CHAPTER 7 Digital Electronics

By the end of this chapter, you will be able to:

understand how resistors are used to make potential dividers in control and logic circuits.

understand elementary logic and memory circuits that exploit devices such as bistable and astable switches, logic gates and resistors as potential dividers.

know that logic circuits are able to store and process binary information and that this can be exploited in an increasingly wide variety of digital instruments.

Keywords

1. astable switches
2. binary information
3. bistable switches
4. logic gates
5. potential dividers

7.1: Introduction

In chapter 2, you were introduced to the concept of resistance and how resistors are used in different circuits. You were also introduced to the concept of diodes. These are some of the components of electronic systems. We use electronics devices in many instances in everyday life. The phones we use, the TVS we use, the radios, computers and many others are all digital electronic devices. But how do they work? How do we get signals on these devices?

In this chapter, you will be able to understand how signals are generated from these electronic devices and how these devices can be applied in a variety of systems to solve daily life problems.

7.2: Potential Dividers

Revision

1. Using the knowledge that you acquired when you studied electric circuits: What happens to the output voltage when resistors (2 or more) are connected in series?
2. Basing on your answer(s) in (1) above, do you think it is necessary to connect the resistors in series? Explain your response. A potential divider consisting two resistors (R, and R) in series can be represented as shown in Figure 7.1.

Using the above equations, it can be understood that the total potential their resistances. By choosing the appropriate resistor values, the potential difference across the resistances can be varied.

7.3: Application of Potential Dividers

Potential dividers are widely used in sensory circuits. The change in the physical property of a sensor has to be processed before it can be displayed or measured. Light-dependent resistors and thermistors are two examples of sensory devices whose resistances vary with light and temperature respectively. The resistance of a light-dependent resistor decreases as the light intensity increases. The resistance of the thermistor decreases with rise in temperature. A potential divider can be used to process the information obtained from these sensory devices.

Consider a potential divider circuit as shown in Figure 7.2. A sensory device can be placed in the position of R2.

7.4: Binary System and Logic Gates

7.4.1: Logic Gates

Activity 7.1 Analysing a logic gate in real life

Key question: Why should a school have a gate?

What you need

Figure 7.6 showing a school gate.

Figure 7.6: School gate

What to do

1. Why do you think schools must have a fence and a gate?

2. What are the challenges related to lack of a gate in a school?

3. Study Figure 7.6. Why do you think School gates are mostly constructed directly in front of the administration block?

4. Discuss reasons why a school needs to have a gate.

5. Relating the experience of your school to an electric circuit, do you think a circuit at some point may need a gate? Explain your answer.

In an electric circuit, a switch acts like a gate; it can allow current to flow in the circuit or not. In electronics, we assign the number 1 to indicate that current is flowing and the number 0 to indicate that current is not flowing. If a switch uses 1 to indicate flow of current in a circuit and 0 to indicate no flow of current in the circuit, such a switch is called a logic gate. This system of using 1 for a true value and 0 for a false value is called binary system and the resulting algebra is known as Boolean algebra.

Activity 7.2 Realising the use of 0 and 1 in a circuit

Key question: How can the binary system be used in a circuit? What you need A cell • A battery What to do Connecting wires A bulb

1. Arrange your set-up as shown in Figure 7.7.

Figure 7.7: Implementing the binary system in a circuit

2. What happens to the bulb when you close the switch? Use 1 or 0 to describe your observation.

3. Open the switch now, what happens to the bulb? Also use 1 or 0 to describe your observation.

4. Make a general conclusion about the use of the binary digits 0 and 1 in an electric circuit.

7.4.2: Types of Logic Gates

There are three types of logic gates namely, the AND gate, the OR gate and the NOT gate. The AND gate requires that all the switches must be ON (they must be at binary level 1) before the output can be a current flowing in the circuit (output is at level 1).

NOTE:

(i) The NOT gate negates the output of an electric circuit that is to say, if the output is a 1, the NOT gate changes it to 0. If the output is a 0, the NOT gate changes it to a 1. \

(ii) The binary system deals with variables that take on two discrete values (0 and 1), which assume logical meaning. These two discrete values of the variables may be called by different names (e.g. true and false, yes and no, high and low e.t.c).

7.4.3: Circuit Representation of the Logic Gates

The AND gate is also known as the multiplication operation and is represented by dot (.) sign in Boolean algebra of digital logic gates. The logic operation A AND B can be written as A.B = AB. Note that A.B = 1 if and only if both A and B have values of 1. The circuit symbol for an AND gate is shown in Figure 7.10.

The OR gate is also known as the Addition operation and is represented by the plus (+) sign in Boolean algebra of digital logic gates. The logic operation A OR B can be written as an A+B = B+A. Note that A+B = 1 if and only if either both A and B have values of 1 or when either of the gates A or B has a value of 1. The circuit symbol for an OR gate is shown in Figure 7.11.

Figure 7.11: The OR gate Figure 7.10: The AND gate

EXERCISE 7.5

Construct the Truth table for the NAND gate and the NOR gate with three inputs.

7.7: Application of Logic Gates

A highway lighting system can be controlled using the three basic gates (switches). If the light is off, clicking any one of the three switches turns it on. If the light is on, clicking any one of the three switches turns it off. A fourth input variable is needed to register the current state of the light (1 = on, 0 = off). The output variable should be 1 when the light is to be turned on and 0 when it is to be turned off.

Logic gates have a lot of applications, but they are mainly based upon their mode of operations or their truth table. Basic logic gates are often found in circuits such as safety thermostat, push-button lock, automatic watering system, light- activated burglar alarm and many other electronic devices. One of the primary benefits is that basic logic gates can be used in a mixture of different combinations if the operations are advanced. Besides, there is no limit to the number of gates that can be used in a single device. However, it can be restricted due to the given physical space in the device.

Research 7.1

Research on how automatic alarm systems, electric sensors use logic gates in their operation and report your findings.

7.8: Logic Circuits

A logic circuit is a circuit that executes a processing or controlling function in a computer. This circuit implements logical operations on information to process it. It utilises two values for a given physical quantity (voltage, for example) to denote the Boolean values true and false or 1 and 0 respectively. They have inputs with the corresponding outputs, which can be dependent on the inputs. In logic circuit diagrams, connection from one circuit’s output to another circuit’s input is displayed as an arrowhead at the input end.

The performances of logic circuits are similar to programming language functions. The inputs are similar to function parameters while the outputs are similar to function returned values. A logic circuit can accommodate multiple outputs.

7.8.1: Types of logic circuitry

Research 7.2

Using the internet or textbooks in the library, research on Combinational Circuitry, Routing, Computational and State circuitry. Also, find out about Processor Datapath and Multivibrators. Make simple notes of your findings.

7.8.2: Definition of Terms Used

1. Active HIGH – if the state change occurs from a “LOW” to a “HIGH” on the clock’s pulse rising edge or during the clock width.

2. Active LOW – if the state change occurs from a “HIGH” to a “LOW” on the clock’s pulses falling edge.

3. Clock Width – this is the time during which the value of the clock signal is equal to a logic “1”, or HIGH.

4. Clock Period – this is the time between successive transitions in the same direction, i.e. between two rising or two falling edges.

5. Duty Cycle – this is the ratio of the clock width to the clock period.

6. Clock Frequency – the clock frequency is the reciprocal of the clock period:

Frequency= 1/clock period (f=1/T)

Clock pulse generation circuits can be a combination of analog and digital circuits that produce a continuous series of pulses (these are called Astable multivibrators) or a pulse of a specific duration (these are called Monostable multivibrators). Combining two or more multivibrator circuit provides generation of a desired pattern of pulses (including pulse width, time between pulses and frequency of pulses).

There are basically three types of clock pulse generation circuits:

1. Astable – A free-running multivibrator that has NO stable states but switches continuously between two states; this action produces a train of square wave pulses at a fixed known frequency.

2. Monostable – A one-shot multivibrator that has only ONE stable state as once externally triggered it returns to its first stable state.

3. Bistable – A flip-flop that has TWO stable states producing a single pulse either HIGH or LOW in value.

One way of producing a very simple clock signal (or pulse) is by the interconnection of digital logic gates. As NAND gates contain current amplification, they can also be used to provide a suitable clock signal or timing pulse with the aid of a single capacitor and resistor to provide the required feedback and timing functions. These timing circuits are often used because of their simplicity and are also useful if a logic circuit once designed has some unused gates which can be utilised to create a monostable or astable oscillator. This simple type of RC Oscillator network is sometimes called a “Relaxation Oscillator”.

Research 7.3

Search on the internet or otherwise about the following and make simple notes:

1. How to construct a bistable switch from two NOR gates and represent this on a diagram.

2. How bistable switches may be used in a binary counting circuit.

3. How logic circuits store and process binary information.

4. How digital instruments use binary information.

Chapter Summary

In this chapter you have learnt that:

1. a potentiometer is a variable resistor connected as a potential divider to give a continuously variable output voltage.
2. AND gate gives an output of 1 if both the two inputs are 1, it gives 0 otherwise.
3. OR gate gives an output of 1 if either of the two inputs are 1, it gives 0 otherwise.
4. NOT gate gives an output of 1 input is 0 and vice-versa.
5. NAND gate (negates AND gate) gives an output of 0 if both inputs are 1, it gives 1 otherwise.
6. NOR gate (negates OR gate) gives an output of 1 if both inputs are 0, it gives O otherwise.
7. a multi-vibrator is a electronic circuit used to implement a variety of simple two stage system such as: Oscillators, Timers and Flip- Flop.
8. a multi-vibrator circuit oscillates between ‘HIGH’ or ‘LOW’ state providing a continuous output.
9. there are basically 3 types of clock pulse generation circuit (multi-vibrators). These are: a) Stable: A free running multivibrator that has NO stable state but switches continuously between the two states; this action produces a train of square wave pulse at a fixed frequency. b) Monostable: A one shot multivibrator that has only one stable state and is triggered externally with it returning to its first stable state. c) Bistable: A flip-flop that has two stable states that produce a single pulse with either positive or negative in values.