S
AFRAH AAMER DARATASSALAM INTERNATIONAL DELHI PUBLIC SCHOOL XII B
This is to certify that Afrah Aamer of class XII B has successfully completed the research on the topic ‘Transistors and Logic Gates’, under the guidance of Mrs. Aparna Mulay, during the year 2016-17, in partial fulfilment of Physics Practical Examination conducted by CBSE.
Physics Teacher
Firstly, I would like to express my special thanks of gratitude to my physics teacher Mrs. Aparna Mulay as well as our principal Mr. Mairaj Mohammed Khan, who gave me the golden opportunity to do this wonderful project on the topic of ‘Logic Gates and Transistors’ which also helped me in doing a lot of Research and I came to know about so many new things I am really thankful
to
them.
Secondly, I would also like to thank my parents and friends who “helped me a lot in finalizing this project within the limited time frame.
Certificate .................................................................................................................................. ii Acknowledgement .............................................................................................................. iii Transistor ......................................................................................................................................3 How is a transistor made? ..............................................................................................4 Working of a junction Transistor ...................................................................................5 Transistors in Computers ......................................................................................................6 Logic Gates ............................................................................................................................... 7 Principle ...................................................................................................................................8 Basic Gates ............................................................................................................................8 OR Gate ................................................................................................................................8 AND Gate.............................................................................................................................9 NOT Gate .............................................................................................................................9 NOR Gate .......................................................................................................................... 10 NAND Gate ....................................................................................................................... 10 XOR Gate ............................................................................................................................11 XNOR Gate .........................................................................................................................11 AFRAH AAMER
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Designing and Stimulating Logic Gate Circuits .................................................... 12 OR ............................................................................................................................................. 12 Apparatus: ......................................................................................................................... 12 Theory: ................................................................................................................................ 12 Truth Table: ....................................................................................................................... 13 AND .......................................................................................................................................... 13 Apparatus: ......................................................................................................................... 13 Theory: ................................................................................................................................ 13 Truth Table: ....................................................................................................................... 14 NOT........................................................................................................................................... 15 Apparatus: ......................................................................................................................... 15 Theory: ................................................................................................................................ 15 Truth Table: ....................................................................................................................... 15 NOR .......................................................................................................................................... 16 Apparatus: ......................................................................................................................... 16 Theory: ................................................................................................................................ 16 Truth Table: ....................................................................................................................... 17 NAND ...................................................................................................................................... 17 Apparatus: ......................................................................................................................... 17 Theory: ................................................................................................................................ 17 Truth Table: ....................................................................................................................... 18 XOR .......................................................................................................................................... 18 Apparatus: ......................................................................................................................... 18 AFRAH AAMER
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Theory: ................................................................................................................................ 18 Truth Table: ....................................................................................................................... 19 XNOR ....................................................................................................................................... 19 Apparatus: ......................................................................................................................... 19 Theory: ................................................................................................................................ 19 Truth Table: ...................................................................................................................... 20 Boolean Algebra ................................................................................................................. 20 References ............................................................................................................................... 21
Transistor Computers contain billions of miniature "brain cells" as well. They're called transistors and they're made from silicon, a chemical element commonly found in sand. Transistors have revolutionized electronics since they were first invented over half a century ago by John Bardeen, Walter Brattain, and William Shockley. A Transistor is a semiconductor device used to amplify or switch electronic power.
signals It
is
and
electrical
composed
of
semiconductor material usually with at
least
three
terminals
for
connection to an external circuit. They can be most fundamentally used as either a switch or an amplifier.
FIGURE 1 REPLICA OF FIRST EVER TRANSISTOR
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How is a transistor made? If we treat silicon (which is neither a conductor nor an insulator)
with
impurities
(doping), we can make it behave in a different way. If we dope silicon with the chemical elements arsenic, phosphorus, or antimony, the silicon gains some extra "free" electrons—ones that can
carry
current—so
an
electric
electrons
will
FIGURE 2 ORIGINAL CONCEPT OF TRANSISTOR
flow out of it more naturally. Because electrons have a negative charge, silicon treated this way is called n-type semiconductor (negative type). We can also dope silicon with other impurities such as boron, gallium, and aluminium. Silicon treated this way has fewer of those "free" electrons, so the electrons in nearby materials will tend to flow into it. We call this sort of silicon p-type semiconductor (positive type). To make a basic p-n junction, a thin wafer of n-type (or p-type) Si crystal is placed on a thin film of Aluminium (or Phosphorus), and heated to a very high temperature of about 580 0C, Al (or P) diffuses into the doped Si crystal, forming p- and n- type layers on either side. Transistors are made by a combination in the form of either n-p-n type or p-n-p type transistor.
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Working of a junction Transistor Taking the case of an n-p-n transistor, let’s call the two contacts joined to the two pieces of n-type silicon the emitter and the collector, and the contact joined to the p-type silicon we'll call the base. When no current is flowing in the transistor, we know the p-type silicon is short of electrons (shown here by the little plus signs, representing positive charges) and the two pieces of n-type silicon have extra electrons (shown by the little minus signs, representing negative charges).
FIGURE 3 AN NPN JUNCTION TRANSISTOR
Another way of looking at this is to say that while the n-type has a surplus of electrons, the p-type has holes where electrons should be. Normally, the holes in the base act like a barrier, preventing any significant current flow from the emitter to the collector while the transistor is in its "Off" State. A transistor works when the electrons and the holes start moving across the two junctions between the n-type and p-type silicon. Upon connecting the transistor up to some power by attaching a small positive voltage to the base, making the emitter negatively charged, and making the collector positively charged, electrons are pulled from the emitter into the base—and then from the base into the collector. And the transistor switches to its "On" State:
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The small current that we turn on at the base makes a big current flow between the emitter and the collector. By turning a small input current into a large output current, the transistor acts like an amplifier. But it also acts like a switch at the same time. When there is no current to the base, little or no current flows between the collector and the emitter. Upon switching on the base current a large amount of current flows. So, the base current switches the whole transistor on and off. We can also understand a transistor by thinking of it like a pair of diodes. With the base positive and the emitter negative, the Base-Emitter junction is like a Forward-Biased Diode, with electrons moving in one direction across the junction and holes going the opposite way (from right to left). The Base-Collector junction is like a Reverse-Biased Diode. The positive voltage of the collector pulls most of the electrons through and into the outside circuit (though some electrons do recombine with holes in the base).
Transistors in Computers Transistors are the Building Blocks of Computer Systems and Calculators, early vacuum tubes (unlike transistors) were big in size and difficult to manage. Recent microprocessors contain millions of transistors e.g. Intel Pentium II contains 7 million, Compaq Alpha 21264 has 15 million Intel Pentium III has 28 million etc. Logically, each transistor acts as a switch combined to implement logic functions like AND, OR, NOT also to build higher level structures like adder, multiplexer, decoder, register, or to build processors like LC-3. Logic gates let computers make very simple decisions using a mathematical technique called Boolean Algebra. It is the foundation stone of computer programs: the logical series of instructions that make computers do things. AFRAH AAMER
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Normally, a junction transistor is "off" when there is no base current and switches to "on" when the base current flows. That means it takes an electric current to switch the transistor on or off. But transistors like this can be hooked up with logic gates so their output connections feed back into their inputs. The transistor then stays on even when the base current is removed. Each time some new base current flows, the transistor "flips" on or off. It remains in one of those stable states (either on or off) until another current comes along and flips it the other way. This kind of arrangement is known as a Flip-Flop and it turns a transistor into a simple memory device that stores a zero (when it's off) or a one (when it's on). Flip-flops are the basic technology behind computer memory chips.
Logic Gates A logic 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 logic gate. The logic gates are building blocks at digital electronics. They are used in digital electronics to AFRAH AAMER
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change on voltage level (input voltage) into another (output voltage) according to some logical statement relating them. 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 Gate is a table that shows all the input and output possibilities for the logic gate
Principle 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, Right/Wrong, True/False, Conducting/Non-Conducting etc. The two values of logic statements one denoted by the binary numbers 1 and 0, where 1 is used to denote the high value. The logical statements that logic gates follow are called Boolean Expressions.
Basic Gates OR Gate INPUT
A B
A+B
OUTPUT
A
B
A+B
0
0
0
0
1
1
1
0
1
1
1
1
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AND Gate INPUT
A B
A.B
OUTPUT
A
B
A.B
0
0
0
0
1
0
1
0
0
1
1
1
NOT Gate
A
Ā
INPUT
OUTPUT
A
Ā
0
1
1
0
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NOR Gate INPUT
A B
A+B
OUTPUT
A
B
A+B
0
0
1
0
1
0
1
0
0
1
1
0
NAND Gate INPUT
A B
A.B
OUTPUT
A
B
A.B
0
0
1
0
1
1
1
0
1
1
1
0
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XOR Gate INPUT
A B
A
B
OUTPUT
A
B
A B
0
0
0
0
1
1
1
0
1
1
1
0
XNOR Gate INPUT
A B
A B
OUTPUT
A
B
A B
0
0
0
0
1
1
1
0
1
1
1
0
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Designing and Stimulating Logic Gate Circuits OR Apparatus: Two ideal p-n junction diode (D1 and D2).
Theory: An OR gate can be realized by the electronic circuit, making use of two diodes D1 and D2. Here the negative terminal of the battery is grounded and corresponds to the 0 level, and the positive terminal of the battery (i.e. voltage 5V in the present case) corresponds to level 1. The output Y is voltage at C w.r.t. Earth. The following interference can be easily drawn from the working of electrical circuit is If Switch A & B are open, lamp does not glow (A=0, B=0), hence Y=0. If Switch A is open & B closed then (A=0, B=1) Lamp glows, hence Y=1. If Switch A is closed & B open then (A=1, B=0) Lamp glows, hence Y=1. If Switch A & B are closed then (A=1, B=1) Lamp glows, hence Y=1.
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Truth Table: INPUT
OUTPUT
A
B
A+B
0
0
0
0
1
1
1
0
1
1
1
1
AND Apparatus: Two ideal p-n junction diode (D1 and D2), a resistance R.
Theory: An AND gate can be realized by the electronic circuit, making use of two diodes D1 and D2 as shown in the figure. The resistance R is connected to the positive terminal of a 5V battery permanently. Here the negative terminal of the battery AFRAH AAMER 13
is grounded and corresponds to the 0 level, and the positive terminal of the battery (i.e. voltage 5V in the present case) corresponds to level 1. The output Y is voltage at C w.r.t. Earth. The following conclusions can be easily drawn from the working of electrical circuit: If Switch A & B are open, lamp does not glow (A=0, B=0), hence Y=0. If Switch A is open & B closed then (A=0, B=1) Lamp does not glow, hence Y=0. If Switch A is closed & B open then (A=1, B=0) Lamp does not glow, hence Y=0. If Switch A & B are closed then (A=1, B=1) Lamp glows, hence Y=1.
Truth Table: INPUT
OUTPUT
A
B
A.B
0
0
0
0
1
0
1
0
0
1
1
1
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NOT Apparatus: An ideal n-p-n transistor.
Theory: A NOT gate cannot be realized by using diodes. However, an electronic circuit of NOT gate can be realized by making use of a n-p-n transistor as shown in the figure. The base B of the transistor is connected to the input A through a resistance R and the emitter E is earthed. The collector is connected to 5V battery. The output Y is voltage at C w.r.t. Earth. The following conclusion can be easily drawn from the working of the electrical circuit: If switch A is open (i.e. A=0), the lump will glow, hence Y=1. If Switch A is closed (i.e. A=1), the lump will not glow, hence Y=0.
Truth Table: INPUT
OUTPUT
A
Ā
0
1
1
0
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NOR Apparatus: Two ideal p-n junction diode (D1 and D2), an ideal n-p-n transistor.
Theory: If we connect the output Y’ of OR gate to the input of a NOT gate the gate obtained is called NOR. The output Y is voltage at C w.r.t. Earth. In Boolean expression, the NOR gate is expressed as Y=A+B, and is being read as ‘A OR B negated’. The following interference can be easily drawn from the working of electrical circuit is: If Switch A & B are open (A=0, B=0) then Lamp will glow, hence Y=1. If Switch A is closed & B open (A=1, B=0) then Lamp will not glow, hence Y=0. If Switch A is open & B is closed (A=0, B=1) then Lamp will not glow, hence Y=0. If switch A & B are closed then (A=1, B=1) Lamp will not glow, hence Y=0. AFRAH AAMER 16
Truth Table: INPUT
OUTPUT
A
B
A+B
0
0
1
0
1
0
1
0
0
1
1
0
NAND Apparatus: 2 ideal p-n junction diode (D1 and D2), an ideal n-p-n transistor, a resistance R.
Theory: If we connect the output Y’ of AND gate to the input of a NOT gate the gate obtained is called NAND. The output Y is voltage at C w.r.t. earth. In Boolean expression, the NAND gate is expressed as Y=A.B, and is being read as ‘A AND B negated’. The following interference can be easily drawn from the working of electrical circuit: If Switch A & B open (A=0, B=0) then Lamp will glow, hence Y=1. If Switch A is open B is closed then (A=0, B=1) Lamp glow, hence Y=1. If switch A is closed & B is open then (A=1, B=0) Lamp glow, hence Y=1. If switch A & B are closed then (A=1, B=1) Lamp will not glow, hence Y=0. AFRAH AAMER 17
Truth Table: INPUT
OUTPUT
A
B
A.B
0
0
1
0
1
1
1
0
1
1
1
0
XOR Apparatus: Two AND gate, an OR gate, two NOT gate
Theory: The operation XOR checks for the exclusivity in the value of the two signals A and B. It means if A and B are not identical (i.e. if A=0 and B=1 or vice versa), the output Y=1, and if both are identical, then the output Y=0. This operation is also called exclusive OR gate, designated XOR. In Boolean expression, the EX OR gate is expressed as Y=A.B + A.B = A
B. The following interference can be
easily drawn from the working of electrical circuit: If both switches A&B are open (A=0, B=0) then lamp will not glow, hence Y=0. If Switch A is open B closed then (A=0, B=1) Lamp glow, hence Y=1. If switch A is closed B open then (A=1, B=0) Lamp glow, hence Y=1.
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If switch A & B are closed then (A=1, B=1) Lamp will not glow, hence Y=0
Truth Table: INPUT
OUTPUT
A
B
A
B
0
0
0
0
1
1
1
0
1
1
1
0
XNOR Apparatus: Two AND gate, an OR gate, three NOT gate
Theory: The operation EXNOR checks for the exclusivity in the value of the two signals A and B. It means if A and B are not identical (i.e. if A=0 and B=1 or vice versa), the output Y=0, and if both are identical, then the output Y=1. This operation is also called exclusive NOR gate, designated XNOR. In Boolean expression, the XNOR gate is expressed as Y=A.B + A. B = A
B. The following interference
can be easily drawn from the working of electrical circuit: If both switches A&B are open (A=0, B=0) then lamp will not glow, hence Y=1. If Switch A is open B closed then (A=0, B=1) Lamp glow, hence Y=0. AFRAH AAMER 19
If switch A is closed B open then (A=1, B=0) Lamp glow, hence Y=0. If switch A & B are closed then (A=1, B=1) Lamp will not glow, hence Y=1.
Truth Table: INPUT
OUTPUT
A
B
A
B
0
0
1
0
1
0
1
0
0
1
1
1
Boolean Algebra NAME
AND
OR
Identity law
1A=A
0+A=A
Null Law
0A=0
1+A=1
Idempotent Law
A.A=A
A+A=A
Inverse Law
A.A’=0
A+A’=1
Commutative Law
A.B = B.A
A+B = B+A
Associative Law
(AB)C=A(BC)
(A+B)+C=A+(B+C)
Distributive Law A+BC=(A+B).(A+C)
A(B+C)=A.B+A.C AFRAH AAMER 20
Absorption Law
A(A+B) = A
A+AB=A
De Morgan’s Law
(AB)’=A’+B’
(A+B)’=A’.B’
References 1. (2012) Available at: http://pages.cs.wisc.edu/~sohi/cs252/Fall2012/lectures/lec03_digi tal_logic.pdf (Accessed: 31 January 2017). 2. Digital electronics- Boolean algebra (part 1) (2013) Available at: http://ebooksforgate.blogspot.com/2013/12/digital-electronicsboolean-algebra.html (Accessed: 31 January 2017). 3. 2007, C.W. (2016) How do transistors work? Available at: http://www.explainthatstuff.com/howtransistorswork.html (Accessed: 31 January 2017). 4. Holdsworth, B. (2002) Digital logic design. Available at: https://www.scribd.com/book/282483878/Digital-Logic-Design (Accessed: 31 January 2017). 5. Veritasium (2013) How does a transistor work? Available at: https://www.youtube.com/watch?v=IcrBqCFLHIY&list=PLkahZjV5 wKe_dajngssVLffaCh2gbq55_ (Accessed: 31 January 2017). 6. Image: Basics of electronics and communication and VLSI ~ RAJESH KUMAR. (no date) Available at: https://www.google.com/imgres?imgurl=http://3.bp.blogspot.co m/-TM9WALhGieM/VZVjHFpDLI/AAAAAAAAAfc/9lqp49Pkn_Q/s1600/bardeen-brattaintransistor-patent.png/ (Accessed: 31 January 2017). (Image: Basics of electronics and communication and VLSI ~ RAJESH KUMAR .., no date) 7. File: Replica-of-first-transistor.jpg (2006) in Wikipedia. Available at: https://en.wikipedia.org/wiki/File:Replica-of-first-transistor.jpg (Accessed: 31 January 2017). (File: Replica-of-first-transistor.jpg, 2006) <HARVARD REFRENCING STYLE>
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