Dr. Chuck Cartledge. 24 Oct. 2017

Transcription

1 4.4 Fun with Fibonacci Chap. 4 review Conclusion References Files CSC-205 Computer Organization Lecture #010 Section 4.4, Gates and machine instructions Dr. Chuck Cartledge 24 Oct /19

2 Table of contents (1 of 1) Bringing the Pep/8 to life 2 Fun with Fibonacci Hystorical perspective (no that isn t a typo) 3 Chap. 4 review Computer architecture 4 Conclusion 5 References 6 Files 2/19

3 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 a computer and computer hardware. The purpose of an operating system is to provide an environment in which a user can execute programs in a convenient and efficient manner. An operating system is software that manages the computer hardware. The hardware must provide appropriate mechanisms to ensure the correct operation of the computer system and to prevent user programs from interfering with the proper operation of the system. Silberschatz, Galvin, and Gange [3] While there are computers without operating systems, they are far from the norm. 3/19

4 Bringing the Pep/8 to life The Pep/8 OS from 30,000 feet. The OS lives in a specific part of RAM. When the Pep/8 is turned on, the OS is automatically loaded into system RAM. Image from [5]. 4/19

5 Bringing the Pep/8 to life The OS, really has two distinct parts, RAM and ROM RAM has data and programs that can change ROM memory locations can not be changed Locations in ROM are hardwired into the OS application ROM locations usually contain pointers to other locations for the real data Two very special ROM locations are: FFFA, and FFFC Image from [5]. 5/19

6 Bringing the Pep/8 to life The Pep/8 OS from 300 feet. Special memory locations: FFF8 - bottom of the user stack FFFA - SP the stack pointer FFFC - PC the program counter FFFE - start of interrupt service vector The loader is responsible for loading a user program into memory, setting the special memory locations to the correct values The I/O buffer is used by the OS for input and output The system stack is for system variables User applications are loaded into lowest numbered memory User variables are created in the user stack Image from [5]. 6/19

7 Bringing the Pep/8 to life Bringing the pieces together 1 The SP and PC registers are in an unknown state 2 The loader from the OS loads a user program into low memory 3 The loader copies the contents of memory location FFFA to the SP register 4 The loader copies the contents or memory location FFFC to the PC register 5 Program execution begins with the user application fetching the contents pointed to by the PC. Image from [5]. 7/19

8 Bringing the Pep/8 to life Same image. Image from [5]. 8/19

9 Hystorical perspective (no that isn t a typo) Leonardo Bonacci (c c. 1250) Considered to be the most talented Western mathematician of the Middle Ages. Most notable work Liber Abaci (1202) introduced: Arabic numbers Place values Promoted his ideas by applying them to bookkeeping Image from [4]. 9/19

10 Hystorical perspective (no that isn t a typo) 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 in a field; 2 Rabbits are able to mate at the age of one month so that at the end of its second month a female can produce another pair of rabbits; 3 Rabbits never die and a mating pair always produces one new pair (one male, one female) every month from the second month. 10/19

11 Hystorical perspective (no that isn t a typo) 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 only 1 pair. 2 At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. 3 At the end of the third month, the original female produces a second pair, making 3 pairs in all in the field. 4 At the end of the fourth month, the original female has produced yet another new pair, the female born two months ago produces her first pair also, making 5 pairs. At the end of the n th month, the number of pairs of rabbits is equal to the number of new pairs (which is the number of pairs in month n - 2) plus the number of pairs alive last month (n - 1). 11/19

12 Hystorical perspective (no that isn t a typo) Fibonacci s rabbits (math) The Fibonacci series: F n = F n 1 + F n 2 It starts: Traditional: F 1 = F 2 = 1 Modern: F 0 = 0, F 1 = 1 Negative Fibonacci number exist as well F n 2 = F n F n 1 F n = ( 1) n+1 F n 12/19

13 Hystorical perspective (no that isn t a typo) Fibonacci numbers (solutions) More than one way to skin a cat (number 49 with duct tape is exciting): For loops Recursive function Function (direct look up) State machine A process queue is left for conjecture. Sample programs are attached to this PDF. Image from [2]. 13/19

14 Hystorical perspective (no that isn t a typo) Fibonacci appears, and reappears all over the place Search for images using: Fibonacci pattern Search for scholarly works using: Fibonacci pattern Search for ArXiv articles using: Fibonacci pattern Ratio of two consecutive Fibonacci numbers is the golden ratio ( ) https: // michaelpaukner/ / 14/19

15 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 a byte, von Neumann, von Neumann, von Neumann, Programming at ISA3, Heap and stack Image from [1]. von Neumann is very, very dumb. 15/19

16 4.4 Fun with Fibonacci Chap. 4 review Conclusion References Files What have we covered? Programming at level ISA3 Chapter review Next period: Test, Section 5.1, Machine instructions and assemblers 16/19

17 References (1 of 2) [1] Barry Sarner, Information Part #2: Information Aggregation using The p.e.e.e Con the-p-e-e-e-concept-information-aggregation-foryour-personal-or-business-success-quest/, [2] Hanson Schmidt-Cornelius, Recursion for Runaways, [3] Abraham Silberschatz, Peter Baer Galvin, and Greg Gange, Operating System Principles, John Wiley and Sons, [4] Wikipedia Staff, Fibonacci, /19

18 References (2 of 2) [5] J. Stanley Warford, Computer Systems, Jones & Bartlett Publishers, /19

19 Files of interest 1 Fibonacci as a for-loop 2 Fibonacci as a function call 5 Fibonacci as a process queue 3 Fibonacci as a function lookup 4 Fibonacci as a number generator 6 Fibonacci as a recursive function 7 Fibonacci as a state machine 19/19