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Miscellanea 6.5 Fun with Fibonacci Break 1.5 Exam Conclusion References

CSC-205 Computer OrganizationLecture #008

Chapter 6, section 5,Chapter 1, section 5

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15 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 201515 July 2015

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Table of contents I

1 Miscellanea

2 6.5

3 Fun with Fibonacci

4 Break

5 1.5

6 Exam

7 Conclusion

8 References

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Corrections and additions since last lecture.

Return chapter 5 homework

Return remaining tests

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Dynamic memory allocation

What is it and why should I care??

Different types of memory allocation:

Static – you know in advance how much you need and youwant to keep stuff around

Allocated by the compiler/translator

Dynamic – you don’t know how much you’ll need and yourneeds may change as the program executes

Allocated by the applicationReleased by the application

Released dynamically allocated memory can cause memory tobecome fragmented and unusable.

Released dynamically allocated memory can be “cleaned up”via garbage collection techniques.

Allocation and consolidation of dynamic memory usuallyhandled by the Operating System.

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Translating global pointers

A new C++ token, the asterisk “*”means the variable points to a memorylocation. It “strips” away one layer ofinformation hiding.

Create three pointers and givethose pointers names.

“new” dynamically sets aside anumber of bytes that the pointer“points to”

Need to tell the compiler to usethe value of the pointer vice thelocation of the pointer (that’swhat all those asterisks are about)

Assembler code uses “indirectaddressing” to get to the actualvalue of things (0x0012 and0x0018 for example) Pages 304 – 305.

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Translating local pointers

Very similar in structure totranslating global pointers.

The variables “live” on thestack.

Pointers point to locationsin the stack.

Pages 309 – 311

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Translating structures (ideas)

What is a structure??

It is a group of dataelements brought togetherunder the same name.

Data elements can be ofdifferent types and sizes

Data elements can be in anyorder

The structure name refers tothe entire group

Structure data elementname refers to the elementwithin the structure

In many ways, like predefined types on steroids.

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Translating structures (example)

Load the offset into theINDEX register (0x0008)

The INPUT a character intothe base memory locationplus the offset in the INDEXregister (0x000B)

Same sort of process tooutput the data (load offsetinto INDEX, output relativeto base address)

Pages 313 – 315.

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Translating linked list structures (ideas)

What is a linked list?? And why do Icare??

A linked list is an ordered set ofdata elements, each containing alink to its successor

What is a ordered list?? Acollection of elements where youcan say one follows (or proceeds)another.

What is a link?? A pointer (ourfriend from before) to the another(usually the next one) element.

The link from the last element tothe next one is usually NULL.

Somehow you have to have apointer to the first item in the list.

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Translating linked list structures (example)

We define a structure thatwe will used to link things.

We create a couple orpointers for the current andnext structure

We create a structure(0x0021), update thestructure’s pointers(0x0018), enter a value,store it into a structure(0x002A based on the baseof the structure and anoffset), and repeat

Pages 317 – 319 (programprob0637.cpp).

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Hystorical perspective (no that isn’t a typo)

Leonardo Bonacci (c. 1170 – c. 1250)

Considered to be the most talentedWestern mathematician of the MiddleAges.

Most notable work Liber Abaci

(1202) introduced:

Arabic numbersPlace valuesPromoted his ideas byapplying them tobookkeeping

Image from [2].

Posed a problem having to do with rabbits.

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Fibonacci’s rabbits (the background)

The growth of an idealized rabbit population, assuming that:

1 A newly born pair of rabbits, one male, one female, are put ina field;

2 Rabbits are able to mate at the age of one month so that atthe end of its second month a female can produce anotherpair of rabbits;

3 Rabbits never die and a mating pair always produces one newpair (one male, one female) every month from the secondmonth.

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Fibonacci’s rabbits (the puzzle)

How many pairs will there be in one year?

1 At the end of the first month, they mate, but there is still only1 pair.

2 At the end of the second month the female produces a newpair, so now there are 2 pairs of rabbits in the field.

3 At the end of the third month, the original female produces asecond pair, making 3 pairs in all in the field.

4 At the end of the fourth month, the original female hasproduced yet another new pair, the female born two monthsago produces her first pair also, making 5 pairs.

At the end of the nth month, the number of pairs of rabbits isequal to the number of new pairs (which is the number of pairs inmonth n - 2) plus the number of pairs alive last month (n - 1).

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Fibonacci’s rabbits (math)

The Fibonacci series:

Fn = Fn−1+Fn−2

It starts:

Traditional: F1 = F2 = 1Modern: F0 = 0,F1 = 1

Negative Fibonacci numberexist as well

Fn−2 = Fn−Fn−1

F−n = (−1)n+1Fn

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Fibonacci numbers (solutions)

More than one way to skin a cat(number 49 with duct tape isexciting):

For loops

Recursive function

Function (direct look up)

State machine

A process queue is left forconjecture.

Image from [1].

Sample programs are attached to this pdf.

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Break time.

Take about 10 minutes.

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Real and floating point numbers

So far we have only looked at integers, the countingnumbers.

What about “real” or “floating point”numbers?? How do we represent thevalue 5.375??

For integers:

n = ∑positionsi=1 vali ∗base

(i−1)

For floating point:

n = ∑positionsi=1 vali ∗base

(i−1−m)

m is the number of bits to theright of the decimal point

If m = 3 then 5.37510 = 101.0112

Like so many other things, we change the definition of the bits.

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So how does this work??

We’ll pick it apart. n = ∑cellSizei=1 vali ∗base

(i−1−m) base = 2,m = 3

How do we represent the decimal point in binary??

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Another mechanical way to convert to binary.

Repeatedly divide theinteger portion by 2 andrecord the remainder

Repeatedly multiply thefractional portion by 2 andrecord the overflow

6.585937510 = 110.100101112

Stop converting when the integer and fractional part are 0.

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What happens with “messy” numbers??

As an exercise, convert1.2(10) to binary.

.2

0 .40 .81 .61 .20 .40 .81 .61 .2...

...

Some fractions can not be represented by a fixed length binarynumber.

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Our friend, scientific notation.

A short hand way of writingnumbers. Makes things likemultiplication and division oflarge numbers trivial. A couple ofexamples.

−328.4 =−3.284∗102

Three parts:1 Sign (- in this case)2 Coefficient (3.284 in this

case), sometimes calledthe significand

3 Exponent (2 in this case)4 Base (10 in this case)

value = SignCoefficient ∗

BaseExponent

Writing numbers in scientific notation is called “normalized” form.

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Remember the question about where do we store thedecimal point??

When dealing with numbers in the normalized form, everyoneknows where the decimal is, so no one has to store it.

And because everyone “knows” that the most significant bithas to be 1, no has to store it.

Hidden and excess bits are conventions that allow more bits to beused where they are needed.

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Special Values

The limitation on the cell size(i.e., the number of bits we canuse) places a limit on the rangeof values we can represent.

We’ve seen how ADDingcan overflow a cell.

Normalization limits thesmallest coefficient that wecan have greater than 0.

Operations using values inrange can result in valuesthat can not be represented.

Sign bit, 7 bit coeff, 5 bit expon.

All of these errors can to caught by the CPU and software.

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There are too many possibilities. We needstandardization.

The IEEE 754 Floating PointStandard to the rescue.

Each CPU manufacturer hadtheir own floating pointrepresentation.

Each felt their’s was thebest.

Application software on onemachine may not runcorrectly on anothermachine.

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IEEE 754 Special Values and Notes

Predefined special values by thespecification:

Positive and negativeinfinity: sign ⇒ 0/1, expon.⇒ all 1s, coeff ⇒ all 0s

Not a Number (NaN): sign⇒ 0/1, expon. ⇒ all 1s,coeff ⇒ anything except all0s

Precision:2−149

≈ 1.17549∗10−38 or2−1074

≈ 4.94066∗10−324

Rounding: nearest, even, 0,+/- infinity

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Steps to succeed on the exam.

General guidelines and directions

Pay attention to theexamples

Understand the homework

Work questions that haveanswers

Ask questions

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Things of real interest in chapter 5

Assembly language:

Understanding figures 1 and2

What do thepseudo-operators do

How does the von Neumanncycle work

What does it mean totranslate from HOL6 toISA3 or ASL5

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Things of real interest in chapter 6

Compiling to the Assembly level

Understanding the stack and theheap

Understanding the addressingmodes (and there are several ofthem)

What purpose does the stack andthe heap serve relative tovariables and functions

How are C++ statementstranslated into Pep/8

How are values passed betweencallers and callees

How are indexes into arrayshandled

What types of memory allocationare there and how are theydifferent

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What have we covered?

Chapter 6, section 5Different ways to have funwith FibonacciRepeat of Chapter 1, section5Preps for the exam coveringchapters 5 and 6

Next week:

Exam covering chapters 5 and 6“Fun” with von Neumann

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References I

[1] Hanson Schmidt-Cornelius, Recursion for runaways,http://livecode.com/recursion-for-runaways/, 2014.

[2] Wikipedia Staff, Fibonacci,https://en.wikipedia.org/wiki/Fibonacci, 2015.

http://livecode.com/recursion-for-runaways/

https://en.wikipedia.org/wiki/Fibonacci

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