chapter-2 fundamentals of digital logic. digital logic digital electronic circuits are used to build...
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CHAPTER-2
Fundamentals of Digital Logic
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Digital Logic
Digital electronic circuits are used to build computer hardware as well as other products (digital hardware)
These circuits are fabricated on silicon wafers which form the chips.
Chips have from tens to millions of transistors
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What is a transistor?
Transistor is a semiconductor device used to control flow of electric current.
It has three connections to an external circuit.
The transistor provides amplification of a signal.
A small current(input)through one pair of terminal causes a large current through the other pair (output).
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Working of a Transistor
Transistor is used as a switch with a binary function: five volts – ON, less than
five volts – OFF 0 volts = on 5 volts = off In a digital circuit, a signal is represented
in one of two states or logic level. 0 = false = no
1 = true = yes
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Working of a transistor
B - BaseC – CollectorE - Emitter
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Logic Gates
Transistors are used to create logic gates.
logic gates are blocks of hardware that produce signals of 0 or 1.
There are seven basic logic gates: AND, OR, XOR, NOT, NAND, NOR, and XNOR
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How are digital circuits built ?
Operations of logic gates are described using Boolean Algebra.
And , or and not are Boolean functions.Transistors construct circuits which
implement Boolean functions.Input and out put relationship of the binary
variables can be represented as truth tables.
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 9: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/9.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 10: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/10.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 11: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/11.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 12: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/12.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 13: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/13.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 14: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/14.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 15: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/15.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 16: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/16.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 17: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/17.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 18: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/18.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 19: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/19.jpg)
The 7400 series TTL integrated circuits
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 21: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/21.jpg)
Combinatorial or combinational circuits:
They consist of basic Boolean operations (AND, OR, NOT), and the output represents a Boolean function.
They are logic circuits whose output depends upon the presently given input only.
They don't have any memory.They are used to perform Boolean algebra on
the present input and stored data.They do not have any clock.
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Sequential circuits
They are logic circuits whose output depend upon past output states.
Flips-Flops (or Bistables) are the basic Sequential Logic Elements.
Sequential circuits have state, which means sequential circuits have memory.
State is updated based on a clock.
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Flip-flop
Flip-flop: It is a state maintaining mechanism. It is a binary cell capable of storing one bit of
information. It has only one out put A flip-flop maintains its state until directed by a clock
pulse .
Clock: It allows the hardware to operate without requiring the input to change.
It emits alternating sequence of 0 and 1.NO. of times the clock cycles through 1 to 0 in a sec is its
speed.
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 25: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/25.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 26: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/26.jpg)
Binary counterA register which goes through a
predetermined sequence of states when input is applied is a counter.
A counter accumulates numeric total, it has multiple outputs
When it reaches the maximum limit the counter is reset to zero, indicating an overflow.
A counter which follows binary sequence is called a binary counter.
N-bit binary counter is a register of n flip flops and sequence of states from 0 to 2N - 1
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 28: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/28.jpg)
State diagram of a 3-bit binary counter.
It requires 3 flip flops and the sequence is 8.
State transition occurs every time the clock pulse occurs.
It takes input from the clock pulse and output depends on internal state (outputs are taken off each flip-flop in the counter
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Multiplexer & de-multiplexer
Multiplexer:It is a digital circuit with multiple signal
inputs, which gives a single output.The out put is selected by a only one
addressing input.De-multiplexer:It is a digital circuit that takes a single data
input, and gives multiple outputsThe addressing inputs select which one of
the outputs will receive the input signal one or more address inputs
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De-multiplexer
n-bit binary number and produces an output on one of 2n output lines.
That means two, three, or four addressing lines, de-multiplex up to four, eight, or sixteen multiplexed signals respectively.
1-to-2 line decoder/de-multiplexer2-to-4 line decoder/de-multiplexer3-to-8 line decoder/de-multiplexer
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 32: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/32.jpg)
Logic symbol for 2-line-to-4-line demultiplexer
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2-line-to-4-line De-multiplexer
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De-multiplexer Function Table
D S1 S0 Y0 Y1 Y2 Y3
D 0 0 D 0 0 0
D 0 1 0 D 0 0
D 1 0 0 0 D 0
D 1 1 0 0 0 D
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 36: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/36.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 37: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/37.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 38: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/38.jpg)
Starting a Sequence
To start the circuit connect another input (e.g. push button)to the counter reset.
When the user pushes the button the counter resets to zero.
Counter’s output becomes 000
When the de-multiplexer receives the input of all zero’s it turns on its first output.
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Replication in hardware
Hardware engineers prefer replication to iteration.
Hence the need for minimization of the circuits.Rule is to optimize the Boolean formula’s forming
the circuits.Ex : not (not x) = x, a pair of directly connected
inverters are removed from the circuit without affecting the result.
x nor (not x) , nor gate and inverter used together will always give a zero.
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From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 41: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/41.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 42: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/42.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.
![Page 43: CHAPTER-2 Fundamentals of Digital Logic. Digital Logic Digital electronic circuits are used to build computer hardware as well as other products (digital](https://reader035.vdocument.in/reader035/viewer/2022062422/56649f325503460f94c4e756/html5/thumbnails/43.jpg)
From Essentials of Computer Architecture by Douglas E. Comer. ISBN 0131491792. © 2005 Pearson Education, Inc. All rights reserved.