14.9 Digital Electronics and Logic Gates

In electronics circuits like amplifiers, and oscillators, introduced to you in earlier sections, the signal (current or voltage) has been in the form of continuous, time-varying voltage or current. Such signals are called continuous or analog signals. A typical analog signal is shown in Figure. 14.27 (a). Fig. 14.27 (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. A binary number has only two digits ‘ 0 ‘ (say, 0 V ) and ‘ 1 ‘ (say, 5V). In digital electronics, we use only these two levels of voltage as shown in Fig. 14.27(b). 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.

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.

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.

14.9.1 Logic gates

A gate is a digital circuit that follows certain logical relationship between the input and output voltages. Therefore, they are generally known as logic gates – gates because they control the flow of information. 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. Truth tables help understand the behaviour of logic gates. These logic gates can be realised using semiconductor devices.

(i) NOT gate

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. 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. 14.28.

(ii) OR Gate

An \(O R\) gate has two or more inputs with one output. The logic symbol and truth table are shown in Fig. 14.29. The output Y is 1 when either input A or input B or both are 1 s, that is, if any of the input is high, the output is high.

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.

Example 14.8: Justify the output waveform (Y) of the OR gate for the following inputs A and B given in Fig. 14.30.

Solution: Note the following:
At \(t<t_1\); \(\mathrm{A}=0, \mathrm{~B}=0 ; \quad\) Hence \(\mathrm{Y}=0\)
For \(t_1\) to \(t_2\); \(\mathrm{A}=1, \mathrm{~B}=0 ;\) Hence \(\mathrm{Y}=1\)
For \(t_2\) to \(t_3\); \(\mathrm{A}=1, \mathrm{~B}=1 ; \quad\) Hence \(\mathrm{Y}=1\)
For \(t_3\) to \(t_4\); \(\mathrm{A}=0, \mathrm{~B}=1 ; \quad\) Hence \(\mathrm{Y}=1\)
For \(t_4\) to \(t_5 ; \quad \mathrm{A}=0, \mathrm{~B}=0 ;\) Hence \(\mathrm{Y}=0\)
For \(t_5\) to \(t_6 ; \quad \mathrm{A}=1, \mathrm{~B}=0 ;\) Hence \(\mathrm{Y}=1\)
For \(t>t_6 ; \quad \mathrm{A}=0, \mathrm{~B}=1 ; \quad\) Hence \(\mathrm{Y}=1\)
Therefore the waveform Y will be as shown in the F1g. 14.30.

(iii) AND Gate

An AND gate has two or more inputs and one output. The output Y of the 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. 14.31

Example 14.9: Take A and B input waveforms similar to that in Example 14.8. Sketch the output waveform obtained from the AND gate.

Solution: 

For \(t \leq t_1\); \(\quad \quad \mathrm{A}=0, \mathrm{~B}=0 ;\quad \quad\)Hence \(Y=0\)
For \(t_1\) to \(t_2\) \(\quad \quad \mathrm{A}=1, \mathrm{~B}=0 \quad \quad\); Hence \(Y=0\)
For \(t_2\) to \(t_3\) \(\quad \quad \mathrm{A}=1, \mathrm{~B}=1 \quad \quad\); Hence \(Y=1\)
For \(t_3\) to \(t_4\); \(\quad \quad \mathrm{A}=0, \mathrm{~B}=1 \quad \quad\); Hence \(Y=0\)
For \(t_4\) to \(t_5\) \(\quad \quad \mathrm{A}=0, \mathrm{~B}=0 \quad \quad\); Hence \(Y=0\)
For \(t_5\) to \(t_6\); \(\quad \quad \mathrm{A}=1, \mathrm{~B}=0 \quad \quad\); Hence \(Y=0\)
For \(t>t_6\) \(\quad \quad \mathrm{A}=0, \mathrm{~B}=1 ;\quad \quad\) Hence \(Y=0\)
Based on the above, the output waveform for the AND gate can be drawn as given below.

(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. Figure 14.33 shows the symbol and truth table of the 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 14.12 and 14.13).

Example 14.10: Sketch the output Y from a NAND gate having inputs A and B given below:

Solution:

For \(t<t_1 ; \quad \mathrm{A}=1, \mathrm{~B}=1 ; \quad\) Hence \(\mathrm{Y}=0\)
For \(t_1\) to \(t_2 ; \quad \mathrm{A}=0, \mathrm{~B}=0 ; \quad\) Hence \(\mathrm{Y}=1\)
For \(t_2\) to \(t_3 ; \quad \mathrm{A}=0, \mathrm{~B}=1 ; \quad\) Hence \(\mathrm{Y}=1\)
For \(t_3\) to \(t_4 ; \quad \mathrm{A}=1, \mathrm{~B}=0 ; \quad\) Hence \(\mathrm{Y}=1\)
For \(t_4\) to \(t_5\); \( \quad \mathrm{A}=1, \mathrm{~B}=1 ; \quad\) Hence \(Y=0\)
For \(t_5\) to \(t_6\) \(\quad \mathrm{A}=0, \mathrm{~B}=0 ;\quad\) Hence \(Y=1\)
For \(t>t_6\); \(\quad \mathrm{A}=0, \mathrm{~B}=1 ;\quad\) Hence \(Y=1\)

(v) NOR Gate

It has two or more inputs and one output. A NOT-operation is 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. 14.35.

NOR gates are considered as universal gates because you can obtain all the gates like AND, OR, NOT by using only NOR gates (Exercises 14.14 and 14.15).

Faster and smaller: the future of computer technology

The Integrated Chip (IC) is at the heart of all computer systems. In fact ICs are found in almost all electrical devices like cars, televisions, CD players, cell phones, etc. The miniaturisation that made the modern personal computer possible could never have happened without the IC. ICs are electronic devices that contain many transistors, resistors, capacitors, and connecting wires – all in one package. You must have heard of the microprocessor. The microprocessor is an IC that processes all information in a computer, like keeping track of what keys are pressed, running programmes, games, etc. The IC was first invented by Jack Kilky at Texas Instruments in 1958 and he was awarded Nobel Prize for this in 2000. ICs are produced on a piece of semiconductor crystal (or chip) by a process called photolithography. Thus, the entire Information Technology (IT) industry hinges on semiconductors. Over the years, the complexity of ICs has increased while the size of its features continued to shrink. In the past five decades, a dramatic miniaturisation in computer technology has made modern-day computers faster and smaller. In the 1970s, Gordon Moore, co-founder of INTEL, pointed out that the memory capacity of a chip (IC) approximately doubled every one and a half years. This is popularly known as Moore’s law. The number of transistors per chip has risen exponentially and each year computers are becoming more powerful, yet cheaper than the year before. It is intimated from current trends that the computers available in 2020 will operate at \(40 \mathrm{GHz}(40,000 \mathrm{MHz})\) and would be much smaller, more efficient and less expensive than present-day computers. The explosive growth in the semiconductor industry and computer technology is best expressed by a famous quote from Gordon Moore: “If the auto industry advanced as rapidly as the semiconductor industry, a Rolls Royce would get half a million miles per gallon, and it would be cheaper to throw it away than to park it”.