CSC-205 Computer Organization Lecture #010 Section 4.4...

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4.4 Fun with Fibonacci Chap. 4 review Conclusion References Files

CSC-205 Computer OrganizationLecture #010

Section 4.4, Gates and machine instructions

Dr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck CartledgeDr. Chuck Cartledge

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Table of contents (1 of 1)

1 4.4Bringing the Pep/8 to“life”

2 Fun with FibonacciHystorical perspective (nothat isn’t a typo)

3 Chap. 4 review

Computer architecture4 Conclusion5 References6 Files

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Bringing the Pep/8 to “life”

Pep/8 needs an operating system.

“An operating system acts as an intermediary (providing communication) between the user of acomputer and computer hardware. The purpose of anoperating system is to provide an environment in which auser can execute programs in a convenient and efficientmanner.An operating system is software that manages thecomputer hardware. The hardware must provideappropriate mechanisms to ensure the correct operationof the computer system and to prevent user programsfrom interfering with the proper operation of the system.”

Silberschatz, Galvin, and Gange [3]

While there are computers without operating systems, they are farfrom the norm.

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The Pep/8 OS from 30,000 feet.

The OS “lives” in a specificpart of RAM.

When the Pep/8 is turnedon, the OS is automaticallyloaded into system RAM.

Image from [5].

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The OS, really has two distinct parts, RAM and ROM

RAM has data and programsthat can change

ROM memory locations cannot be changed

Locations in ROM are“hardwired” into the OSapplication

ROM locations usuallycontain “pointers” to otherlocations for the “real” data

Two very special ROMlocations are: FFFA, andFFFC Image from [5].

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The Pep/8 OS from 300 feet.

Special memory locations:

FFF8 - bottom of the user stackFFFA - SP the stack pointerFFFC - PC the program counterFFFE - start of interrupt service vector

The loader is responsible for “loading” auser program into memory, setting thespecial memory locations to the correctvalues

The I/O buffer is used by the OS forinput and output

The system stack is for system variables

User applications are loaded into lowestnumbered memory

User variables are created in the userstack

Image from [5].

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Bringing the pieces together

1 The SP and PC registers are inan unknown state

2 The loader from the OS loads auser program into low memory

3 The loader copies the contents ofmemory location FFFA to the SPregister

4 The loader copies the contents ormemory location FFFC to the PCregister

5 Program execution begins withthe user application fetching thecontents pointed to by the PC.

Image from [5].

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Same image.

Image from [5].

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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 [4].

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−2It starts:

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

Negative Fibonacci numberexist as well

Fn−2 = Fn − Fn−1F−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 [2].

Sample programs are attached to this PDF.

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Fibonacci appears, and reappears all over the place

Search for images using:Fibonacci pattern

Search for scholarly worksusing: Fibonacci pattern

Search for ArXiv articlesusing: Fibonacci pattern

Ratio of two consecutiveFibonacci numbers is the“golden ratio”(≈ 1.6180327868852)

https:

//www.flickr.com/photos/

michaelpaukner/4260592085/

https://www.flickr.com/photos/michaelpaukner/4260592085/https://www.flickr.com/photos/michaelpaukner/4260592085/https://www.flickr.com/photos/michaelpaukner/4260592085/

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Computer architecture

The hardware “nuts and bolts”

Pep/8 hardware model,

Machine code (page 159),

Memory addressing modes(immediate, direct, indirect,etc.),

Load, store, and output abyte,

von Neumann, vonNeumann, von Neumann,

Programming at ISA3,

Heap and stack Image from [1].

von Neumann is very, very dumb.

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What have we covered?

Programming at level ISA3Chapter review

Next period:

Test, Section 5.1, Machine instructions and assemblers

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References (1 of 2)

[1] Barry Sarner,Information Part #2: Information Aggregation using ’The p.e.e.e Concept’: Practice, Explore, Experiment, Experience,http://www.itsallpossible.com/information-part-2-

the-p-e-e-e-concept-information-aggregation-for-

your-personal-or-business-success-quest/, 2017.

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

[3] Abraham Silberschatz, Peter Baer Galvin, and Greg Gange,Operating System Principles, John Wiley and Sons, 2006.

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

http://www.itsallpossible.com/information-part-2-the-p-e-e-e-concept-information-aggregation-for-your-personal-or-business-success-quest/http://www.itsallpossible.com/information-part-2-the-p-e-e-e-concept-information-aggregation-for-your-personal-or-business-success-quest/http://www.itsallpossible.com/information-part-2-the-p-e-e-e-concept-information-aggregation-for-your-personal-or-business-success-quest/http://livecode.com/recursion-for-runaways/https://en.wikipedia.org/wiki/Fibonacci

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References (2 of 2)

[5] J. Stanley Warford, Computer Systems, Jones & BartlettPublishers, 2010.

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Files of interest

1 Fibonacci as a for-loop2 Fibonacci as a function call

3 Fibonacci as a function

lookup4 Fibonacci as a number

generator

5 Fibonacci as a process

queue

6 Fibonacci as a recursive

function

7 Fibonacci as a state

machine

#include using namespace std;

// http://www.miniwebtool.com/list-of-fibonacci-numbers/?number=100

int main () { int number; int first = 0; int second = 1; int next = 0; cout > number;

switch(number) { case 0: next = 0; break; case 1: case 2: next = 1; break; default:

for (int i = number - 1; i; i --){ next = first + second; first = second; second = next;} }

cout

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