for Digital Students

7/27/2019 for Digital Students

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Chapter 1 1

CS370 Computer Architecture

Instructor: Tao Xie

Email address: [email protected]: GMCS 544Office hours: MW 11 am 12 pm (noon)Course website:http://www-rohan.sdsu.edu/~taoxie/cs370/index.htmlPrerequisite: CS237 or equivalent, please show meyour transcript in next class (Monday, Jan. 28).


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Chapter 1 2

Grader & Lab Software

Andres BlancoEmail: [email protected] hours: Wednesday 4 pm - 5 pm,Tuesday&Thursday 1:30 pm- 3:30 pm at GMCS 401

LogicWorks5 is needed for our lab assignment


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Chapter 1 3

Evaluation

Test1 75-minute close book & in class ...15%

Test2 75-minute close book & in class ...15%Homework assignment1 ~ 3 ...24% (8% each)Lab1 (6)% ; Lab2-3 (10% each).One 2-hr comprehensive final exam ...20%Weekly exercises* ...0%Please check our class web page regularly.


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Chapter 1 4

Class Guidelines

Prerequisite : The prerequisite for this course is CS237. This prerequisite will be strictlyenforced.There will be NO make-up tests without a verified excuse.I will not sign late drop slips!The final exam is scheduled on Monday (May 13), 13:00-15:00. Failure to appear for thefinal exam will result in a grade of F in the course, unless you make prior arrangementswith me for an Incomplete.Incompletes : To receive a grade of Incomplete (I) in this class, you must meet all of thefollowing criteria:..There will be NO extra credit in any assignments, tests, and final exam.All homeworks are due at the start of class on the indicated due day. No late homework will

be accepted.All the exams are close-book, close-notes . You can only bring one piece of paper (size A4,one side) as cheating sheet .Any questions about grading must be brought to the attention of the grader or the instructor within one week after the item in question is returned.No cell phones, No Pagers, No speaking in class.Cheating : Any one caught cheating/collaborating on an exam or any assignment will receive

an F in the course. The incident will be reported to the Office of Judicial Affairs for disciplinary proceedings. Note: If, for instance, you allow your assignment be copied by aclassmate, you are considered as guilty as the copier.


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Chapter 1 5

Grading Policy

100 90 86 82 78 74 70 66 62 58 54 50 0

| A | A- | B+ | B | B- | C+ | C | C- | D+ | D | D- | F |


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Tips for CS370

After each class, spend 1 hour to digest lectureslides.After each class, spend another 1 hour to read thetextbook.Each week, spend 1 hour to do Weekly Exercises.On average, spend 4 to 5 hours per week on CS 370.

Pay close attention on example questions on theslides and make sure you fully understand how to

solve them.


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Why We Need to Learn Hardware?

Always ImportantEvery hardware system is differentUnderstanding hardware more efficient algorithms, programs(Microsoft developers say so!)Understanding hardware more effective use of OSUnderstanding hardware more efficient database designTimelyMulticore, hyper-threading, security, . .Opens doors

Yet another option!You wont know what you need until you need it(and this will probably be after you graduate)


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Software and Hardware

1-8

Software

Hardware

Application

Language

Machine Architecture, ISA (CS572)

Microarchiture

Logic and IC (CS370)

Device

Algorithm & Data Structure


9/48Chapter 1 92013/1/22 9

Computer System Design


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System, Component, Logic Circuit, IC, Transistor

Transistor MOSFET PMOS/NMOS

CMOS

Logic Gate NOT/NAND/NOR

Functional Block ALU FPU

CPU chip SOC chip


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The Implementation of Computer System


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Charles Kime & Thomas Kaminski

2004 Pearson Education, Inc.Terms of Use(Hyperlinks are active in View Show mode)

Chapter 1 DigitalComputers and Information

Logic and Computer Design Fundamentals


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Overview

Digital Systems and Computer SystemsInformation RepresentationNumber Systems [binary, octal andhexadecimal]Arithmetic OperationsBase ConversionDecimal Codes [BCD (binary codeddecimal), parity]


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Digital System

Takes a set of discrete information inputs and discreteinternal information (system state) and generates a set

of discrete information outputs.

System State

DiscreteInformationProcessingSystem

DiscreteInputs Discrete

Outputs


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Types of Digital Systems

No state present Combinational Logic System

Output = Function(Input)State present State updated at discrete times

=> Synchronous Sequential System State updated at any time

=> Asynchronous Sequential System State = Function (State, Input) Output = Function (State)

or Function (State, Input)


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Digital System Example:

A Digital Counter (e. g., odometer):

1 30 0 5 6 4Count Up

Reset

Inputs: Count Up, ResetOutputs: Visual Display

State: "Value" of stored digits


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A Digital Computer Example

Synchronous or

Asynchronous

Inputs:Keyboard,

mouse, modem,microphone

Outputs: CRT,LCD, modem,speakers


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Signal

An information variable represented by physicalquantity (e.g., voltages and currents).

For digital systems, the variable takes on discretevalues.Two level, or binary values are the most prevalentvalues in digital systems.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 values or ranges of values of physical quantities (see Figure 1-1)


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Signal Examples Over Time

Analog

Asynchronous

Synchronous

Time

Continuous invalue & time

Discrete invalue &

continuousin time

Discrete in

value & time

Digital

Difference between Asy and Syn?


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Signal Example Physical Quantity: Voltage

ThresholdRegion


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What are other physical quantities

represent 0 and 1? CPU Voltage

Disk

CD Dynamic RAM

Binary Values: Other Physical Quantities

Magnetic Field DirectionSurface Pits/Light

Electrical Charge


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Chapter 1 22

Number Systems Representation

Positive radix, positional number systemsA number with radix r is represented by astring of digits:

An - 1 An - 2 A1 A0 . A - 1 A - 2 A - m + 1 A - min which 0 A i < r and . is the radix point .The string of digits represents the power series:

( ) ( )(Number) r = + j = - m

j j

i

i = 0i r A r A

(Integer Portion) + (Fraction Portion)

i = n - 1 j = - 1


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Chapter 1 23

Number Systems Examples

General Decimal Binary

Radix (Base) r 10 2

Digits 0 => r - 1 0 => 9 0 => 10123

Powers of 4Radix 5

-1-2-3-4

-5

r 0

r 1

r 2

r 3

r 4

r 5

r-1

r -2

r -3

r -4

r -5

110

1001000

10,000100,000

0.10.01

0.0010.0001

0.00001

1248

1632

0.50.25

0.1250.0625

0.03125


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Chapter 1 24

Special Powers of 2

210 (1024) is Kilo, denoted "K"

220 (1,048,576) is Mega, denoted "M"

230 (1,073, 741,824)is Giga, denoted "G"


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Chapter 1 26

To convert to decimal, use decimal arithmetic

to form

(digit respective power of 2).Example:Convert 11010 2 to N 10 :

Converting Binary to Decimal


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Chapter 1 27

Method 1 Subtract the largest power of 2 (see slide 19) that gives

a positive remainder and record the power. Repeat, subtracting from the prior remainder and

recording the power, until the remainder is zero. Place 1s in the positions in the binary result

corresponding to the powers recorded; in all otherpositions place 0s.Example: Convert 625 10 to N 2

Converting Decimal to Binary


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Chapter 1 28

Commonly Occurring Bases

Name Radix Digits

Binary 2 0,1Octal 8 0,1,2,3,4,5,6,7

Decimal 10 0,1,2,3,4,5,6,7,8,9Hexadecimal 16 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F

The six letters (in addition to the 10integers) in hexadecimal represent: ?


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Chapter 1 29

Decimal(Base 10)

Binary(Base 2)

Octal(Base 8)

Hexadecimal(Base 16)

00 00000 00 0001 00001 01 0102 00010 02 0203 00011 03 0304 00100 04 04

05 00101 05 0506 00110 06 0607 00111 07 0708 01000 10 0809 01001 11 09

10 01010 12 0A11 01011 13 0B12 01100 14 0C13 01101 15 0D14 01110 16 0E

15 01111 17 0F16 10000 20 10

Good idea to memorize!

Numbers in Different Bases


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Chapter 1 30

Conversion Between Bases

Method 2

To convert from one base to another:1) Convert the Integer Part

2) Convert the Fraction Part

3) Join the two results with a radix point


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Chapter 1 31

Conversion Details

To Convert the Integral Part:Repeatedly divide the number by the new radix and

save the remainders. The digits for the new radix arethe remainders in reverse order of their computation .If the new radix is > 10, then convert all remainders >

10 to digits A, B, To Convert the Fractional Part:

Repeatedly multiply the fraction by the new radix andsave the integer digits that result. The digits for thenew radix are the integer digits in order of theircomputation. If the new radix is > 10, then convert all

integers > 10 to digits A, B,


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Chapter 1 32

Example: Convert 46.6875 10 To Base 2

Convert 46 to Base 2

Convert 0.6875 to Base 2:

Join the results together with the

radix point:


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Chapter 1 33

Additional Issue - Fractional Part

Note that in this conversion, the fractional partbecame 0 as a result of the repeated

multiplications.In general, it may take many bits to get this tohappen or it may never happen.

Example: Convert 0.65 10 to N 2 0.65 = 0.1010011001001 The fractional part begins repeating every 4 steps

yielding repeating 1001 forever!Solution: Specify number of bits to right of radix point and round or truncate to this

number.


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Chapter 1 34

Checking the Conversion

To convert back, sum the digits times theirrespective powers of r.

From the prior conversion of 46.6875 10101110 2 = 1 32 + 0 16 +1 8 +1 4 + 1 2 +0 1

= 32 + 8 + 4 + 2= 46

0.1011 2 = 1/2 + 1/8 + 1/16= 0.5000 + 0.1250 + 0.0625= 0.6875


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Chapter 1 35

Binary Numbers and Binary Coding

Flexibility of representation Within constraints below, can assign any binary

combination (called a code word) to any data as longas data is uniquely encoded.

Information Types

NumericMust represent range of data neededVery desirable to represent data such that simple,straightforward computation for common arithmetic

operations permittedTight relation to binary numbers

Non-numericGreater flexibility since arithmetic operations not applied.Not tied to binary numbers


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Chapter 1 36

Given n binary digits (called bits), a binary codeis a mapping from a set of represented elements

to a subset of the 2 n binary numbers.Example: Abinary codefor the sevencolors of therainbowCode 100 isnot used

Non-numeric Binary Codes

Binary Number000001010011

101110111

ColorRedOrangeYellowGreen

BlueIndigoViolet


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Chapter 1 37

Given M elements to be represented by abinary code, the minimum number of

bits, n , needed, satisfies the followingrelationships:

2 n > M > 2 ( n 1)

n = log 2 M where x , called the ceiling function, is the integer greater than orequal to x .

Example: How many bits are required torepresent decimal digits with a binarycode?

Number of Bits Required


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Chapter 1 38

Number of Elements Represented

Given n digits in radix r, there are r ndistinct elements that can be represented.

But, you can represent m elements, m < r n

Examples: You can represent 4 elements in radix r = 2with n = 2 digits: (00, 01, 10, 11).

You can represent 4 elements in radix r = 2with n = 4 digits: (0001, 0010, 0100, 1000). This second code is called a "one hot" code.


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Chapter 1 39

Binary Coded Decimal (BCD)

The BCD code is the 8,4,2,1 code.This code is the simplest, most intuitive binarycode for decimal digits and uses the samepowers of 2 as a binary number, but onlyencodes the first ten values from 0 to 9.Example: 1001 (9) = 1000 (8) + 0001 (1)How many invalid code words are there?

What are the invalid code words?


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Chapter 1 40

Warning: Conversion or Coding?

Do NOT mix up conversion of a decimalnumber to a binary number with codinga decimal number with a BINARYCODE.

13 10 = 1101 2 (This is conversion)13 0001|0011 (This is coding)


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Chapter 1 41

Binary Arithmetic

Single Bit Addition with Carry

Multiple Bit AdditionSingle Bit Subtraction with Borrow

Multiple Bit SubtractionMultiplication


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Chapter 1 42

Single Bit Binary Addition with Carry

Given two binary digits (X,Y), a carry in (Z) we get thefollowing sum (S) and carry (C):

Carry in (Z) of 0:

Carry in (Z) of 1: Z 1 1 1 1

X 0 0 1 1+ Y + 0 + 1 + 0 + 1

C S 0 1 1 0 1 0 1 1

Z 0 0 0 0X 0 0 1 1

+ Y + 0 + 1 + 0 + 1

C S 0 0 0 1 0 1 1 0


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Chapter 1 43

Extending this to two multiple bitexamples:

Carries 0 0Augend 01100 10110Addend +10001 +10111

SumNote: The 0 is the default Carry-In to theleast significant bit.

Multiple Bit Binary Addition


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Chapter 1 44

Given two binary digits (X,Y), a borrow in (Z) weget the following difference (S) and borrow (B):

Borrow in (Z) of 0:

Borrow in (Z) of 1:

Single Bit Binary Subtraction with Borrow

Z 1 1 1 1

X 0 0 1 1

- Y -0 -1 -0 -1

BS 11 1 0 0 0 1 1

Z 0 0 0 0X 0 0 1 1

- Y -0 -1 -0 -1

BS 0 0 1 1 0 1 0 0


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Chapter 1 45

Extending this to two multiple bit examples:

Borrows 0 0Minuend 10110 10110

Subtrahend - 10010 - 10011Difference

Notes: The 0 is a Borrow-In to the least significantbit. If the Subtrahend > the Minuend, interchangeand append a to the result.

Multiple Bit Binary Subtraction


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Chapter 1 46

Binary Multiplication

The binary multiplication table is simple:

0 0 = 0 | 1 0 = 0 | 0 1 = 0 | 1 1 = 1Extending multiplication to multiple digits :

Multiplicand 1011Multiplier x 101Partial Products 1011

0000 -1011 - -

Product 110111


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Chapter 1 47

Weekly Exercise 1-1

Problems (P31 on text book)1-1; 1-4; 1-7; 1-8; 1-9, 1-12 (a); 1-16 (a)Memorize the table on slide 29


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