Physics Investigatory Project On Logic Gates 4q6w2f
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1|Page
CERTIFICATE This is to certify that
of class XII has satisfactorily completed the project on “LOGIC GATES” under the guidance of
during the session 2013-2014.
2|Page
VALUED BY
TEACHER EXTERNAL EXAMINER
PRINCIPAL
3|Page
DATE:
ACKNOWLEDGME NT I'd like to express my greatest gratitude to the people who have helped & ed me throughout my project. I’ m grateful to our school’s PHYSICS faculty I thank
for her continuous for the project, from initial advice & encouragement to this day. Special thanks of mine goes to my colleagues who helped me in completing the project by giving necessary information on the apparatus used in this experiment, made this project easy and accurate.
4|Page
I wish to thank my parents for their undivided & interest who inspired me & encouraged me to go my own way without which I would be unable to complete my project. At last but not the least I want to thanks my friends who appreciated me for my work & motivated
me.
CONTENT •Introduction
• Experiment 1. Aim
10
5|Page
2. Apparatus 3. Theory
10 11
4. Procedure
16
5. Circuits Prepared
22
6. Observations
24
7. Result
26
6|Page
Bibliography
27
INTRODUCTION
Logic Gates: 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. 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 behavior of logic gates.
(i)
NOT gate (Inverter)
This is the most basic gate, with one input and one output. 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.
A
Y=A’
0
1
7|Page
1
0
(ii) OR Gate An OR gate has two or more inputs with one output. 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.
A
B
Y=A OR B(A+B)
0 0 1 1
0 1 0 1
0 1 1 1
(iii) AND Gate 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. It kind of looks for the minimum of the two signals.
A
B
Y=A AND B(A.B)
0 0
0 1
0 0
8|Page
1 1
1
0 1
0 1
Some Basic Logic Gates and Their Truth Tables
Circuit diagrams
AND GATE
NOT GATE
OR GATE
Experiment
AIM To design and simulate basic logic gates and to design an appropriate logic gate combination for a given truth table.
APPARATUS
A project board Two N4007 diodes Two LED A 9v battery with a connector
Two BPJ-BC547 transistors Two 100, three 560 resistors Connecting wires
THEORY
The three basic logic gates and their combinations are the building block of the digital circuit. 1. OR gate A
+ B
B
A
The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation. CIRCUIT DIAGRAM:
2. AND Gate A
A.B
B The AND gate is an electronic circuit that gives high output only if all inputs are high
CIRCUIT DIAGRAM :
3. NOT Gate
The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an inverter.
A CIRCUIT DIAGRAM:
A’
0 1
PROCEDURE
Design of basic logic gates.
DESIGN OF AND GATE
COMPONENTS: Two p-n junction diode, A LED, A
100 resistors CONSTRUCTION: An AND gate can be realized
by connecting the diodes as shown in the figure. A resistance of 100 is connected in series with the LED to prevent its malfunction. PROJECT BOARD CIRCUIT: GROUND
HIGH
DESIGN OF OR GATE
COMPONENTS: Two p-n junction diode, A LED, A
100 resistors CONSTRUCTION: An OR gate can be realized by connecting the diodes as shown in the figure. Here also there is a need for a 100 resistor in series with LED
PROJECT BOARD CIRCUIT:
DESIGN OF NOT GATE COMPONENTS: A transistor, two LEDs, three 560
resistors. CONSTRUCTION: not gate circuit can be realized by connecting an NPN transistor as shown in the figure. The base of the transistor is connected to the input through resistance of 560 and emitter is connected to the negative
terminal. The collector is connected to the positive terminal and the output voltage at collector is with respect to negative. PROJECT BOARD CIRCUIT: 1 2 3 Ground High line 1=2=3=600
Logic gate combination for given truth table
1. Write product term for each input (minterm), Combination where Boolean function has output 2. While writing min, complement the variable whose value is 0 otherwise write it in the direct form (without complement). 3. Add all the min to obtain the Boolean function. 3. Draw the circuit using basic LOGIC Gates.
So we, choose the given Truth Table. A
B
Y=A.B
Y’
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
The Boolean Function F(x,y) is obtained as: F(x,y)= X’.Y’+X.Y’+X’Y = Y’+X’Y
= (X’+Y’)(Y+Y’)
= X’+Y’
= (XY)’
So, our expression reduces to that of a NAND Gate logic (Not of AND).
LOGIC CIRCUIT IS: F=(x.y)’
x
CIRCUIT DIAGRAM High line Ground
Circuits Prepared:-
AND gate
OR gate
NOT gate
NAND gate
1.
OBSERVATION S
Stimulation of AND gate The following conclusions can be easily drawn from the working of electrical circuit:
a) If both switches are open (A=0, B=0) then LED will not glow, hence Y=0. b) If Switch one switch is open and the other is closed (A=1, B=0 or A=0, B=1) then LED will not glow, hence Y=0. c) If switch A & B both closed (A=1, B=1) then LED wi ll glow, Hence Y=1.
2.
Stimulation of OR gate The following conclusions can be easily drawn from the working of electrical circuit: a) If both switches are open (A=0, B=0) then LED will not glow, hence Y=0. b) If Switch one switch is open and the other is closed (A=1, B=0 or A=0, B=1) then LED will glow, hence Y=0. c) If switch A & B both closed (A=1, B=1) then LED wi ll glow, Hence Y=1.
3.
Stimulation of NOT gate a) If switch A is open (i.e. A=0), the LED will glow, hence Y=1.
b) If Switch A is closed (i.e. A=1), the LED will not glow, hence Y=0.
4.
Stimulation of NAND gate a) If Switch A & B open (A=0, B=0) then LED will glow, hence Y=1. b) If Switch A open B closed then (A=0, B=1) LED will glow, hence Y=1. c) If switch A closed B open then (A=1, B=0) LED will glow, hence Y=1. d) If switch A & B are closed then (A=1, B=1) LED will not glow, hence Y=0
Re sul t:
Basic logic gates were designed and simulated and logic circuit was prepared for the given truth table
BIBLIOGRAPHY:
Wikipedia
Electronic devices and circuits by J B Gupta
Conceptual physics by G C Agarwal
Encarta
CERTIFICATE This is to certify that
2|Page
VALUED BY
TEACHER EXTERNAL EXAMINER
PRINCIPAL
3|Page
DATE:
ACKNOWLEDGME NT I'd like to express my greatest gratitude to the people who have helped & ed me throughout my project. I’ m grateful to our school’s PHYSICS faculty I thank
4|Page
I wish to thank my parents for their undivided & interest who inspired me & encouraged me to go my own way without which I would be unable to complete my project. At last but not the least I want to thanks my friends who appreciated me for my work & motivated
me.
CONTENT •Introduction
• Experiment 1. Aim
10
5|Page
2. Apparatus 3. Theory
10 11
4. Procedure
16
5. Circuits Prepared
22
6. Observations
24
7. Result
26
6|Page
Bibliography
27
INTRODUCTION
Logic Gates: 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. 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 behavior of logic gates.
(i)
NOT gate (Inverter)
This is the most basic gate, with one input and one output. 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.
A
Y=A’
0
1
7|Page
1
0
(ii) OR Gate An OR gate has two or more inputs with one output. 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.
A
B
Y=A OR B(A+B)
0 0 1 1
0 1 0 1
0 1 1 1
(iii) AND Gate 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. It kind of looks for the minimum of the two signals.
A
B
Y=A AND B(A.B)
0 0
0 1
0 0
8|Page
1 1
1
0 1
0 1
Some Basic Logic Gates and Their Truth Tables
Circuit diagrams
AND GATE
NOT GATE
OR GATE
Experiment
AIM To design and simulate basic logic gates and to design an appropriate logic gate combination for a given truth table.
APPARATUS
A project board Two N4007 diodes Two LED A 9v battery with a connector
Two BPJ-BC547 transistors Two 100, three 560 resistors Connecting wires
THEORY
The three basic logic gates and their combinations are the building block of the digital circuit. 1. OR gate A
+ B
B
A
The OR gate is an electronic circuit that gives a high output (1) if one or more of its inputs are high. A plus (+) is used to show the OR operation. CIRCUIT DIAGRAM:
2. AND Gate A
A.B
B The AND gate is an electronic circuit that gives high output only if all inputs are high
CIRCUIT DIAGRAM :
3. NOT Gate
The NOT gate is an electronic circuit that produces an inverted version of the input at its output. It is also known as an inverter.
A CIRCUIT DIAGRAM:
A’
0 1
PROCEDURE
Design of basic logic gates.
DESIGN OF AND GATE
COMPONENTS: Two p-n junction diode, A LED, A
100 resistors CONSTRUCTION: An AND gate can be realized
by connecting the diodes as shown in the figure. A resistance of 100 is connected in series with the LED to prevent its malfunction. PROJECT BOARD CIRCUIT: GROUND
HIGH
DESIGN OF OR GATE
COMPONENTS: Two p-n junction diode, A LED, A
100 resistors CONSTRUCTION: An OR gate can be realized by connecting the diodes as shown in the figure. Here also there is a need for a 100 resistor in series with LED
PROJECT BOARD CIRCUIT:
DESIGN OF NOT GATE COMPONENTS: A transistor, two LEDs, three 560
resistors. CONSTRUCTION: not gate circuit can be realized by connecting an NPN transistor as shown in the figure. The base of the transistor is connected to the input through resistance of 560 and emitter is connected to the negative
terminal. The collector is connected to the positive terminal and the output voltage at collector is with respect to negative. PROJECT BOARD CIRCUIT: 1 2 3 Ground High line 1=2=3=600
Logic gate combination for given truth table
1. Write product term for each input (minterm), Combination where Boolean function has output 2. While writing min, complement the variable whose value is 0 otherwise write it in the direct form (without complement). 3. Add all the min to obtain the Boolean function. 3. Draw the circuit using basic LOGIC Gates.
So we, choose the given Truth Table. A
B
Y=A.B
Y’
0
0
0
1
0
1
0
1
1
0
0
1
1
1
1
0
The Boolean Function F(x,y) is obtained as: F(x,y)= X’.Y’+X.Y’+X’Y = Y’+X’Y
= (X’+Y’)(Y+Y’)
= X’+Y’
= (XY)’
So, our expression reduces to that of a NAND Gate logic (Not of AND).
LOGIC CIRCUIT IS: F=(x.y)’
x
CIRCUIT DIAGRAM High line Ground
Circuits Prepared:-
AND gate
OR gate
NOT gate
NAND gate
1.
OBSERVATION S
Stimulation of AND gate The following conclusions can be easily drawn from the working of electrical circuit:
a) If both switches are open (A=0, B=0) then LED will not glow, hence Y=0. b) If Switch one switch is open and the other is closed (A=1, B=0 or A=0, B=1) then LED will not glow, hence Y=0. c) If switch A & B both closed (A=1, B=1) then LED wi ll glow, Hence Y=1.
2.
Stimulation of OR gate The following conclusions can be easily drawn from the working of electrical circuit: a) If both switches are open (A=0, B=0) then LED will not glow, hence Y=0. b) If Switch one switch is open and the other is closed (A=1, B=0 or A=0, B=1) then LED will glow, hence Y=0. c) If switch A & B both closed (A=1, B=1) then LED wi ll glow, Hence Y=1.
3.
Stimulation of NOT gate a) If switch A is open (i.e. A=0), the LED will glow, hence Y=1.
b) If Switch A is closed (i.e. A=1), the LED will not glow, hence Y=0.
4.
Stimulation of NAND gate a) If Switch A & B open (A=0, B=0) then LED will glow, hence Y=1. b) If Switch A open B closed then (A=0, B=1) LED will glow, hence Y=1. c) If switch A closed B open then (A=1, B=0) LED will glow, hence Y=1. d) If switch A & B are closed then (A=1, B=1) LED will not glow, hence Y=0
Re sul t:
Basic logic gates were designed and simulated and logic circuit was prepared for the given truth table
BIBLIOGRAPHY:
Wikipedia
Electronic devices and circuits by J B Gupta
Conceptual physics by G C Agarwal
Encarta
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