The Nature of Computing INEL 4206 Microprocessors Lecture

The Nature of Computing INEL 4206 – Microprocessors Lecture 2 Bienvenido Vélez Ph. D. School of Engineering University of Puerto Rico - Mayagüez The Nature of Computing INEL 4206 - Microprocessors - Spring 2003

Some Inaccurate (Although Popular) Perceptions of Computing • Computing = (Electronic) Computers • Computing = Programming • Computing = Software The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 2

Computing = Computers Computing is about solving problems using computers A. K. A. The Computing Device View of Computing The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 3

Computing = Programming Computing is about writing programs for computers A. K. A. The Programming Language view of Computing The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 4

Computing = Software Computing is not concerned with hardware design A. K. A. The “Floppy Disk” view of Computing The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 5

Outline • • What is Computing? Computing Models and Computability Interpretation and Universal Computers Abstraction and Building Blocks The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 6

What is computing then? Input Information Algorithmic Computation Function Output Information Computing is the study of Computation: the process of transforming information The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 7

The Computation Process encode compute 0110110 0101010 0101… Problem The Nature of Computing decode 0110110 0101010 0101… Solution INEL 4206 - Microprocessors - Spring 2003 8

Fundamental Questions Addressed by the Discipline of Computing • • What is the nature of computation? What can be computed efficiently? How to build practical computing devices? The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 9

Computers as Integer Functions encode compute 0110110 0101010 0101… decode 0110110 0101010 0101… Problem Solution Integer The Nature of Computing Integer Function INEL 4206 - Microprocessors - Spring 2003 Integer 10

Computability All Integer Functions (IF) IF ≠ ≟ CF Computable Integer Functions (CF) Halting Problem The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 11

The Halting Problem (Alan Turing 1936) Given a program P and an input I to P determine if P stops on I Program P Input I Computer P Halts on I? We cannot build this machine … period The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 12

Computability All Integer Functions (IF) IF ≠ ≟ CF Computable Integer Functions (CF) We want to formally describe the set of computable functions. BUT HOW? ? ? The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 Halting Problem 13

Mathematical Computers: The Turing Machine (1936) 0 1 Tape Head Infinite I/O TAPE 0/{0, R} 0 1 FSM 1/{1, L} Alan Turing The Nature of Computing Turing demonstrated how to solve several problems using his LCM computing model INEL 4206 - Microprocessors - Spring 2003 14

Mathematical Computers: The Turing Machine (1936) 0 1 Tape Head Infinite I/O TAPE 0/{0, R} 0 1 FSM 1/{1, L} Alan Turing The Nature of Computing Turing demonstrated how to solve several problems using his LCM computing model INEL 4206 - Microprocessors - Spring 2003 15

A TM Machine Recognizing n n ab Rutgers Turing Machine Example http: //www. rci. rutgers. edu/~cfs/472_html/TM/anbn. TM. html The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 16

The Halting Problem Proof Sketch (Blackboard) Given a program P and an input I to P determine if P stops on I Program P Input I Computer P Halts on I? Cannot build this … period The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 17

Ad-hoc Turing Machines We know we can build TM’s to solve many interesting problems. But building a TM is a lot of work FSM FSM Sorting. FSM TM Sorting. TM TM FSM Searching TM FSM Integrating TM Can we build ONE general purpose TM? The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 18

The Universal Turing Machine (UTM) The Paradigm for Modern General Purpose Computers Encoded TM M Software • just bits • weightless • effective computing models Encoded Tape for M Universal TM Hardware • heavy • expensive • cumbersome computing model • Capable of Emulating Every other TM • Shown computable by Alan Turing (1936) BIG IDEAS: INTERPRETATION & PROGRAMMABILITY!!! The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 19

Other Familiar Models of Computation • • • Combinational Circuits Sequential Circuits (FSM’s) Pentium Instruction Set Architecture Lambda Calculus Recursive Functions C, C++, Java, C#, etc… Can you tell which ones are Turing Universal, or which ones can emulate any other Turing Machine? The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 20

Church’s Thesis “Any realizable computing device can be simulated by a Turing machine” “All the models of computation yet developed, and all those that may be developed in the future, are equivalent in power. ” Alonso Church Issues not considered: Size, Programmability, Performance But they must be considered if one is to build … The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 21

Practical Universal Computers (John) Von Neumann Architecture (1945) Memory CPU Data. Paths AC Program This looks just like a TM Tape ALU PC ABR status control Data Control Unit (FSM) CPU is a universal TM An interpreter of some programming language (PL) The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 22

Computing in Perspective Mat. Lab Excel Pascal C++ All have embedded PL’s PSpice Build Many Fortran Assembler 1 Multiple Coexisting Levels of Interpretation Assembler 2 ISA FSM Gate CMOS Assembler 3 Build One Programming is the art/science of encoding algorithms The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 23

Computing in Perspective people Computer Human Interaction, User Interfaces Application Programs CS 1/CS 2, Programming, Data Structures High-Level Language Programming Languages, Compilers Assembly INEL Language 4206 Computer Architecture Machine Language (ISA) People The Nature of Computing computers Each abstraction layer implements an INTERPRETER of some computing/programming model INEL 4206 - Microprocessors - Spring 2003 24

Why Abstraction Layers? • Resilience to change: – Each layer provides a level of indirection • Divide and Conquer Approach: – Can work on one small semantic gap at a time • Building Block Approach: Because we know of no – Can build many higher layer on same lower layer other way of doing anything The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 25

Hardware Building Blocks A B A O SEL B sel O A 2 -1 multiplexer Gate-Level Logic Provides a Computing Model The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 26

Software Building Blocks The function is one of the most ubiquitous abstraction tools // MUX – Implements a bool MUX(bool a, bool switch(sel) { case 0: return a; case 1: return b; } } 2 -1 binary multiplexer b, bool sel) { break; Other abstraction tools include: structures, classes, modules The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 27

What Makes a Good Building Block • • Provides a clear and simple contract The contract hides irrelevant detail The contract is general and orthogonal The contract is easy to remember The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 28

Some Properties of a Good Programming Language • • Does not hide expressive power of lower layers Can be efficiently interpreted Provides adequate higher level abstractions Provides a variety of constructs for creating new abstractions, layers and modules • Achieves all of the above with minimal complexity The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 29

Summary • • Computing = Information Transformation = Integer Functions Some integer functions are not computable Turing Machine computations = All computations Universal Computer = Universal TM Interpretation => Programmability => Flexibility Building blocks are abstract contracts The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 30

Summary "Computer Science is no more about computers than Astronomy is about telescopes" E. W. Dijkstra 1930 -2002 1972 Turing Award The Nature of Computing INEL 4206 - Microprocessors - Spring 2003 31