01 EEE 2103 Lec 01 DE Logic Gates.ppt

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EEE 2103 : Digital Electronics

Lec-01

Digital Logic Basics

Md. Zahidul Islam

Assistant Professor

Dept. of EEE, University of Dhaka

E-mail:

[email protected]

Web:

https://sites.google.com/site/mzislamraju

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Course Contents

• Digital Logic Basics: Switches and logic gates (basic and universal), Logic functions, truth tables and variables,

• Introduction to Combinational Logic: Boolean axioms and laws, Sum of Products (SOP), Product of Sums (POS), Combinational Logic Optimization (Using Boolean Algebra and Karnaugh Map), “Don't Care” conditions, Technology: Logic voltage levels (TTL, CMOS, ECL), NMOS and CMOS logic gates, Multilevel logics, Real propagation delay, Timing Diagram, Timing analysis of digital circuits, Introduction to Verilog (a language for describing hardware) and associated CAD tools,

• Sequential Logic: NOR/NAND gates based gated latch, Various Flip-flops (FF), Master-Slave FF, Shift registers, Counters, Set-up & hold time, Finite State Machines: State diagrams, Moore-type and Mealy-type machines, State machine synthesis, State machines in Verilog, State encoding,

• Digital Numbers and Arithmetic: Number representation schemes, Basic adder and subtractor (half and full adder), Ripple carry adder, Carry look ahead Adder, BCD adder, Special Circuits: ring counter, Johnson counter, Multiplexors & tristate gates, Encoder, decoders, Real world interfacing: ADC, DAC,

• Introduction to programmable logic devices: PLD, PLA, FPGA.

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Ref. Books:



Digital Systems, Principles and Applications

by R J Tocci, N R Widmer & G L Moss



Digital Fundamentals by Floyd



Digital Electronics by Anil K. Maini



Hand Notes/ Links/Supporting other documents

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What is Digital Electronics ?

Digital Electronics is a branch of Electronics which deals

with Digital systems and signals.

If you consider any electronic (digital) components like

ICs, FPGA boards, Soc chips, Memory devices, these are

composed of Logic gates, MOSFETs, transistors, flip-flops,

latches ADC’s DAC’s etc etc..!!

So in order to understand the concept of working of

digital system, it is important to study fundamentals of

Digital Electronics.

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Gate Truth Table & Operations

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Gate Truth Table & Operations

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Gate Truth Table & Operations

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Gate Truth Table & Operations

10

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Universal Gate

11

A universal gate is a gate which can implement any Boolean

function without need to use any other gate type.

The NAND and NOR gates are universal gates.

In practice, this is advantageous since NAND and NOR

gates are economical and easier to fabricate and are the

basic gates used in all IC digital logic families.

In fact, an AND gate is typically implemented as a NAND

gate followed by an inverter not the other way around!!

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NAND Gate & Universality

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NAND Gate & Universality

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NAND Gate & Universality

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NOR Gate & Universality

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NOR Gate & Universality

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NOR Gate & Universality

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Equivalent Gates

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Boolean algebra & Logic functions

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[1] x + 0 = x

[3] x + 1 = 1

[5] x + x = x

[7] x + x’ = 1

[9] x + y = y + x

[11] x + (y + z) = (x + y) + z

[13] x(y + z) = xy +xz

[15] (x + y)’ = x’y’

[17] (x’)’ = x

[2] x • 0 = 0

[4] x • 1 = x

[6] x • x = x

[8] x • X’ = 0

[10] xy = yx

[12] x(yz) = (xy)z

De Morgan’s Theorem:

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Boolean algebra & Logic functions

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Usefulness of Boolean Identities:



_{Simplification of the Boolean function}



_{Derivation of equivalent Boolean functions to}

obtain logic

diagrams

utilizing different logic gates



_{Ordinarily ANDs, ORs, and Inverters}



_{But a certain different form of Boolean}

function



_{may be convenient to obtain circuits with}

NANDs or NORs

Applications of De Morgan’s Theorem:

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21

X

Y

X'

Y'

X • Y X' •Y' Z

0

1

0 1 1

0

1

0

0 0 0

1

0

1

0 0 0

1

0

1 0 1

X

Y

X'

Z

0

1

0

1

0

1

0

0 X

Y

Z

0

1

0

1

0

1

1 Logic functions and Boolean algebra

• Any

logic function that is expressible as a truth table

can be written in Boolean algebra using +, •, and '

Z=X•Y

_Z=X'•Y

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Converting between circuits and

equations

• Find the output of the following circuit

x

y

x

+

y

(

x

+

y

)

y

__

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23

x

y

Converting between circuits and

equations

• Find the output of the following circuit

• Answer: xy

x

y

x y

_ _

___

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24

Converting between circuits and

equations

• _{Write the circuits for the following}

Boolean algebraic expressions

a)

x

+

y

x

y

x

y

x

y

__

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25

x

y

x

y

x

y

Converting between circuits and equations

• _{Write the circuits for the following}

Boolean algebraic expressions

b) (

_______

x

+

y

)

x

y

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Writing xor using and/or/not

• x



y



(x + y)(

xy

)

x

y

x



y

1

0

1

0

1

0

1

0

0 x

y

x

+

y

xy

(

x

+

y

)(xy)

____

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27

Converting decimal numbers to

binary

• 53

= 32 + 16 + 4 + 1

= 2

5

+ 2

4

+ 2

2

+ 2

0

= 1*2

5

+ 1*2

4

+ 0*2

3

+ 1*2

2

+ 0*2

1

+ 1*2

0

= 110101 in binary

= 00110101 as a full byte in binary

• 211= 128 + 64 + 16 + 2 + 1

= 2

7

+ 2

6

+ 2

4

+ 2

1

+ 2

0

= 1*2

7

+ 1*2

6

+ 0*2

5

+ 1*2

4

+ 0*2

3

+ 0*2

2

+

1*2

1

+ 1*2

0

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Converting binary numbers to

decimal

• What is 10011010 in decimal?

10011010

= 1*2

7

+ 0*2

6

+ 0*2

5

+ 1*2

4

+ 1*2

3

+

0*2

2

_{+ 1*2}

1

_{+ 0*2}

0

= 2

7

+ 2

4

+ 2

3

+ 2

1

= 128 + 16 + 8 + 2

= 154

• What is 00101001 in decimal?

00101001 = 0*2

7

+ 0*2

6

+ 1*2

5

+ 0*2

4

+ 1*2

3

+

0*2

2

+ 0*2

1

+ 1*2

0

= 2

5

+ 2

3

+ 2

0

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