Fig.16.1: Digital systems and analog systems

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1 UNIT 16 LOGIC GATES Structure Introduction Objectives Boolean Algebra Logic Gates AND Gate OR Gate NOT Gate NAND Gate NOR Gate NAND and NOR Gates as Universal Gates Circuits for Logic Gates Elementary Ideas about ICs Applications of Logic Gates Summary Terminal Questions Solutions and Answers 16.1 INTRODUCTION So far your students have been dealing with analog quantities, without, of course, knowing the term. The signals that they have been using are analog signals - their values vary in a continuous fashion over a broad range with respect to time. Now you will be introducing another way of representing physical quantities: the digital mode. In the digital mode of representation, physical quantities assume only discrete values called digits. Your students are now going to lean about an important part of electronics, which involves such discrete signals or digits - that is why it is called digital electronics. Digital electronics is based on the binary number system that involves only two digits 0 and 1. Digital Systems Assume only discrete values Analog systems Values vary over a broad range continuously Fig.16.1: Digital systems and analog systems The digital representation based on two numbers (0,l) is the basis for sophisticated computers. Logically. these numbers can be used to perform varying operations that involve even mimicking the functions of the human brain. The Binary digits together form what is referred to as the "bit" in digital logic. Under the positive system of logic, we can identify the following operations: 0 = False = Off = No, and 1 = True = On = Yes.

2 Atomic,. Nuclear Physics and Electronics The "on" and "off' are used to represent flow and stoppage of current in any arcjog circuit. In most circuits 5V (analog DCV) represents it as being switched ON and 0'8; (analog (DCV) or ground as switched OFF. Using this two-valued logic system, every statement or condition must either be "true" or "false"; it cannot be partly true and partly false. While this approach may seem limited, it actually works quite nice!y, and can be expanded to express very complex relationships and interactions among any number of individual conditions. In fact, digital'or binary logic is the basis of al: digital electronics today. One essential reason for basing logical operations on the binary number systen:.; k!#-,, it is easy to design simple, stable electronic circuits that can switch back and f-4- between two clearly defined states, with no ambiguity attached. It is also possible to design and build circuits that will remain indefinitely in one state unless and until they are deliberately made to switch over to the other. Examples from analog electronics include thep-n junction diode (in its forward and reverse bias) and the bi-polar junction transistor (BJT) between its saturation and cut-off values. We can connect these devices to form logic gates, the basic components of digital circuits. A digital circuit is designed for a desired application by a combination of several logic gates. In this unit, we discuss the teaching of the basic concepts of Boolean algebra, different logic gates: AND, OR, NOT, NAND and NOR, and electronic circuits for logic gates. We also deal with integrated circuits in brief and give some real world applications of logic gates, which you can use in your teaching. Objectives After studying this unit, you should be able to: a explain better to your students; - the concepts of boolean algebra, - the operation of basic logic gates (AND, OR, NOT) and their truth tables, - the NAND and NOR gates and truth tables,. - The electronic circuits of logic gates, - integrated circuits, - the applications of logic gates. devise practical activities for helping students learn about logic gates; and assess how well your strategies have worked BOOLEAN ALGEBRA You know that Boolean algebra forms the basis of digital electronics. It is used to represent logic operations. Boolean algebra can be used to simplify logic circuits, as normal algebra is used to simplify mathematical expressions. anecdotes about his life on the following URLs: You could tell your students that b Boolean algebra is a way of describing a circuit in the form of a mathematical formula. It refers to the use of Boolean expressions to describe the relationship between the input and the output.

3 It is based on only two numbers, 0 and I, commonly thought of as "low or false" and "high or true", respectively. Binary numbers and Boolean algebra are natural to use with modern digital computers, which deal with switches and electrical currents that are either on or off.. Logic Gates Tt involves the use of three basic operations on the binary digits 0 and 1. These are called the NOT, AND and OR operations and defined as follows: > The NOT operator operates on one value (the operand) (0 or 1) and negates it: NOT 0 is 1 and NOT 1 is 0. It is represented by a bar over the Boolean variable. For example: X = Not X. (Explain to your students that operand means the value operated upon). P 'P The OR operator operates on at least two operands, and yields a high value if any of its operands (or both) are high (1 or true). It is represented by a + sign. For example: X + Y = X OR Y. The AND operator operates o,n at least two operands, and yields a high (1 or true) value if all of its operands are high (1 or true.) It is represented by a dot (0). For example: X Y = X AND Y. You can explain the NOT, AND and OR operations using Fig NOT* AND+ o 1 1 0R+l Fig.16.2: Pictorial representation of NOT, AND and OR operations These basic operations can be combined in many ways to give different outputs for combinations of inputs. You can tell your students that just as we carry out arithmetic operations on algebraic'functions, we can carry out these three operations on Boolean functions for several practical applications. The three operations can be carried out practically using electronic logic gates. Any Boolean function can be practically implemented by using these logic gates LOGIC GATES By definition, a logic gate is a circuit with one or more input voltages but only one I! output voltage. Logic gates work according to some logical relationship (involving the three logical operations AND, OR and NOT) between input and output voltages. The gates are used in digital electronics to change one voltage level (input voltage) into another (output) according to the logical relationship between them. We express the relation between possible values of input and output voltages in the,form of a table called the Truth table.

4 Atomic, Nuclear Physics and Electronics These basic logic circuits perform the logical operations of AND, OR and NOT. Do tell your students the following points so that they have a better understanding of logic gates: Electronic logic gates require a power supply to function. INPUTS to the gates are voltages having two discrete values, e.g., OV and 5V representing logic 0 and logic 1, respectively (under positive logic of operation). The OUTPUT of a gate provides one of the two values of voltage only, e.g. OV and 5V representing logic 0 and logic 1, respectively. There exist other logical gates, like the NAND, NOR, and XOR gates. NAND and NOR gates are also known as universal gates since all other operations like NOT, AND, OR, XOR and XNOR can be simulated using them. After a basic introduction to logic gates, you can go into the details of the basic logic gates AND, OR and NOT as follows: AND Gate The AND gate implements the Boolean AND function. The standard symbol of AND gate is given in Fig (In the symbol, the input terminals (A and B) are at left and the output terminal is at right.) Fig.16.3: Symbol of AND gate You can ask your students to construct the truth table for a two-input AND gate on the basis of its definition The Boolean expression for the AND gate is Point out that > The AND gate gives a high output (1) only if all its inputs are high. The AND gate is so named because it acts in the same way as the logical "AND" operator.

5 OR Gate Logic Gates I The OR gate implements the Boolean-OR function where the output is 1 when any one input is logical 1. OR gate is so named as it implements the logical "OR" operation. The standard symbol for OR gate is shown in Fig Fig.16.4: Symbol of OR gate You can have your students arrive at the truth table for a two-input OR gate using its definition. - The Boo1,ean expression for the OR gate is Point out that 1 > The OR gate gives a high output if one or more of its inputs are high. I NOT Gate The NOT gate implements the Boolean NOTfunction where the output is the inverse or complement of the input. It is also known as an inverter. If the input variable is A, the inverted output is known as NOT A. This is also shown as A', or A with a bar over the top (A). Tell students that Tbe NOT gate has only one input. The standard symbol for NOT gate is given in Fig. 16,5.

6 Atomic, Nuclear Physics and Electronics NOT Gate (an-inverter) INPUT X=Af. Presence of small circle always denotes inversion Fig.16.5: Symbol of NOT gate Let students write the truth table for the NOT gate The Boolean expression for the NOT gate is Now you can introduce some simple combinations of the basic gates such as the NAND gate and the NOR gate NAND Gate The NAND gate is an AND gate followed by a NOT gate. The symbol of the NAND gate is shown in Fig Two Inputs NAND Gate INPUTS B n u A- B- II OUTPUTS - X = (AB)' ~enbtes Inversion X = (AB)' Fig.16.6: Symbol of NAND gate It acts in the mznner of the logical operation "AND" followed by negation. Let your students construct the truth table for the NAND gate:

7 Point out that Logic Gates P The output of NAND gate is high if any of the inputs are low NOR Gate The NOR gate is a combination OR gate followed by a NOT gate. NOR means 'neither A nor B'. Thus, the output is 1 only when neither A nor B is I. The symbol for NOR gate is shown in Fig Two Inputs NOR Gate INPUTS OUTPUTS ':=(A +B)' \ Denotes Inversion Fig.16.7: Symbol of NOR gate The truth table for the NOR gate can be determined by your students Point out that P the output is 1 when none of the inputs are 0. In other words, the outputs of all NOR gates are low if any of the inputs is high. J Tell your students that if n is the number of input variables the total number of possible input combinations (N) is given by: N= 2". You can give your students some quick problems to solve before you proceed further. SAQ 1 Devise a set of questions to help students check their understanding. You could include questions like the following: a) Fill in the blanks i) In gate an output 1 is obtained when both inputs are at 1 state. ii) In NOR gate a high output is obtained when inputs are at ---- state etc. b) What will be the boolean expression for the following circuits? Give a few circuits.

8 Atomic, Nuclear Physics and Electronics You can make use of Table 16.1 to compare different logic gates. Table 16.1: Comparison of logic gates Basic Logic Gates Logic Symbol Boolean Truth English ay Expression Table Expression A B Y The only time the output is HIGH is AND Y= A-B when all the inputs are high. B A Dy A B Y The output will be HIGH when any OR Y= A+B one or all inputs are B high..a 1. A 1 Y 1 NOT NAND A + Y The output is the 0 1 opposite of the Y=A 1 0 input. A B Y The output is HIGH provided all the Y= A-B inputs are not highs B NAND and NOR Gates as Universal Gates You could explain the NAND Gate Operations as a universal gate, as follows: NAND gates can be used as NOT, AND and OR gate as shown below in Fig.16.8: - a) When the same input is given at both terminals, the output is A. b) The use of two NAND gates in succession yields the output A.B. c) Two single input NAND gates followed by another NAND gate result in the output A+ B. Explain each of these operations to your students. Ask them to construct the truth tables for each case and verify the results for themselves. 1 y-. Am NAND B Fig.16.8: Construction of NOT, AND and OR gates from NAND gates

9 NOR gate operations.~o~ic Gates NOR gates can also be used as NOT, AND and OR gate as shown in Fig Explain each of these operations to your students. Ask them to construct the truth tables for each case and verify the results for themselves. Fig.16.9: Construction of NOT, AND and OR gates frdm NOR gate You can also do the following activity to show these gates to your students. Activity 1 Take a 7400 IC (Quad 2 input NAND gates) and show the realization of all other gates (NAND, NOT, OR, AND, NOR, XOR, XNOR). It is a 14 pin DIP (Dual in line package) IC. You will need the following components to show the working of the gates: Bread-board 1 PCB (Printed Circuit Board) 1 Chassis 14 pin or greater IC base LEDs (Green, Red, Orange, Yellow) -to differentiate between the input states and output states. 5V dc supply, Connecting wires Resistance - 1 K, 3.3K to fiction as current limiting resistors Typical cost of the 7400 IC is Rs.71- We give in the margin the diagram of the 7400 IC with the interconnections: Connect the pin 14 of the 7400 IC to the positive of the 5V dc supply and pin 7 to the ground terminal (negative in this case). The binary high (1) and low (0) states will be +5V and OV, respectively. - Now connect the NAND gates as in Fig to show the basic gates: AND, OR and This activity should help stydents acquire a feel for what logic gates are about: they allow an output for given inputs according to certain logical operations. Now you could explain the electronic circuits that make up these gates.

10 Atomic, Nuclear Physics and Electronics 16.4 CIRCUITS FOR LOGIC GATES We give the electronic circuits for the basic logic gates. AND, OR and NOT. a) AND gate The circuit for the two input AND gate is shown in Fig It has two p-n junction diodes (of silicon). L A. +5v -T Output - 'Y Fig.16.10: Circuit of AND gate using diodes The resistor in the circuit controls the current passing through the diodes. Repeat to your students that a low value (0 bit) is assigned OV and high value (1 bit) is assigned 5V. But point out that such accurate values are not possible at the output in practical electronic circuits. In fact, a low value is assigned a'voltage range OV to 0.8 V and a high value is assigned a voltage range of 3 V to 5V. You can explain the operation of this circuit as follows: 1) A=O and B=O. When the inputs are connected to ground terminal or OV, then both the diodes are forward biased and hence conduct. The entire voltage appears across R. Thus the output voltage which is the voltage drop across each diode is low (0.7V) or 0. 2) A=O and B=l. When input A is connected to the ground terminal and input B is connqcted to the positive terminal of the battery (5V), then diode Dl is forward biased ut diode D2 is not biased (as both p and n sides of diode are connected to the Sam a voltage 5V). Thus output voltage is voltage drop across diode Dl (which is 0.7 V). It is thus low or 0. 3) A=l and B=O. When input A is connected to the 5V battery and input B is connected to ground, then like the previous case only one diode is forward biased or conducts which in this case is diode D2 The output voltage is the voltage drop across this diode and is 0.7 V, i.e., low or 0. 4) A=l and B=l. When both the inputs are connected to the 5V battery then both the sides of the diodes (Dl and D2) are at same voltage and hence both diodes are not conducting. Therefore the output voltage is the battery voltage which is 5V, i.e., high or 1.

11 t Draw all four circuit diagrams on the board or an OHP transparency and explain each step clearly. Logic Gates All these four cases satisfy the truth table of AND gate. ~o;more input AND gate the number of diodes will be more. There will be as many diodes as the number of inputs. You can show your students an AND gate in the lab. You can use the following components: Diodes - IN4001 R-lKc2 The power supply is a 5V dc source Use LEDs along with the diodes to show which of the signal diodes (ln4001) is actually conducting. b) OR gate The circuit of an OR gate has two p-n junction diodes as shown in Fig v +re' Dl 1, Be R I Output 'Y Fig.16.11: Circuit of OR gate using diodes The input voltage is applied to the terminals A and B. It can be either 0 or 5V. You can again explain the following cases: 1) A=O and B=O. When the inputs are connected to ground terminal or OV, then both the diodes are not biased or do not conduct (as both p and n sides of diode are connected to same voltage OV) and hence no current flows through the diodes. Thus the output voltage is lop or 0. 2) A=O and B=l. 1 When input A is connected to the ground terminal and input B is connected to the positive terminal of the battery (5V), then diode Dl is not biased or does not conduct (as both p and n sides of diode are connected to same voltage OV) but diode D2 is forward biased with 0.7 V voltage drop across it and 4.3 V(5-0.7 V) across the resistor. Point out that the output in this case is the voltage drop across the resistor. Thus output voltage is high or 1.

12 Atomic, Nuclear Physics and Electronics ' 3) A=l and B=O. When input A is connected to the 5V battery and input B is connected to ground, then like the previous case only me diode is forward biased or conducts which in this case is diode Dl Thus output voltage is high or I. 4) A=l and B=l. When both the inputs are connected to the 5V battery then both the sides of the diodes (Dl and D2) are at same voltage and hence both diodes are forward biased or conducting and the voltage drop across the resistor. R continues to be 4.3 V. Therefore, the output voltage is high or I. All these four cases satish the truth table of OR gate. The components used to set up the AND gate can be used here also. You can demonstrate the OR gate to your students or ask them to connect the circuit and verify its operation. c) NOT gate The circuit for the NOT gate has a transistor as shown in Fig Fig.16.12: Circuit for NOT gate using transistor in CE configuration The base of the transistor is connected to input A fhrough the resistor RB, while the emitter is earthed. The collector is earthed through a resistor Rc and 5V battery. You can explain the operation of this circuit as follows: When the input A is connected to the ground terminal of the battery, then the base of the transistor also gets earthed. Therefore, emitter-base junction is not forward biased (as both the emitter and base are earthed or connected to same OV). Moreover since the base current is zero, the collector current is also zero. This is said to be the cut-off mode of the transistor. Since there is no voltage drop across Rc, the output voltage will be equal to the voltage of the battery (5V) connected to the collector, i.e., high or 1. When the input A is connected to the positive terminal.of battery (5V), then the emitter base junction gets forward biased. It leads to a very large base current resulting in a very large collector current. The transistor is then in the saturation mode. This indicates that most of the bias voltage (-5V) drops across Rc and the output voltage is low or 0.

13 To demonstrate the NOT gate, use a transistor in BC 148 series. The main idea is to switch the transistor between its saturation and cut-off values based on the input and not allow it to function in the active region. You can use the following components: Logic Gates Rc=1KRto1OKl2 Rb=lOKR The voltage source can be a 5V dc supply. SAQ 2 Demonstrate the working of logic gates to your students.. Write a report on how well these worked in helping them understand the concept better ELEMENTARY IDEAS ABOUT ICs All the logic elements and most of the circuits we have looked at so far are available in off-the-shelf packages called integated circuits (ICs). In an integrated circuit, all components are fabricated on a single, semiconductor silicon wafer (a few microns thick) by the method of diffusion. The components and interconnections (achieved through metallic coatings) are an integral part of the chip and hence the name integrated circuit. Pins are provided on the IC to Connect the circuit to external signals. An IC may contain up to lakhs of individual gates on a silicon chip in a plastic or a metallic package. The first integrated ciricuit (IC) on a silicon wafer was fabricated in the 1960s having only a few gates. IC chips are usually de$ned in terms of the number of logic gates that they contain and the complexity.increases with the number of gates. Table 16.2 shows the classification of ICs according to the number of gates in them. able 16.2: Classification of ICs ' Classification SSI (Small Scale Integration) MSI(Medium Scale integration) LSI (Large Scale Integration) VLSI (Very Large Scale Integration) Complexity Less than 10 gates 10 to 100 gates I00 to 5000 gates More than 5000 gates Examples Independent logic gates like 2 input OR or NAND gates etc. IC's that perform one standard function (Adders, Flip Flops, Counters, Decoders) IC's that perform relatively complex functions (Memory devices, Arithmetic logic units (ALU)) Microprocessors (32 and 64 bit), memory chips. ULSI( Ultra Large Scale Integration). More than 50,000 (50K) gates Random Access Memories (RAMS), ULSI technology is used mostly in Japan You could tell your students that., *:* In the real world of digital electronics it is simply impractical to produce single logic gate structures and instead ICs are preferred which contain multiple logic circuits.

14 Atomic, Nuclear Physics and Electronics Advantage of ICs on conventional electronic circuits: Small size; Low power consumption; High speed; Highly reliable because all components are fabricated simultaneously and there are no soldered joints; Low cost due to processing of large quantities of components. You would have already shown ICs to your students while demonstrating NAND gates. We now discuss some applications of Logic Gates APPLICATIONS OF LOGIC GATES Logic gates form the building blocks of all digital systems. The basic logic gates comprise of AND, OR and NOT. It is these gates, used in differing combinations, that allow the computer to execute its operations using binary language. Today, all our computers employ Boole's logic system - using microchips that contain thousands of tiny electronic switches arranged into logical 'gates' that produce predictable and reliable conclusions. In recent years digital systems have become an integral part of our every day lives. We wake up to the music of a digital alarm clock. Cars have digitally controlled fuel injection systems and electronics. There are computer-coded grocery items in shops. Nowadays digital systems are extensively used as memory devices. Digital systems are employed for storage and transmission of data. In laboratories we make use of digital multimeters for checking electronic components and digital CRO's for time and frequency measurement. Computers are undoubtedly the best known and most prominent class of digital systems. Satellite communication systems, space vehicles, telephone networks, industrial production lines and home appliances are some of the other application areas that make use of digital electronics. Digital traff~controllers are used to measure traffic flow on crossroads and adjust the period of traffic lights to maximize flow. Digital anti-skid devices measure the speed of truck wheels and adjust braking force to prevent skids. Digital ignition controllers measure the carburetion and timing of airtomobiles engine to reduce emission. The flight pattern of a plane landing on an aircraft carrier takes on continuing values but a digital pulse radar tracking system sends out radar pulses periodically so that returning signals form a finite sequence of numbers that approximate the planes present position, present velocity and future position. We now summarise the contents of this unit.

15 16.7 SUMMARY Logic Gates Boolean algebra is used to describe the input and output relationship with the help of boolean expression. Logic gates are digital circuits that work according to some logical relationship between input and output voltages. Digital systems are constructed by using three basic logic gates viz. AND, OR and NOT gate. Output of AND gate is high (1) only when all the inputs are high. The output of OR gate is low (0) only when all inputs are low. The output of NOT,gate is inverse or complement of the input. NOT gates can be cdmbined with AND or OR to give NAND (not and) or NOR (not or) gates. The NAND and NOR are called universal gates since with either one the AND, OR and NOT gates can be generated. In a truth table the total number of possible input combinations is 2" where n is the number of input variables. The circuits of logic gates can be made with the help of diodes or transistors etc. An integrated circuit (IC) contains from several to millions of individual gates on a silicon chip in a plastic package. The different sizes of the integration (SSI, MSI, LSI, VLSI and ULSI) of IC chips are usually defined in terms of the number of logic gates or number of components fabricated on a chip. Logic gates form the building blocks of a digital systems and have wide ranging applications in life today TERMINAL QUESTIONS 1. Construct a set of problems for your students having questions of the following kind: a) Differentiate between digital and analog systems. b) What is the output of following logic circuit? (Explain with the help of boolean expression and truth table) Give Logic circuits c) Which of the following circuits will have high or 1 output? Give circuits d) Write the truth table for following combination of gates. Give combinations e) What arc the criteria of classifying the ICYs? f) Explain the importance of logic gates in our lives. And so on. 2. How did your students perform on the test? What were their difficulties? What moredo you need to do to improve their understanding?

16 Atomic, Nuclear Physics and Electronics $6.9 SOLUTIONS AND ANSWERS SAQs 1. (a) (i) AND (ii) 0 (b) Depends on the circuit you used. 2. Bring your report to the ECP. Terminal Questions 1. Bring the set of problems you designed and some responses of your students to the ECP. a) The digital system is one that processes a Gnite set of data in digital (numeric) form rather than processing continuous variables and is capable of manipulating discrete elements of information. Whereas in analog systems data values show a continuous variation over a broad range. See details in Sec Bring your report to the ECP.