Computer Architecture Lecture No. 2
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Lab 7: Floating-Point Addition 0.0
Lab 7: Floating-Point Addition 0.0 Introduction In this lab, you will write a MIPS assembly language function that performs floating-point addition. You will then run your program using PCSpim (just as you did in Lab 6). For testing, you are provided a program that calls your function to compute the value of the mathematical constant e. For those with no assembly language experience, this will be a long lab, so plan your time accordingly. Background You should be familiar with the IEEE 754 Floating-Point Standard, which is described in Section 3.6 of your book. (Hopefully you have read that section carefully!) Here we will be dealing only with single precision floating- point values, which are formatted as follows (this is also described in the “Floating-Point Representation” subsec- tion of Section 3.6 in your book): Sign Exponent (8 bits) Significand (23 bits) 31 30 29 ... 24 23 22 21 ... 0 Remember that the exponent is biased by 127, which means that an exponent of zero is represented by 127 (01111111). The exponent is not encoded using 2s-complement. The significand is always positive, and the sign bit is kept separately. Note that the actual significand is 24 bits long; the first bit is always a 1 and thus does not need to be stored explicitly. This will be important to remember when you write your function! There are several details of IEEE 754 that you will not have to worry about in this lab. For example, the expo- nents 00000000 and 11111111 are reserved for special purposes that are described in your book (representing zero, denormalized numbers and NaNs). -
Pdp11-40.Pdf
processor handbook digital equipment corporation Copyright© 1972, by Digital Equipment Corporation DEC, PDP, UNIBUS are registered trademarks of Digital Equipment Corporation. ii TABLE OF CONTENTS CHAPTER 1 INTRODUCTION 1·1 1.1 GENERAL ............................................. 1·1 1.2 GENERAL CHARACTERISTICS . 1·2 1.2.1 The UNIBUS ..... 1·2 1.2.2 Central Processor 1·3 1.2.3 Memories ........... 1·5 1.2.4 Floating Point ... 1·5 1.2.5 Memory Management .............................. .. 1·5 1.3 PERIPHERALS/OPTIONS ......................................... 1·5 1.3.1 1/0 Devices .......... .................................. 1·6 1.3.2 Storage Devices ...................................... .. 1·6 1.3.3 Bus Options .............................................. 1·6 1.4 SOFTWARE ..... .... ........................................... ............. 1·6 1.4.1 Paper Tape Software .......................................... 1·7 1.4.2 Disk Operating System Software ........................ 1·7 1.4.3 Higher Level Languages ................................... .. 1·7 1.5 NUMBER SYSTEMS ..................................... 1-7 CHAPTER 2 SYSTEM ARCHITECTURE. 2-1 2.1 SYSTEM DEFINITION .............. 2·1 2.2 UNIBUS ......................................... 2-1 2.2.1 Bidirectional Lines ...... 2-1 2.2.2 Master-Slave Relation .. 2-2 2.2.3 Interlocked Communication 2-2 2.3 CENTRAL PROCESSOR .......... 2-2 2.3.1 General Registers ... 2-3 2.3.2 Processor Status Word ....... 2-4 2.3.3 Stack Limit Register 2-5 2.4 EXTENDED INSTRUCTION SET & FLOATING POINT .. 2-5 2.5 CORE MEMORY . .... 2-6 2.6 AUTOMATIC PRIORITY INTERRUPTS .... 2-7 2.6.1 Using the Interrupts . 2-9 2.6.2 Interrupt Procedure 2-9 2.6.3 Interrupt Servicing ............ .. 2-10 2.7 PROCESSOR TRAPS ............ 2-10 2.7.1 Power Failure .............. -
The Hexadecimal Number System and Memory Addressing
C5537_App C_1107_03/16/2005 APPENDIX C The Hexadecimal Number System and Memory Addressing nderstanding the number system and the coding system that computers use to U store data and communicate with each other is fundamental to understanding how computers work. Early attempts to invent an electronic computing device met with disappointing results as long as inventors tried to use the decimal number sys- tem, with the digits 0–9. Then John Atanasoff proposed using a coding system that expressed everything in terms of different sequences of only two numerals: one repre- sented by the presence of a charge and one represented by the absence of a charge. The numbering system that can be supported by the expression of only two numerals is called base 2, or binary; it was invented by Ada Lovelace many years before, using the numerals 0 and 1. Under Atanasoff’s design, all numbers and other characters would be converted to this binary number system, and all storage, comparisons, and arithmetic would be done using it. Even today, this is one of the basic principles of computers. Every character or number entered into a computer is first converted into a series of 0s and 1s. Many coding schemes and techniques have been invented to manipulate these 0s and 1s, called bits for binary digits. The most widespread binary coding scheme for microcomputers, which is recog- nized as the microcomputer standard, is called ASCII (American Standard Code for Information Interchange). (Appendix B lists the binary code for the basic 127- character set.) In ASCII, each character is assigned an 8-bit code called a byte. -
Appendix D an Alternative to RISC: the Intel 80X86
D.1 Introduction D-2 D.2 80x86 Registers and Data Addressing Modes D-3 D.3 80x86 Integer Operations D-6 D.4 80x86 Floating-Point Operations D-10 D.5 80x86 Instruction Encoding D-12 D.6 Putting It All Together: Measurements of Instruction Set Usage D-14 D.7 Concluding Remarks D-20 D.8 Historical Perspective and References D-21 D An Alternative to RISC: The Intel 80x86 The x86 isn’t all that complex—it just doesn’t make a lot of sense. Mike Johnson Leader of 80x86 Design at AMD, Microprocessor Report (1994) © 2003 Elsevier Science (USA). All rights reserved. D-2 I Appendix D An Alternative to RISC: The Intel 80x86 D.1 Introduction MIPS was the vision of a single architect. The pieces of this architecture fit nicely together and the whole architecture can be described succinctly. Such is not the case of the 80x86: It is the product of several independent groups who evolved the architecture over 20 years, adding new features to the original instruction set as you might add clothing to a packed bag. Here are important 80x86 milestones: I 1978—The Intel 8086 architecture was announced as an assembly language– compatible extension of the then-successful Intel 8080, an 8-bit microproces- sor. The 8086 is a 16-bit architecture, with all internal registers 16 bits wide. Whereas the 8080 was a straightforward accumulator machine, the 8086 extended the architecture with additional registers. Because nearly every reg- ister has a dedicated use, the 8086 falls somewhere between an accumulator machine and a general-purpose register machine, and can fairly be called an extended accumulator machine. -
POINTER (IN C/C++) What Is a Pointer?
POINTER (IN C/C++) What is a pointer? Variable in a program is something with a name, the value of which can vary. The way the compiler and linker handles this is that it assigns a specific block of memory within the computer to hold the value of that variable. • The left side is the value in memory. • The right side is the address of that memory Dereferencing: • int bar = *foo_ptr; • *foo_ptr = 42; // set foo to 42 which is also effect bar = 42 • To dereference ted, go to memory address of 1776, the value contain in that is 25 which is what we need. Differences between & and * & is the reference operator and can be read as "address of“ * is the dereference operator and can be read as "value pointed by" A variable referenced with & can be dereferenced with *. • Andy = 25; • Ted = &andy; All expressions below are true: • andy == 25 // true • &andy == 1776 // true • ted == 1776 // true • *ted == 25 // true How to declare pointer? • Type + “*” + name of variable. • Example: int * number; • char * c; • • number or c is a variable is called a pointer variable How to use pointer? • int foo; • int *foo_ptr = &foo; • foo_ptr is declared as a pointer to int. We have initialized it to point to foo. • foo occupies some memory. Its location in memory is called its address. &foo is the address of foo Assignment and pointer: • int *foo_pr = 5; // wrong • int foo = 5; • int *foo_pr = &foo; // correct way Change the pointer to the next memory block: • int foo = 5; • int *foo_pr = &foo; • foo_pr ++; Pointer arithmetics • char *mychar; // sizeof 1 byte • short *myshort; // sizeof 2 bytes • long *mylong; // sizeof 4 byts • mychar++; // increase by 1 byte • myshort++; // increase by 2 bytes • mylong++; // increase by 4 bytes Increase pointer is different from increase the dereference • *P++; // unary operation: go to the address of the pointer then increase its address and return a value • (*P)++; // get the value from the address of p then increase the value by 1 Arrays: • int array[] = {45,46,47}; • we can call the first element in the array by saying: *array or array[0]. -
Computer Organization & Architecture Eie
COMPUTER ORGANIZATION & ARCHITECTURE EIE 411 Course Lecturer: Engr Banji Adedayo. Reg COREN. The characteristics of different computers vary considerably from category to category. Computers for data processing activities have different features than those with scientific features. Even computers configured within the same application area have variations in design. Computer architecture is the science of integrating those components to achieve a level of functionality and performance. It is logical organization or designs of the hardware that make up the computer system. The internal organization of a digital system is defined by the sequence of micro operations it performs on the data stored in its registers. The internal structure of a MICRO-PROCESSOR is called its architecture and includes the number lay out and functionality of registers, memory cell, decoders, controllers and clocks. HISTORY OF COMPUTER HARDWARE The first use of the word ‘Computer’ was recorded in 1613, referring to a person who carried out calculation or computation. A brief History: Computer as we all know 2day had its beginning with 19th century English Mathematics Professor named Chales Babage. He designed the analytical engine and it was this design that the basic frame work of the computer of today are based on. 1st Generation 1937-1946 The first electronic digital computer was built by Dr John V. Atanasoff & Berry Cliford (ABC). In 1943 an electronic computer named colossus was built for military. 1946 – The first general purpose digital computer- the Electronic Numerical Integrator and computer (ENIAC) was built. This computer weighed 30 tons and had 18,000 vacuum tubes which were used for processing. -
Subtyping Recursive Types
ACM Transactions on Programming Languages and Systems, 15(4), pp. 575-631, 1993. Subtyping Recursive Types Roberto M. Amadio1 Luca Cardelli CNRS-CRIN, Nancy DEC, Systems Research Center Abstract We investigate the interactions of subtyping and recursive types, in a simply typed λ-calculus. The two fundamental questions here are whether two (recursive) types are in the subtype relation, and whether a term has a type. To address the first question, we relate various definitions of type equivalence and subtyping that are induced by a model, an ordering on infinite trees, an algorithm, and a set of type rules. We show soundness and completeness between the rules, the algorithm, and the tree semantics. We also prove soundness and a restricted form of completeness for the model. To address the second question, we show that to every pair of types in the subtype relation we can associate a term whose denotation is the uniquely determined coercion map between the two types. Moreover, we derive an algorithm that, when given a term with implicit coercions, can infer its least type whenever possible. 1This author's work has been supported in part by Digital Equipment Corporation and in part by the Stanford-CNR Collaboration Project. Page 1 Contents 1. Introduction 1.1 Types 1.2 Subtypes 1.3 Equality of Recursive Types 1.4 Subtyping of Recursive Types 1.5 Algorithm outline 1.6 Formal development 2. A Simply Typed λ-calculus with Recursive Types 2.1 Types 2.2 Terms 2.3 Equations 3. Tree Ordering 3.1 Subtyping Non-recursive Types 3.2 Folding and Unfolding 3.3 Tree Expansion 3.4 Finite Approximations 4. -
A Variable Precision Hardware Acceleration for Scientific Computing Andrea Bocco
A variable precision hardware acceleration for scientific computing Andrea Bocco To cite this version: Andrea Bocco. A variable precision hardware acceleration for scientific computing. Discrete Mathe- matics [cs.DM]. Université de Lyon, 2020. English. NNT : 2020LYSEI065. tel-03102749 HAL Id: tel-03102749 https://tel.archives-ouvertes.fr/tel-03102749 Submitted on 7 Jan 2021 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. N°d’ordre NNT : 2020LYSEI065 THÈSE de DOCTORAT DE L’UNIVERSITÉ DE LYON Opérée au sein de : CEA Grenoble Ecole Doctorale InfoMaths EDA N17° 512 (Informatique Mathématique) Spécialité de doctorat :Informatique Soutenue publiquement le 29/07/2020, par : Andrea Bocco A variable precision hardware acceleration for scientific computing Devant le jury composé de : Frédéric Pétrot Président et Rapporteur Professeur des Universités, TIMA, Grenoble, France Marc Dumas Rapporteur Professeur des Universités, École Normale Supérieure de Lyon, France Nathalie Revol Examinatrice Docteure, École Normale Supérieure de Lyon, France Fabrizio Ferrandi Examinateur Professeur associé, Politecnico di Milano, Italie Florent de Dinechin Directeur de thèse Professeur des Universités, INSA Lyon, France Yves Durand Co-directeur de thèse Docteur, CEA Grenoble, France Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2020LYSEI065/these.pdf © [A. -
CS31 Discussion 1E Spring 17’: Week 08
CS31 Discussion 1E Spring 17’: week 08 TA: Bo-Jhang Ho [email protected] Credit to former TA Chelsea Ju Project 5 - Map cipher to crib } Approach 1: For each pair of positions, check two letters in cipher and crib are both identical or different } For each pair of positions pos1 and pos2, cipher[pos1] == cipher[pos2] should equal to crib[pos1] == crib[pos2] } Approach 2: Get the positions of the letter and compare } For each position pos, indexes1 = getAllPositions(cipher, pos, cipher[pos]) indexes2 = getAllPositions(crib, pos, crib[pos]) indexes1 should equal to indexes2 Project 5 - Map cipher to crib } Approach 3: Generate the mapping } We first have a mapping array char cipher2crib[128] = {‘\0’}; } Then whenever we attempt to map letterA in cipher to letterB in crib, we first check whether it violates the previous setup: } Is cipher2crib[letterA] != ‘\0’? // implies letterA has been used } Then cipher2crib[letterA] should equal to letterB } If no violation happens, } cipher2crib[letterA] = letterB; Road map of CS31 String Array Function Class Variable If / else Loops Pointer!! Cheat sheet Data type } int *a; } a is a variable, whose data type is int * } a stores an address of some integer “Use as verbs” } & - address-of operator } &b means I want to get the memory address of variable b } * - dereference operator } *c means I want to retrieve the value in address c Memory model Address Memory Contents 1000 1 byte 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 Memory model Address Memory -
Chapter 9: Memory Management
Chapter 9: Memory Management I Background I Swapping I Contiguous Allocation I Paging I Segmentation I Segmentation with Paging Operating System Concepts 9.1 Silberschatz, Galvin and Gagne 2002 Background I Program must be brought into memory and placed within a process for it to be run. I Input queue – collection of processes on the disk that are waiting to be brought into memory to run the program. I User programs go through several steps before being run. Operating System Concepts 9.2 Silberschatz, Galvin and Gagne 2002 Binding of Instructions and Data to Memory Address binding of instructions and data to memory addresses can happen at three different stages. I Compile time: If memory location known a priori, absolute code can be generated; must recompile code if starting location changes. I Load time: Must generate relocatable code if memory location is not known at compile time. I Execution time: Binding delayed until run time if the process can be moved during its execution from one memory segment to another. Need hardware support for address maps (e.g., base and limit registers). Operating System Concepts 9.3 Silberschatz, Galvin and Gagne 2002 Multistep Processing of a User Program Operating System Concepts 9.4 Silberschatz, Galvin and Gagne 2002 Logical vs. Physical Address Space I The concept of a logical address space that is bound to a separate physical address space is central to proper memory management. ✦ Logical address – generated by the CPU; also referred to as virtual address. ✦ Physical address – address seen by the memory unit. I Logical and physical addresses are the same in compile- time and load-time address-binding schemes; logical (virtual) and physical addresses differ in execution-time address-binding scheme. -
Chapter 5 the LC-3
Instruction Set Architecture ISA = Programmer-visible components & operations • Memory organization Address space -- how may locations can be addressed? Addressibility -- how many bits per location? • Register set Chapter 5 How many? What size? How are they used? • Instruction set The LC-3 Opcodes Data types Addressing modes All information needed to write/gen machine language program Based on slides © McGraw-Hill Additional material © 2004/2005 Lewis/Martin CSE 240 5-2 LC-3 Overview: Memory and Registers LC-3 Overview: Instruction Set Memory Opcodes • Address space: 216 locations (16-bit addresses) • 16 opcodes • Addressibility: 16 bits • Operate instructions: ADD, AND, NOT, (MUL) • Data movement instructions: LD, LDI, LDR, LEA, ST, STR, STI Registers • Control instructions: BR, JSR, JSRR, RET, RTI, TRAP • Temporary storage, accessed in a single machine cycle • Some opcodes set/clear condition codes, based on result Memory access generally takes longer N = negative (<0), Z = zero (=0), P = positive (> 0) • Eight general-purpose registers: R0 - R7 Data Types Each 16 bits wide • 16-bit 2’s complement integer How many bits to uniquely identify a register? Addressing Modes • Other registers • How is the location of an operand specified? Not directly addressable, but used by (and affected by) • Non-memory addresses: register, immediate (literal) instructions PC (program counter), condition codes, MAR, MDR, etc. • Memory addresses: base+offset, PC-relative, indirect CSE 240 5-3 CSE 240 5-4 1 LC-3 Instruction Summary Operate Instructions (inside back cover) Only three operations • ADD, AND, NOT Source and destination operands are registers • Do not reference memory • ADD and AND can use “immediate” mode, (i.e., one operand is hard-wired into instruction) Will show abstracted datapath with each instruction • Illustrate when and where data moves to accomplish desired op. -
Instruction Set Architecture
Instruction Set Architecture EE3376 1 –Adapted from notes from BYU ECE124 Topics to Cover… l MSP430 ISA l MSP430 Registers, ALU, Memory l Instruction Formats l Addressing Modes l Double Operand Instructions l Single Operand Instructions l Jump Instructions l Emulated Instructions – http://en.wikipedia.org/wiki/TI_MSP430 2 –Adapted from notes from BYU ECE124 Levels of Transformation –Problems –Algorithms – C Instructions –Language (Program) –Programmable –Assembly Language – MSP 430 ISA –Machine (ISA) Architecture –Computer Specific –Microarchitecture –Manufacturer Specific –Circuits –Devices 3 –Adapted from notes from BYU ECE124 Instruction Set Architecture l The computer ISA defines all of the programmer-visible components and operations of the computer – memory organization l address space -- how may locations can be addressed? l addressibility -- how many bits per location? – register set (a place to store a collection of bits) l how many? what size? how are they used? – instruction set l Opcodes (operation selection codes) l data types (data types: byte or word) l addressing modes (coding schemes to access data) l ISA provides all information needed for someone that wants to write a program in machine language (or translate 4 from a high-level language to machine language). –Adapted from notes from BYU ECE124 MSP430 Instruction Set Architecture l MSP430 CPU specifically designed to allow the use of modern programming techniques, such as: – the computation of jump addresses – data processing in tables – use of high-level languages such as C. l 64KB memory space with 16 16-bit registers that reduce fetches to memory. l Implements RISC architecture with 27 instructions and 7 addressing modes.