switches.