# Appendix III: Conversion of Analog and Digital Information

Today, the term digital is a word we hear frequently because digital circuits are becoming so widely used in computation, robotics, medical science and technology, communication, transportation, etc. Digital electronics developed from the principle that the circuitry of a transistor could be designed and fabricated easily to have an output of one or two voltage levels, based on its input voltage.

A transistor is a semiconductor used in circuits that acts as a high-speed switch or to provide amplification. Transistors have taken the place of vacuum tubes.

The two voltage levels are usually 5 volts (high) and 0 volts (low); the levels can be represented by 1 and 0. The binary numbering system (base-2 numbering system) is one of the numbering systems used in digital electronics. A digital value is represented by a combination of on and off voltage levels written as a string of 1s and 0s. When applying technology, we are constantly dealing with quantities that must be measured, monitored, recorded, or manipulated. These values must be able to be represented efficiently and accurately. Two ways of representing these values are analog and digital.

In analog representation, a quantity is represented as on a voltage meter movement or current; the representation is proportional to the value of the quantity. One example is a column of mercury in a thermometer. The height of the mercury represents the temperature, and its height changes as the temperature rises or falls. Another example is an audio microphone, in which sound waves from the voice alter as they impinge on the microphone; these variations cause output voltage to vary proportionally. The important point to remember about analog representation is that the output represented can have a continuous range of values, i.e., the temperature in a room can have any value ranging from say 60° F to 85° F, and the height of the mercury would respond accordingly.

Digital, on the other hand, utilizes circuitry whereby quantities are represented not proportionally, but by symbols called digits. An example is the digital watch, which displays the time in the form of decimal digits. Even though the time of the day is changing continuously, the digital watch changes in steps or increments of a minute, or second, or hour. Put another way, an analog value is continuous, but a digital value is discrete; because of this difference, when reading a digital value there is no uncertainty but the value of an analog quantity depends on how the person reads it and the value may be different from that which the next person reads.

Consider the following examples and indicate whether they are analog or digital:

1. ten-position switch
2. water flowing out of a meter
3. temperature of a room
4. grains of sand on a beach
5. speedometer on an automobile

Answers: A. digital, B. analog, C. analog, D. digital (the number of grains is a discrete value), E. analog if it’s the needle type, and digital if it’s the numerical readout type. Digital systems are usually electronic, but they can be mechanical, pneumatic, or magnetic. Examples are digital computers and the telephone system, the world’s largest digital system.

1. They are easier to design because switching circuits are used.
2. Storage of information is easy because switching circuits can latch onto information and hold as long as needed.
3. If more accuracy and precision is necessary, there is more of both, because additional switching circuits simply need to be added.
4. More complex programming can be done.
5. Circuits are not affected as much by noise or fluctuation in voltage.
6. Integrated circuit chips have a higher degree of integration.

Digital quantification of values does have some limitations. Values in the real world, e.g., temperature, position, pressure, velocity, and flow rate, are mainly analog. We may digitally express these quantities by saying the temperature is 80°, but we are simply making a digital estimation of an inherently analogical quantity.

To represent accurately a complicated musical signal such as a digital string, several samples of the analog signal must be taken. The analog signal is produced when sound waves hit the microphone. The waves make a diaphragm move back and forth in proportion to the sound pressure received. This diaphragm (a conductor) moving back and forth in a magnetic field creates a voltage. Notice that the voltage trace in Figure 10 is constantly changing in value. The first point taken is at 2 volts; this converts to the binary number 0000 0010. (See figure 1.) Figure 10. Graphical representation of the analog to digital conversion process.

Next, more and more points are taken as samples. To play back the music, this process is reversed. The more samples taken, the more exact the reproduction of the original conversion can be. Extra steps are involved, but when imperfections are introduced into a digital signal, variation in the digital level does not change the “on” to the “off” level. The human ear picks up this variation in an analog level, however. So “digitizing” can eliminate certain unwanted signals. Because it can help electronic noise, this characteristic of digital electronics is beneficial in RTR. Moreover, the number of steps (resolution) that the analog signal can be divided into is determined by converter’s bit number. If you were converting an analog signal ranging from 0 - 16 volts and you had a 2-bit converter, the number of steps would be 22 = 4, or four steps. Each value of analog voltage sampled, therefore, would be digitized and given one of four voltage values. This would not be very accurate or useful. If you used an 8-bit converter, however, the resolution in 28=256, and now each step will equal 16/256 or 0.0625 volt (1/16 volt). This would provide much greater accuracy. Many converters currently used in RTR systems are 8 bit. Range of grays, which provides contrast, to be at 256 different values, where 0 equals black and 255 equals white. In RTR, use of A-to-D and D-to-A converters common because of the advantages of each, but they do take time and add complexity and some expense to the system.