Class 12th Logic Gates

Class 12th Logic Gates

1. Logic Gates Class 12 th Priyanka Jakhar Physics Lecturer GGIC Vijay Nagar Ghaziabad U.P.

2. Digital electronics ( Logic gates )   Is a field of  electronics  involving the study of  digital signals  and the engineering of devices that use or produce them. This is in contrast to  analog electronics  and  analog signals .

3. Difference Between Analog And Digital Signal Analog Signals Digital Signals Continuous signals Discrete signals Represented by sine waves Represented by square waves Human voice, natural sound, analog electronic devices are few examples Computers, optical drives, and other electronic devices Continuous range of values Discontinuous values Records sound waves as they are Converts into a binary waveform. Only be used in analog devices. Suited for digital electronics like computers, mobiles and more.

4. Analog And Digital Signal:-   Analog and Digital signals are the types of signal carrying information. Both these signals are used in  electronic communication system  to transfer information from one place to another. Digital circuits :-- A digital circuit comprises various components each of which is used to perform a specific task. These components are of two types: active components and passive components. The active components are the diodes and transistors . The passive components are the registers, inductors,  capacitors , etc. Along with that, a power source is also required which is used to provide DC power supply to the circuit.

5. Analog circuits:-   operate on analog signals, commonly known as continuous valued signals.   Analog circuits are typically routine made and lack flexibility.     Digital circuits:-  function on signals that exist at only two levels, i.e., zeros and ones. # Digital circuits have a high degree of elasticity. #  Digital circuits are more reliable. # Digital circuits are easy to design and cheaper than analog circuits. # The effect of distortion, noise, and interference is much less in digital signals as they are less affected. # Communication can be kept “private” and “secured” through the use of encryption. #   It has higher accuracy, programmability. # Transmitted signals are not degraded over long distances.  # Digital Signals can be stored easily.

6. Digital circuits are of two types Combinational Logic Circuit The  combinatorial logic circuit  is made up of logic gates whose output is determined by the present input only. The output does not depend on the previous outputs of the circuit. This type of circuit is widely used in the electronic industries for various purposes. The circuits are designed by combining the different logic gates. Two types of combinatorial circuits are encoder and decoder. Other examples include half adder, full adder, and multiplexer. Sequential Logic Circuit The  sequential logic circuit  is one such circuit in which the output of the circuit not only depends on the present input but it also depends on the past outputs. Sequential circuits have the ability to store the past output in various memory devices. They are designed using finite state machines. Different kinds of sequential logic circuits are counters and flip flops.   Disadvantages of Digital Circuits Digital circuits consume more energy as compared to any other circuits. Digital circuits require a power supply.

7. Positive logic:--   The use of the higher voltage level to represent the Boolean value 1 and the lower voltage level to represent the Boolean value 0.   Negative logic:--   The use of the higher voltage level to represent the Boolean value 0 and the lower voltage level to represent the Boolean value 1.  Positive and negative logic:-- we know that in Digital circuit voltage or current has only two values or levels. Two levels of circuits can also be written as (low and high) or( on and off ) or (true and false ) etc. Digital circuits are based on Boolean Algebra of two variables developed by George Boole. This algebra is based on logic. Digital circuit is also known as logical circuit. The two level of voltage in Digital circuit known as logic levels. They are not represented by their actual value but they are represented by binary digit 0 and1. It can be represented in two

8. Logic gates    # Logic gates are the basic building blocks of any digital system. # Logic gates are used in calculators, digital watches, computers, robots, industrial control systems, and in telecommunications. # It is an electronic circuit having one or more than one input and only one output. # The relationship between the input and the output is based on a certain logic . Based on this, logic gates are named as AND gate, OR gate, NOT gate etc. # A logic gate is an idealized or physical electronic device implementing a Boolean function, # Gate means that it can control the flow of information. # Logic gate is a digital circuit which follows a definite logical relationship between input and output voltages.  

9. Basic gates:--   In this type of gates, we can represent the boolean functions either in the sum of products form or in the product of sums form. The basic logic gates are AND, OR and NOT gates. Universal gates:--   These are the logic gates using which all other gates can be constructed. NAND and NOR are the two universal gates. Special gates:--   EX-OR and EX-NOR are the two special gates as they are the two special cases of OR and NOR gates.

10. Truth Table:- The truth table of a logic gate is a table which shows all possible input logical levels and their corresponding outputs. The working of a logic gate is Defined by a table which is known as truth table of that Gate. The input of a gate are expressed by A, B,……… and the output of gate is represented by Y. Only two levels 0 and 1 are possible for input and output of gate . The gate having n input has 2 combination of input levels in its truth table. Boolean algebra:-   is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively. Boolean Expression :- The expression/equation representing the logical relationship between input and output of a gate is known as Boolean expression of the gate. (i) OR operation is represented by + sign. (ii) A AND operation is represented by • sign. (iii) N NOT operation is represented by putting – sign (bar sign) over the boolean variable. A B Y n

11. BOOLEAN ALGEBRA OR RULES ( ADDITION) 0 + 0 = 0 0 + 1 = 1 1 + 0 = 1 1 + 1 = 1 A + 0 = A A + 1 = 1 7 A + A ( bar ) =1 AND RULES (MULTIPLICATION) 1. 0.0  = 0 2. 0.1  = 0 3. 1.0  = 0 4. 1.1  = 1 5. A.1  = A 6. A.0  = 0 7. A.A = A 8. A.A ( bar )  = 0

12. 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. , # It produces an inverted version of the input at its output. This is why it is also known as an inverter. Symbol:- Boolean expression of:- Truth Table:- A B Y 1 1 1 1 1 1 Y = A Y A

13. A Y 1 1 U U U A A Y I I I NOT gate is a logic gate that inverts the digital input signal . A NOT gate always has high output when its input is low. NOT gate always has low output when the input is high. 1. If A switches is open ( A = 0), the bulb will glow by Y = 1. 2. If A switches is closed ( A = 1), the bulb will not glow by Y = 0. . V

14. OR gate  # An OR gate is a logic gate that has two or more inputs but only one output. # The output Y of an OR gates is LOW when all inputs are LOW. # The output is high if any or all the inputs are high. # OR gate is sometimes called "any or all gate". Boolean expression  :- A + B = Y . Symbol:- Truth Table:- Y A B Y 1 1 1 1 1 1 1 A Y B

15. A B Y 1. If both switches are open ( A = 0 and B = 0 ), the bulb will not glow by Y = 0 2. If switch A is open and B is closed ( A = 0 and B = 1 ), the bulb will glow Y = 1 3. If switch A is closed and B is open ( A = 1 and B = 0 ), the bulb will glow Y = 1 4. If both switches are closed ( A = 1 and B = 1 ), the bulb will glow Y = 1 U U U A B Y 1 1 1 1 1 1 1 I I I I I V V OR gate is called an any or all gate. Because it produces high when at least one input is high and output is low when all inputs are low.

16. AND Gate Diode Circuit Diagram Normally an AND gate is designed by either diodes or transistors . When diodes are used to design AND gate, it is called a diode AND gate. The basic circuit of a diode AND gate is shown below R D D 1 Y 2 C A B Y A B Y 1 1 1 1 1 1 1 1 5 v Diode in forward biased – closed ( working ) Diode in reversed biased – open ( not working ) I I

17. AND gate  # The AND gate is a logic gate that has two or more inputs but only one output. # The output Y of an AND gates is HIGH when all inputs are HIGH # AND gate is sometimes called "all or nothing gate. Symbol:- Boolean expression:- A.B = y Truth Table:- A B Y 1 1 1 1 1

18. A B Y U U U A B Y A B Y 1 1 1 1 1 I I I 1. If both switches are open ( A = 0 and B = 0 ), the bulb will not glow by Y = 0 2. If switch A is open and B is closed ( A = 0 and B = 1 ), the bulb will glow Y = 3. If switch A is closed and B is open ( A = 1 and B = 0 ), the bulb will glow Y = 4. If both which are closed ( A = 1 and B = 1 ), the bulb will glow Y = 1 V AND gate is called an all or nothing gate. Because it produce high only when all its inputs are high. In all other case its output is low.

19. AND Gate Diode Circuit Diagram Normally an AND gate is designed by either diodes or transistors . When diodes are used to design AND gate, it is called a diode AND gate. The basic circuit of a diode AND gate is shown below R D D 1 2 C 1 5 v

20. Condition 1 : When A = 0 V (level 0), B = 0 V (level 0). Diode D1 and D2 both are forward biased, so they will behave as closed switch. Current flows through them, ∴ Y = YD = 0 V (level 0) Condition 2 : When A = 0 V (level 0), B = 5 V (level 1) . Diode D1 is forward biased (like closed switch) and diode D2 is unbiased (like open switch). So, current I flows through D1. Since, VD = 0 V, Y = YD = 0 V (level 0) Condition 3 : When A = 5 V (level 1), B = 0 V (level 0) . Diode D1 is unbiased (like open switch) and diode D2 is forward biased (like closed switch). So, current I flows through diode D2 Y = YD = 0 V (level 0) Condition 4 : When A = 5 V (level 1), B = 5 V (level 1) . Diode D1 and D2 are unbiased (like open switch). Therefore, no current flows in the circuit. , Y = 5 − IR

21. NAND gate # NAND gate is a logic gate which produces an output which is false only if all its inputs are true. # The Logic NAND Gate is generally classed as a “Universal” gate. # NAND gate has better ratio of output high drive and output low drive as compared to NOR gate. # We need three NAND gates to get an or gate. Symbol:- Boolean expression:- Truth Table:- A B Y 1 1 1 1 1 1 1 Y = A . B A B Y

22. Y A B 1 1 1 1 1 A .B 1 1 1 1. When A = 0 and B = 0 ,Y =1 2. When A = 0 and B = 1 ,Y =1 3. When A = 1 and B = 0 ,Y =1 4. When A = 1 and B = 1 ,Y =0 U U U Y I I V A B R

23. NAND gate as universal gate 1 . NOT gate 3 . AND gate 2 . OR gate B B B A A A A A .B Y = A . A = A Y = A . B = A + B = A + B Y = A .B = A .B

24. Nor Gate # This gate has two or more inputs and one output. # The value of output Y in NOR gate will be 1 only when all the inputs are 0. # On using a NOT gate next to OR gate, a NOT-OR combination is obtained. It is known as NOR gate. Symbol:- Boolean expression:- Truth Table:- A B A + B 1 1 1 1 1 1 1 Y 1 Y = A + B

25. 1. When A = 0 and B = 0 ,Y =1 2. When A = 0 and B = 1 ,Y =0 3. When A = 1 and B = 0 ,Y =0 4. When A = 1 and B = 1 ,Y =0 A B A + B 1 1 1 1 1 1 1 Y 1 U U U Y V A B R I I

26. NOR gate as universal gate 1 . NOT gate 2 . AND gate 3 . OR gate Y = A + B B B A A A Y = A + A = A Y = A + B = A + B A B Y = A + B = A . B = A . B

27. Integrated circuits # The components like diode, transistor, resistor, inductor, and capacitor are connected by soldering wires in desired manner, to make conventional circuits         # But still such circuits are still bulky; They are also less reliable and less shock proof # The concept of fabricating an entire circuit on a small single chip of semiconductor is called Integrated circuit . The chip dimensions are as small as 1mm * 1 mm or even less than that        # The integrated chip can be categorized into (a) linear or analog IC (b) digital IC # Linear or Analog IC – The signals change continuously over a range of values between maximum and minimum; The output varies linearly as the input ; The most useful linear IC is an operational amplifier # Digital IC – These have two values – high and low; These contain logical gates. – Depending upon the number of circuit components or logic gates used, they can be classified into SSI, MSI , LSI or VLSI # If the number of gates is less than or equal to 10, we call it as SSI – small scale integration # If the number of gates is less than or equal to 100, we call it as MSI – medium scale integration # If the number of gates is less than or equal to 1000, we call it as LSI – large scale integration # If the number of gates is greater than 1000, we call it as VLSI – very large scale integration