Lecture DLD

8/10/2019 Lecture DLD

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EE220 Digital Logic Design


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Text Book for the course

Required Textbook:Digital Logic and ComputerDesign M Morris Mano ,

Digital Design, Principles &Practices, Edition John F. Wakerly(Recommended )



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Digital Design Principles and Practices, 3rd Edition


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Grading Policy

Assignments+Quizzes: 25%Mid Term: 25%Final Exam (Conceptual): 50%



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Lecture 1: Introduction to

Digital Logic Design


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Outlines

Administration Motivation

Scope



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Motivation Microprocessors have revolutionized our world

Cell phones, internet, rapid advances inmedicine, etc.

The semiconductor industry has grown from $21billion in 1985 to $213 billion in 2004.



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Robert Noyce, 1927 - 1990

Nicknamed Mayor of Silicon

Valley Cofounded Fairchild

Semiconductor in 1957

Cofounded Intel in 1968

Co-invented the integratedcircuit



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Gordon Moore, 1929 - Cofounded Intel in

1968 with RobertNoyce.

Moores Law: thenumber of transistorson a computer chip

doubles every year(observed in 1965)

Since 1975, transistorcounts have doubledevery two years.



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Moores Law

If the automobile had followed the same development

cycle as the computer, a Rolls-Royce would today cost

$100, get one million miles to the gallon, and explode

once a year . . .

Robert CringleyEE220 Digital Logic Design


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Scope

The purpose of this course is that we: Learn whats under the hood of an electronic com

Learn the principles of digital design

Learn to systematically debug increasingly compledesigns

Design and build a digital system



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Scope

Hiding details

when they arentimportant

Physics

Devices

Analog

Circuits

DigitalCircuits

Logic

Micro-

architecture

Architecture

Operating

Systems

Application

Software

electrons

transistors

diodes

amplifiers

filters

AND gatesNOT gates

adders

memories

datapaths

controllers

instructions

registers

device drivers

programs

focus

ofthis

course



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Major Components of CourseBoolean Algebra (Ch 1-3)

Combinational Logic (Ch 4-5)- Sequential Networks (Ch-6)

- Registers Counters and Memory Unit (Ch-



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Overall Picture of EE220

Control

Subsystem

Conditions

Control

Mux

Memory File

ALU

Memory

Register

Conditions

Input

Pointer

CLK: Synchronizing C



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Chapter 1Digital Systems and

Binary Numbers

Digital Logic Design


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EE220 Lectures: 3 hours/week

Digital Logic Design Credits: 3

Number systems & codes, Digital logic: Boolean algebra, De-Morga

Theorems, logic gates and their truth tables, canonical form

combinational logic circuits, minimization technique, Arithmetic a

data handling logic circuits, decoders and encoders, multiplexes and d

multiplexers, Combinational circuit design, Flip-flops, race arou

problems; Counters: asynchronous counters, synchronous counters a

their applications; PLA design; Synchronous and asynchronous logdesign; State diagram, Mealy and Moore machines; Sta

minimizationsand assignments; Pulse mode logic; Fundamental mo

design.


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Outline of Chapter 1

1.1 Digital Systems

1.2 Binary Numbers

1.3 Number-base Conversions

1.4 Octal and Hexadecimal Numbers

1.5 Complements

1.6 Signed Binary Numbers

1.7 Binary Codes

1.8 Binary Storage and Registers

1.9 Binary Logic


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Digital Systems and Binary Num

Digital age and information age

Digital computers General purposes Many scientific, industrial and commercial applications

Digital systems Telephone switching exchanges Digital camera

Electronic calculators, Digital TV

Discrete information-processing systems Manipulate discrete elements of information For example, {1, 2, 3, } and {A, B, C, }


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Analog and Digital Signal Analog system

The physical quantities or signals may vary continuously overa specified range.

Digital system The physical quantities or signals can assume only discrete

values.

Greater accuracy

t

X(t)

t

X(t)

Analog signal Digital signal


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Binary Digital Signal

An information variable represented by physical quantit

For digital systems, the variable takes on discrete values Two level, or binary values are the most prevalent va

Binary values are represented abstractly by: Digits 0 and 1 Words (symbols) False (F) and True (T)

Words (symbols) Low (L) and High (H) And words On and Off

Binary values are represented by valuesor ranges of values of physical quantities.

V(t)

Binary digital sign

Logi

Logi

unde


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Decimal Number System Base (also called radix) = 10

10 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 } Digit Position

Integer & fraction

Digit Weight

Weight = (Base)Position

Magnitude

Sum of Digitx Weight

Formal Notation

1 0 -12

5 1 2 7

10 1 0.1100

500 10 2 0.7

d2*B2+d1*B

1+d0*B

0+d-1*B

-1+

(512.74)10


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Octal Number System

Base = 8

8 digits { 0, 1, 2, 3, 4, 5, 6, 7 }

Weights


Magnitude


Formal Notation

1 0 -12

8 1 1/864

5 1 2 7

5 *82+1 *8

1+2 *8

0+7 *8

-1+4

=(330.9375)10

(512.74)8


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Binary Number System Base = 2

2 digits { 0, 1 }, called binary digitsor bits

Weights


Magnitude

Sum of Bitx Weight

Formal Notation

Groups of bits 4 bits = Nibble

8 bits = Byte

1 0 -12

2 1 1/24

1 0 1 0

1 *22+0 *2

1+1 *2

0+0 *2

-1+

=(5.25)10

(101.01)2

1 0 1 1

1 1 0 0 0 1 0 1


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Hexadecimal Number System Base = 16

16 digits { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F }

Weights


Magnitude


Formal Notation

1 0 -12

16 1 1/16256

1 E 5 7

1 *162+14 *16

1+5 *16

0+7 *16

-1+

=(485.4765625)1

(1E5.7A)16


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The Power of 2

n 2n

0 20

=11 21=2

2 22=4

3 23=8

4 24=16

5 25=32

6 26=64

7 27=128

n 2n

8 28

=2569 29=512

10 210=1024

11 211=2048

12 212=4096

20 220=1M

30 230=1G

40 240=1T

Me

Gig

Ter

Kil


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Addition Decimal Addition

5 5

55+

011

= Ten Base

Subtract a Base

11 Carry


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Binary Addition Column Addition

1 0 1111

1111 0+

0000 1 11

(2)10

111111

= 61

= 23

= 84


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Binary Subtraction Borrow a Base when needed

0 0 1110

1111 0

0101 1 10

= (10)22

22 2

1

0001

= 77

= 23

= 54


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Binary Multiplication Bit by bit

01 1 1 101 1 0

00 0 0 0

01 1 1 1

01 1 1 1

0 0 000

0110111 0

x


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Number Base Conversions

Decimal(Base 10)

Octal(Base 8)

Binary(Base 2)

Hexadecimal(Base 16)

EvaluateMagnitude

EvaluateMagnitude

Evaluate

Magnitude


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Decimal (Integer) to Binary Convers Divide the number by the Base (=2)

Take the remainder (either 0 or 1) as a coeffici

Take the quotient and repeat the division

Example: (13)10

Quotient Remainder Coefficient

Answer: (13)10= (a3 a2 a1 a0)2= (1101)2

MSB LSB

13/ 2 = 6 1 a0 =1

6 / 2 = 3 0 a1 =03 / 2 = 1 1 a2 =11 / 2 = 0 1 a3 =1


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Decimal (Fraction) to Binary Conver Multiply the number by the Base (=2)

Take the integer (either 0 or 1) as a coefficient

Take the resultant fraction and repeat thedivision

Example: (0.625)10Integer Fraction Coefficient

Answer: (0.625)10= (0.a-1 a-2 a-3)2= (0.101)2

MSB LSB

0.625 * 2 = 1 . 25

0.25 * 2 = 0 . 5 a-2 =00.5 * 2 = 1 . 0 a-3 =1

a-1 =1


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Decimal to Octal ConversionExample: (175)10

Quotient Remainder Coefficient

Answer: (175)10= (a2 a1 a0)8= (257)8

175 / 8 = 21 7 a0 =721 / 8 = 2 5 a1 =5

2 / 8 = 0 2 a2 =2

Example: (0.3125)10

Integer Fraction Coefficient

Answer: (0.3125)10= (0.a-1 a-2 a-3)8= (0.24)8

0.3125 * 8 = 2 . 5

0.5 * 8 = 4 . 0 a-2 =4

a-1 =2


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Binary Octal Conversion 8 = 23

Each group of 3 bitsrepresents an octal digit

Octal Bina

0 0 0

1 0 0

2 0 1

3 0 1

4 1 0

5 1 0

6 1 1

7 1 1

Example:

( 1 0 1 1 0 . 0 1 )2

( 2 6 . 2 )8

Assume Zeros

Works bothways (Binaryto Octal& Octalto Binary)


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Binary Hexadecimal Conversion 16 = 24

Each group of 4 bitsrepresents a hexadecimal digit

Hex0

1

2

3

4

5

6

7

8

9

A B

C

D

E

F

Example:

( 1 0 1 1 0 . 0 1 )2

( 1 6 . 4 )16

Assume Zeros

Works bothways (Binaryto Hex& Hex to Binary)


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Octal Hexadecimal Conversion Convert to Binaryas an intermediate step

Example:

( 01 0 1 1 0 . 0 1 0 )2

( 1 6 . 4 )16

Assume Zeros

Works bothways (Octalto Hex& Hex to Octal)

( 2 6 . 2 )8

Assume Zeros


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Decimal, Binary, Octal and HexadecDecimal Binary Octal Hex

00 0000 00 0

01 0001 01 102 0010 02 2

03 0011 03 3

04 0100 04 4

05 0101 05 5

06 0110 06 6

07 0111 07 7

08 1000 10 8

09 1001 11 910 1010 12 A

11 1011 13 B

12 1100 14 C

13 1101 15 D

14 1110 16 E

15 1111 17 F

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Lecture DLD