`color{blue}{star}` DIGITAL ELECTRONICS AND LOGIC GATES

`color{blue}{star}` INTEGRATED CIRCUITS

`color{blue}{star}` INTEGRATED CIRCUITS

`color{blue} ✍️`In electronics circuits like amplifiers, oscillators, introduced to you in earlier sections, the signal (current or voltage) has been in the form of continuous, time-varying voltage or current.

`color{blue} ✍️`Such signals are called continuous or analogue signals. A typical analogue signal is shown in Figure. 14.34(a). Fig. 14.34(b) shows a pulse waveform in which only discrete values of voltages are possible. It is convenient to use binary numbers to represent such signals.

`color{blue} ✍️`A binary number has only two digits ‘0’ (say, 0V) and ‘1’ (say, 5V). In digital electronics we use only these two levels of voltage as shown in Fig. 14.34(b).

`color{blue} ✍️`Such signals are called Digital Signals. In digital circuits only two values (represented by 0 or 1) of the input and output voltage are permissible.

`color{blue} ✍️`This section is intended to provide the first step in our understanding of digital electronics. We shall restrict our study to some basic building blocks of digital electronics (called Logic Gates) which process the digital signals in a specific manner. Logic gates are used in calculators, digital watches, computers, robots, industrial control systems, and in telecommunications.

`color{blue} ✍️`A light switch in your house can be used as an example of a digital circuit. The light is either ON or OFF depending on the switch position. When the light is ON, the output value is ‘1’. When the light is OFF the output value is ‘0’. The inputs are the position of the light switch. The switch is placed either in the ON or OFF position to activate the light.

`color{brown}ulbb("Logic gates")`

`color{blue} ✍️`A gate is a digital circuit that follows curtain logical relationship between the input and output voltages. Therefore, they are generally known as logic gates - gates because they control the flow of information.

`color{blue} ✍️`The five common logic gates used are NOT, AND, OR, NAND, NOR. Each logic gate is indicated by a symbol and its function is defined by a truth table that shows all the possible input logic level combinations with their respective output logic levels.

`color{blue} ✍️`Truth tables help understand the behaviour of logic gates. These logic gates can be realised using semiconductor devices.

`color{brown}bbul("(i) NOT gate")`

`color{blue} ✍️`This is the most basic gate, with one input and one output. It produces a ‘1’ output if the input is ‘0’ and vice-versa.

`color{blue} ✍️`That is, it produces an inverted version of the input at its output. This is why it is also known as an inverter. The commonly used symbol together with the truth table for this gate is given in Fig. 14.35.

`color{brown}bbul("(ii) OR Gate")`

An OR gate has two or more inputs with one output. The logic symbol and truth table are shown in Fig. 14.36. The output Y is 1 when either input A or input B or both are 1s, that is, if any of the input is high, the output is high.

`color{blue} ✍️`Apart from carrying out the above mathematical logic operation, this gate can be used for modifying the pulse waveform as explained in the following example.

`color{brown}bbul("(iii) AND Gate")`

`color{blue} ✍️`An AND gate has two or more inputs and one output. The output Y of AND gate is 1 only when input A and input B are both 1. The logic symbol and truth table for this gate are given in Fig. 14.38

`color{brown}bbul("(iv) NAND Gate")`

This is an AND gate followed by a NOT gate. If inputs A and B are both ‘1’, the output Y is not ‘1’. The gate gets its name from this NOT AND behaviour.

`color{blue} ✍️`Figure 14.40 shows the symbol and truth table of NAND gate. NAND gates are also called Universal Gates since by using these gates you can realise other basic gates like OR, AND and NOT (Exercises 14.16 and 14.17).

`color{brown}bbul("(v) NOR Gate")`

`color{blue} ✍️`It has two or more inputs and one output. A NOT- operation applied after OR gate gives a NOT-OR gate (or simply NOR gate). Its output Y is ‘1’ only when both inputs A and B are ‘0’, i.e., neither one input nor the other is ‘1’. The symbol and truth table for NOR gate is given in Fig. 14.42.

`color{blue} ✍️`NOR gates are considered as universal gates because you can obtain all the gates like AND, OR, NOT by using only NOR gates (Exercises 14.18 and 14.19).

`color{blue} ✍️`Such signals are called continuous or analogue signals. A typical analogue signal is shown in Figure. 14.34(a). Fig. 14.34(b) shows a pulse waveform in which only discrete values of voltages are possible. It is convenient to use binary numbers to represent such signals.

`color{blue} ✍️`A binary number has only two digits ‘0’ (say, 0V) and ‘1’ (say, 5V). In digital electronics we use only these two levels of voltage as shown in Fig. 14.34(b).

`color{blue} ✍️`Such signals are called Digital Signals. In digital circuits only two values (represented by 0 or 1) of the input and output voltage are permissible.

`color{blue} ✍️`This section is intended to provide the first step in our understanding of digital electronics. We shall restrict our study to some basic building blocks of digital electronics (called Logic Gates) which process the digital signals in a specific manner. Logic gates are used in calculators, digital watches, computers, robots, industrial control systems, and in telecommunications.

`color{blue} ✍️`A light switch in your house can be used as an example of a digital circuit. The light is either ON or OFF depending on the switch position. When the light is ON, the output value is ‘1’. When the light is OFF the output value is ‘0’. The inputs are the position of the light switch. The switch is placed either in the ON or OFF position to activate the light.

`color{brown}ulbb("Logic gates")`

`color{blue} ✍️`A gate is a digital circuit that follows curtain logical relationship between the input and output voltages. Therefore, they are generally known as logic gates - gates because they control the flow of information.

`color{blue} ✍️`The five common logic gates used are NOT, AND, OR, NAND, NOR. Each logic gate is indicated by a symbol and its function is defined by a truth table that shows all the possible input logic level combinations with their respective output logic levels.

`color{blue} ✍️`Truth tables help understand the behaviour of logic gates. These logic gates can be realised using semiconductor devices.

`color{brown}bbul("(i) NOT gate")`

`color{blue} ✍️`This is the most basic gate, with one input and one output. It produces a ‘1’ output if the input is ‘0’ and vice-versa.

`color{blue} ✍️`That is, it produces an inverted version of the input at its output. This is why it is also known as an inverter. The commonly used symbol together with the truth table for this gate is given in Fig. 14.35.

`color{brown}bbul("(ii) OR Gate")`

An OR gate has two or more inputs with one output. The logic symbol and truth table are shown in Fig. 14.36. The output Y is 1 when either input A or input B or both are 1s, that is, if any of the input is high, the output is high.

`color{blue} ✍️`Apart from carrying out the above mathematical logic operation, this gate can be used for modifying the pulse waveform as explained in the following example.

`color{brown}bbul("(iii) AND Gate")`

`color{blue} ✍️`An AND gate has two or more inputs and one output. The output Y of AND gate is 1 only when input A and input B are both 1. The logic symbol and truth table for this gate are given in Fig. 14.38

`color{brown}bbul("(iv) NAND Gate")`

This is an AND gate followed by a NOT gate. If inputs A and B are both ‘1’, the output Y is not ‘1’. The gate gets its name from this NOT AND behaviour.

`color{blue} ✍️`Figure 14.40 shows the symbol and truth table of NAND gate. NAND gates are also called Universal Gates since by using these gates you can realise other basic gates like OR, AND and NOT (Exercises 14.16 and 14.17).

`color{brown}bbul("(v) NOR Gate")`

`color{blue} ✍️`It has two or more inputs and one output. A NOT- operation applied after OR gate gives a NOT-OR gate (or simply NOR gate). Its output Y is ‘1’ only when both inputs A and B are ‘0’, i.e., neither one input nor the other is ‘1’. The symbol and truth table for NOR gate is given in Fig. 14.42.

`color{blue} ✍️`NOR gates are considered as universal gates because you can obtain all the gates like AND, OR, NOT by using only NOR gates (Exercises 14.18 and 14.19).

Q 3119580419

Justify the output waveform (Y) of the OR gate for the following inputs A and B given in Fig. 14.37.

Class 12 Chapter 14 Example 11

Class 12 Chapter 14 Example 11

Note the following:

`• At t < t_1; A = 0, B = 0; \ \ \ \ \ "Hence" \ \Y = 0`

`• For t_1\ \ "to"\ \t_2; A = 1, B = 0; \ \ "Hence" \ \Y = 1`

`• For t_2 \ \ "to" \ \t_3; A = 1, B = 1;\ \ "Hence" \ \ Y = 1`

`• For t_3\ \"to" \ \ t_4; A = 0, B = 1; \ "Hence" \ \Y = 1`

`• For t_4\ \"to" \ \t_5; A = 0, B = 0; \ "Hence" \ \Y = 0`

`• For t_5 \ \ "to" \ \ t_6; A = 1, B = 0; \ \ "Hence" \ \Y = 1`

`• For t > t_6; A = 0, B = 1; \ \ \ \ "Hence" \ \Y = 1`

Therefore the waveform Y will be as shown in the Fig. 14.37.

Q 3159680514

Take A and B input waveforms similar to that in Example 14.11. Sketch the output waveform obtained from AND gate.

Class 12 Chapter 14 Example 12

Class 12 Chapter 14 Example 12

`• For t =< t_1; \ \ \ \ \ \ A = 0, B = 0;\ \ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t_1 \ \ "to"\ \ t_2;\ \ \A = 1, B =\ \ \ \ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t_2\ \ "to" \ \ t_3; \ \ A = 1, B = 1; \ \ \ \ \ \ \ \ \ \ \"Hence" Y = 1`

`• For t_3\ \ "to" \ \t_4; A = 0, B = 1; \ \ \ \ \ \ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t_4\ \ "to" \ \t_5; A = 0, B = 0; \ \ \ \ \ \ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t_5\ \ "to" \ \t_6; A = 1 B = 0; \ \ \ \ \ \ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t>t_6: \ \ \ \ \ \ \ A = 0, B = 1; \ \ \ \ \ \ \ \ \ \ \ "Hence" Y = 0`

Based on the above, the output waveform for AND gate can be drawn as given below.

Q 3179680516

Sketch the output Y from a NAND gate having inputs A and B given below:

Class 12 Chapter 14 Example 13

Class 12 Chapter 14 Example 13

`• For t < t_1; \ \ \ A = 1, B = 1;\ \ \ \ \ \ \ \ "Hence" Y = 0`

`• For t_1\ \ \ \ \ "to" \ \ \ \ \ t_2; A = 0, B = 0;\ \ \ \ \ "Hence" Y = 1`

`• For t_2\ \ \ \ \ "to"\ \ \ \ \ t_3; A = 0, B = 1;\ \ \ \ \ "Hence" Y = 1`

`• For t_3\ \ \ \ \ "to" \ \ \ \ \ t_4; A = 1, B = 0; \ \ \ \ \ "Hence" Y = 1 `

`• For t_4\ \ \ \ \ "to"\ \ \ \ \ t_5; A = 1, B = 1; \ \ \ \ \ \ \"Hence" Y = 0`

`• For t_5\ \ \ \ \ "to" \ \ \ \ \t_6; A = 0, B = 0;\ \ \ \ \ \ \ "Hence" Y = 1`

`• For t > t_6; \ \ \ \ \ \ \ \ \ \ \ \ A = 0, B = 1; \ \ \ \ \ \ \"Hence" Y = 1`

`color{blue} ✍️`The conventional method of making circuits is to choose components like diodes, transistor, R, L, C etc., and connect them by soldering wires in the desired manner. Inspite of the miniaturisation introduced by the discovery of transistors, such circuits were still bulky.

`color{blue} ✍️`Apart from this, such circuits were less reliable and less shock proof. The concept of fabricating an entire circuit (consisting of many passive components like R and C and active devices like diode and transistor) on a small single block (or chip) of a semiconductor has revolutionised the electronics technology.

`color{blue} ✍️`Such a circuit is known as Integrated Circuit (IC). The most widely used technology is the Monolithic Integrated Circuit. The word monolithic is a combination of two greek words, monos means single and lithos means stone.

`color{blue} ✍️`This, in effect, means that the entire circuit is formed on a single silicon crystal (or chip). The chip dimensions are as small as `1mm × 1mm` or it could even be smaller. Figure 14.43 shows a chip in its protective plastic case, partly removed to reveal the connections coming out from the ‘chip’ to the pins that enable it to make external connections.

`color{blue} ✍️` Depending on nature of input signals, IC’s can be grouped in two categories: (a) linear or analogue IC’s and (b) digital IC’s. The linear IC’s process analogue signals which change smoothly and continuously over a range of values between a maximum and a minimum.

`color{blue} ✍️`The output is more or less directly proportional to the input, i.e., it varies linearly with the input. One of the most useful linear IC’s is the operational amplifier.

`color{blue} ✍️`The digital IC’s process signals that have only two values. They contain circuits such as logic gates. Depending upon the level of integration (i.e., the number of circuit components or logic gates), the ICs are termed as Small Scale Integration, SSI (logic gates < 10);

`color{blue} ✍️`Medium Scale Integration, MSI (logic gates `<=` 100); Large Scale Integration, LSI (logic gates `<=` 1000); and Very Large Scale Integration, VLSI (logic gates > 1000). The technology of fabrication is very involved but large scale industrial production has made them very inexpensive.

`color{blue} ✍️`Apart from this, such circuits were less reliable and less shock proof. The concept of fabricating an entire circuit (consisting of many passive components like R and C and active devices like diode and transistor) on a small single block (or chip) of a semiconductor has revolutionised the electronics technology.

`color{blue} ✍️`Such a circuit is known as Integrated Circuit (IC). The most widely used technology is the Monolithic Integrated Circuit. The word monolithic is a combination of two greek words, monos means single and lithos means stone.

`color{blue} ✍️`This, in effect, means that the entire circuit is formed on a single silicon crystal (or chip). The chip dimensions are as small as `1mm × 1mm` or it could even be smaller. Figure 14.43 shows a chip in its protective plastic case, partly removed to reveal the connections coming out from the ‘chip’ to the pins that enable it to make external connections.

`color{blue} ✍️` Depending on nature of input signals, IC’s can be grouped in two categories: (a) linear or analogue IC’s and (b) digital IC’s. The linear IC’s process analogue signals which change smoothly and continuously over a range of values between a maximum and a minimum.

`color{blue} ✍️`The output is more or less directly proportional to the input, i.e., it varies linearly with the input. One of the most useful linear IC’s is the operational amplifier.

`color{blue} ✍️`The digital IC’s process signals that have only two values. They contain circuits such as logic gates. Depending upon the level of integration (i.e., the number of circuit components or logic gates), the ICs are termed as Small Scale Integration, SSI (logic gates < 10);

`color{blue} ✍️`Medium Scale Integration, MSI (logic gates `<=` 100); Large Scale Integration, LSI (logic gates `<=` 1000); and Very Large Scale Integration, VLSI (logic gates > 1000). The technology of fabrication is very involved but large scale industrial production has made them very inexpensive.