ACKNOWLEDGEMENT
First and foremost, I would extend our deepest gratitude to the Almighty God for showering love and grace on me and made me complete the project. I would like to appreciate the co-operation and vivacity offered by my colleagues and friends that made this project easy and feasible. They helped me in the domains of creativeness, designing, managing and in demonstration of new ways to accomplish my tasks. I express my deep sense of gratitude to my parents for their love and support all over the way, giving us valuable v aluable solutions and new ideas. Sincere thanks to my kind and helpful physics teacher Miss Sapna Vishwakarma, who always encouraged me in my projects and its completion and in the rectification of my doubts. I am extremely indebted and grateful to our Head of the Institution, Mr R P Shahi for providing me the sources, so that I can successfully complete out project.
(Name)
INDEX
Introduction
Types of gates
The OR gate
The AND gate
The NOT gate
The NOR gate
The NAND gate
The XOR gate
The XNOR gate
Universal logic gates
De Morgan’s equivalent symbols
PREFACE
I hereby feel immense pleasure in presenting this project file as per the requirements of the CBSE board for AISSCE practicals. Best possible efforts have been made to present this project in a very interactive way. Great care has been taken to make one understand the subjective approach of this project through this presentation. I hope that my project will fulfill the needs of the viewers and I would receive nice complements from them.
(Rishabh Dhakar)
INTRODUCTION
A gate is defined as a digital circuit which follows some logical relationship between the input and output voltages. It is a digital circuit which either allows a signal to pass through as stop, it is called a gate. A logic gate is an idealized or physical device implementing a Boolean function, that is, it performs a logical operation on one or more logic inputs and produces a single logic output. The Logic Gates are building blocks at digital electronics. They are used in digital electronics to change on voltage
level (input voltage) into another (output voltage) according to some logical statement relating them. Depending on the context, the term may refer to an ideal logic gate, one that has for instance zero rise time and unlimited fanout, or it may refer to a non-ideal physical device Logic gates are primarily implemented using diodes or transistors acting as electronic switches, but can also be constructed using electromagnetic relays (relay logic), fluidic logic, pneumatic logic, optics, molecules, or even mechanical elements. With amplification, logic gates can be cascaded in the same way that Boolean functions can be composed, allowing the construction of a physical model of all of Boolean logic, and therefore, all of the algorithms and mathematics that can be described with Boolean logic. A logic gate may have one or more inputs, but it has only one output. The relationship between the possible values of input and output voltage is expressed in the form of a table called truth table or table of combinations.
Truth table of a Logic Gates is a table that shows all the input and output
possibilities for the logic gate. George Boole in 1980 invented a different kind of algebra based on binary nature at the logic, this algebra of logic called BOOLEAN ALGEBRA. A logical statement can have only two values, such as HIGH/LOW, ON/OFF, CLOSED/OPEN, YES/NO, TRUE/FALSE, CONDUCTING/NON-CONDUCTING etc. The two values of logic statements one denoted by the binary number 1 and 0. The binary number 1 is used to denote the HIGH value. The logical statements that logic gates follow are called Boolean expression.
TYPES OF GATES
There are three types of basic logic gates which follows Boolean expression. i.
OR gate
ii.
AND gate
iii.
NOT gate
iv.
NOR gate
v.
NAND gate
vi.
XOR gate
vii.
XNOR gate
THE “OR GATE”
The OR gate is a two inputs and one output logic gate. It combines the input A and B with the output Y following the Boolean expression. Y=A+B The Boolean algebra, the addition symbol (+) is called OR (i.e. OR operation OR operator). The various possible combinations of the input and output of the OR gate can be easily understand with the help of the electrical circuit. In this electric circuit, a parallel combination of two switches A and B is connected to a battery and a lump L. The following interference can be easily drawn from the working of electrical circuit is : a)
If switch A & B are open lamp do not glow (A=0, B=0)
b)
If Switch A open B closed then (A=0, B=1) Lamp glow.
c)
If switch A closed B open then (A=1, B=0) Lamp glow.
d)
If switch A & B are closed then (A=1, B=1) Lamp glow.
As we see truth table we found same as it is observation.
THE “AND GATE”
The AND gate is also a two inputs and one output logic gate. It combines the input A and B with the output Y following the Boolean expression. Y=A.B The Boolean algebra, the multiplication symbol (. dot or x Gross) is taken to mean AND. Y = A . B have Y is equal to A AND B. The various possible combination of the input and outputs of the AND gate can be easily found with the help of the electrical circuit. Here a series combination of the switch A and B is connected to a battery and a lump L. The following conclusions can be easily drawn from the working of electrical circuit : a) (y=0)
If both switches A&B are open (A=0, B=0) then lamp will not glow.
b)
If Switch A closed & B open (A=1, B=0) then Lamp will not glow. (y=0)
c)
If switch A open & B closed (A=0, B=1) then Lamp will not glow. (y=0)
d)
If switch A & B both closed (A=1, B=1) then Lamp will glow. (y=1)
As we see truth table we found same as it is observed experimentally.
THE “NOT GATE”
The NOT gate is a one inputs and one output logic gate. It combines the input A with the output following the Boolean expression. Y=A i.e. Y not equal A. The way, the NOT gate gives the output it is also called inverter. It is represented by the symbol. The Boolean algebra, the negative sign (-) is called NOT. The equation Y= A called Boolean expression. The possible input and output combination of a NOT gate can be easily discussed with the help of electrical circuit. Here, the switch is connected in parallel to the lump of the battery. The following conclusion can be easily drawn from the working of the electrical circuit. a)
If switch A is open (i.e. A=0), the lump will glow (i.e. Y=1)
b)
If Switch A is closed (i.e. A=1), the lump will not glow (Y=0).
It follows that in the given electrical circuit, the lump glows (or output is obtained), when the switch A is not closed. Far this reason, the electrical circuit is called not gate. The two possible input-output combinations can be written in the form of the table. It is called truth table of NOT gate.
Some more logic gates are also there derived from three basic gates (i.e AND, OR and NOT). These gates are more popular than AND,OR and NOT and are widely used in industry. These gates are NOR, NAND, XOR, XNOR gates.
THE “NOR GATE”
The NOR gate has two or more input signals but only one output signal. If all the inputs are 0 (i.e low), then the output signal is 1 (high). If either of the two inputs is 1 (high), the output will be 0 (low). NOR gate is nothing but inverted OR gate. The NOR gate can have as many inputs as desired. No matter how many inputs aare there the action of NOR gate iis the same i.e., all 0 (low) inputs produce output as 1. INPUT OUTPUT A B A NOR B NOR
0 0 1 0 1 0 1
0 0
THE “NAND GATE”
The NAND gate has two or more input signals but only one output signal. If all of the inputs are 1 (high), then the output produced is 0 (low). NAND gate is inverted AND gate. Thus for all 1 (high) inputs, it produces 0 (low) output, otherwise for any other input combination, it produces a 1 (high) output. NAND gate can also have as many inputs as desired. INPUT OUTPUT A B A NAND B NAND
0 0 1 0 1 1 1
0 1
1 1 0
THE “XOR GATE”
The XOR gate can also have two or more inputs but produces one output signal. XOR gate is different from OR gate. OR gate produces output 1for any input combination having one or more 1’s, but XOR gate produces output 1 for only those input combinations that have odd number of 1’s.
In Boolean algebra (+) sign stands for XOR operation. INPUT OUTPUT A B A XOR B XOR
0 0 0 0 1 1 1
0 1
1 1 0
THE “X-NOR GATE”
The XNOR gate is logically equivalent to an inverted XOR i.e., XOR gate followed by a NOT gate (inverter). Thus XNOR produces 1 (high) output when the input combination has even number of 1’s.
INPUT OUTPUT A B A XNOR B XNOR
or
0 0 1 0 1 0 1
0 0
1 1 1
UNIVERSAL LOGIC GATES
Charles Sanders Peirce (winter of 1880–81) showed that NOR gates alone (or alternatively NAND gates alone) can be used to reproduce the functions of all the other logic gates, but his work on it was unpublished until 1933. The first published proof was by Henry M. Sheffer in 1913, so the NAND logical operation is sometimes called Sheffer stroke; the logical NOR is sometimes called Peirce's arrow. Consequently, these gates are sometimes called universal logic gates.
DE MORGAN EQUIVALENT SYMBOLS
By use of De Morgan's theorem, an AND function is identical to an OR function with negated inputs and outputs. Likewise, an OR function is identical to an AND function with negated inputs and outputs. Similarly, a NAND gate is equivalent to a NOR gate with negated inputs, and a NOR gate is equivalent to a NAND gate with negated inputs. The leads to an alternative set of symbols for basic gates that use the opposite core symbol (AND or OR) but with the inputs and outputs negated. Use of these alternative symbols can make logic circuit diagrams much clearer and help to show accidental connection of an active high output to an active low input or vice-versa. Any connection that has logic negations at both ends can be replaced by a negation less connection and a suitable change of gate or vice-versa. Any connection that has a negation at one end and no negation at the other can be made easier to interpret by instead using the De Morgan equivalent symbol at either of the two ends. When negation or polarity indicators on both ends of a connection match, there is no logic negation in that path (effectively, bubbles "cancel"), making it easier to follow logic states from one symbol to the next. This is commonly seen in real logic diagrams - thus the reader must not get into the habit of associating the shapes exclusively as OR or AND shapes, but also take into account the bubbles at both inputs and outputs in order to determine the "true" logic function indicated.
All logic relations can be realized by using NAND gates (this can not also be done using NOR gates). De Morgan's theorem is most commonly used to transform all logic gates to NAND gates or NOR gates. This is done mainly since it is easy to buy logic gates in bulk and because many electronics labs stock only NAND and NOR gates.
BIBLIOGRAPHY
I would like to declare the array of references hereby and submit that I took help from following sources1- Comprehensive Physics Practical A textbook for Physics practicals ISBN 978-81-318-0384-4
2- Wikipedia.com The Online Encyclopedia indexing world’s best articles with genuine references.
3- TCYonline.com An online video tutorial and educational centre.
4- Meritnation.com The leading educational site in India.
5- http://projects.icbse.com/forums Online help for CBSE projects.
6- Print Partner- Ãliartis ePrints © Muhammad Wamiq Hussain, Gorakhpur
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