CS302 Highlighted Handouts

Lesson No. 01 AN OVERVIEW & NUMBER SYSTEMS

Analogue versus Digital

Most of the quantities in nature that can be measured are continuous. Examples include Intensity of light during the da y: The intensity of light gradually increases as the sun rises in the morning; it remains constant throughout the day and then gradually decreases as the sun sets until it becomes completely dark. The change in the light throughout the day is gradual and continuous. Even with a sudden change in weather when the sun is obscured by a cloud the fall in the light intensity although very sharp however is still continuous and is not abrupt. Rise and fall in temper ature during a 24-hour period: The temperature also rises and falls with the passage of time during the day and in the night. The change in temperature is never abrupt but gradual and continuous. Velocity of a car travelling from A to B: The velocity of a car travelling from one city to another varies in a continuous manner. Even if it abruptly accelerates or stops suddenly, the change in velocity seemingly very sudden and abrupt is never abrupt in reality. This can be confirmed by measuring the velocity in short time intervals of few milliseconds.

The measurable values generally change over a continuous range having a minimum and maximum value. The temperature values in a summer month change between 23 0C to 45 0C. A car can travel at any velocity between 0 to 120 mph.

Digital representing of quantities

Digital quantities unlike Analogue quantities are not continuous but represent quantities measured at discrete intervals. Consider the continuous signal as shown in the figure 1.1.

To represent this signal digitally the signal is sampled at fixed and equal intervals. The continuous signal is sampled at 15 fixed and equal intervals. Figure 1.2. The set of values (1, 2, 4, 7, 18, 34, 25, 23, 35, 37, 29, 42, 41, 25 and 22) measured at the sampling points represent the continuous signal. The 15 samples do not exactly represent the original signal but only approximate the original continuous signal. This can be confirmed by plotting the 15 sample points. Figure 1.3. The reconstructed signal from the 15 samples has sharp corners and edges in contrast to the original signal that has smooth curves.

If the number of samples that are collected is reduced by half, the reconstructed signal will be very different from the original. The reconstructed signal using 7 samples have missing peak and dip at 34 0C and 23 0C respectively. Figure 1.4. The reason for the difference between the original and the reconstructed signal is due to under-sampling. A more accurate representation of the continuous signal is possible if the number of samples and sampling intervals are increased. If the sampling is increased to infinity the number of values would still be discrete but they would be very close and closely match the actual signal.

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2021-02-13 18:11:03

registers important Figure 1.3 Reconstructed Signal by plotting 15 sampled values

Figure 1.4 Reconstructed Signal by plotting 7 sampled values

Electronic Processing of Continuous and Digital Quantities

Electronic Processing of the continuous quantities or their Digital representation requires that the continuous signals or the discrete values be converted and represented in terms of voltages. There are basically two types of Electronic Processing Systems. Analogue Electronic Sy stems: These systems accept and process continuous signals represented in the form continuous voltage or current signals. The continuous quantities are converted into continuous voltage or current signals by transducers. The block diagram describes the processing by an Analogue Electronic System. Figure 1.5.

samples · samples · 0C · 0C

Digital Electronic Sy stems: These systems accept and process discrete samples representing the actual continuous signal. Analogue to Digital Converters are used to sample the continuous voltage signals representing the original signal.

Do the Digital Electronic Systems use voltages to represent the discrete samples of the continuous signal? This question can be answered by considering a very simple example of a calculator which is a Digital Electronic System. Assume that a calculator is calibrated to represents the number 1 by 1 millivolt (mV). Thus the number 39 is represented by the calculator in terms of voltage as 39 mV. Calculators can also represent large numbers such as

6. 25 x 1018 (as in 1 Coulomb = 6.25 x 1018 electrons). The value in terms of volts is 6.25 x 1015 volts! This voltage value can not be practically represented by any electronic circuit. Thus Digital Systems do not use discrete samples represented as voltage values.

Figure 1.5 Analogue Electronic System processing continuous quantities

Digital Systems and Digital Values

Digital systems are designed to work with two voltage values. A +5 volts represents a logic high state or logic 1 state and 0 volts represents a logic low state or logic 0 state. The Digital Systems which are based on two voltage values or two states can easily represent any two values. For example, The numbers ‘0’ and ‘1’ The state of a switch ‘on’ or ‘off’ The colour ‘black’ and ‘white’ The temperature ‘hot’ and ‘cold’ An object ‘moving’ or ‘stationary’

Representing two values or two states is not very practical, as many naturally occurring phenomenons have values or state that are more than two. For example, numbers have widely varying ranges, a colour palette might have 64 different shades of the colour red, the temperature of boiling water at room temperature varies from 30 0C to 100 0C. Digital Systems are based on the Binary Number system which allows more than two or multiple values to be represented very conveniently.