Instruction Set Architecture
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Frequently Asked Questions in Mathematics
Frequently Asked Questions in Mathematics The Sci.Math FAQ Team. Editor: Alex L´opez-Ortiz e-mail: [email protected] Contents 1 Introduction 4 1.1 Why a list of Frequently Asked Questions? . 4 1.2 Frequently Asked Questions in Mathematics? . 4 2 Fundamentals 5 2.1 Algebraic structures . 5 2.1.1 Monoids and Groups . 6 2.1.2 Rings . 7 2.1.3 Fields . 7 2.1.4 Ordering . 8 2.2 What are numbers? . 9 2.2.1 Introduction . 9 2.2.2 Construction of the Number System . 9 2.2.3 Construction of N ............................... 10 2.2.4 Construction of Z ................................ 10 2.2.5 Construction of Q ............................... 11 2.2.6 Construction of R ............................... 11 2.2.7 Construction of C ............................... 12 2.2.8 Rounding things up . 12 2.2.9 What’s next? . 12 3 Number Theory 14 3.1 Fermat’s Last Theorem . 14 3.1.1 History of Fermat’s Last Theorem . 14 3.1.2 What is the current status of FLT? . 14 3.1.3 Related Conjectures . 15 3.1.4 Did Fermat prove this theorem? . 16 3.2 Prime Numbers . 17 3.2.1 Largest known Mersenne prime . 17 3.2.2 Largest known prime . 17 3.2.3 Largest known twin primes . 18 3.2.4 Largest Fermat number with known factorization . 18 3.2.5 Algorithms to factor integer numbers . 18 3.2.6 Primality Testing . 19 3.2.7 List of record numbers . 20 3.2.8 What is the current status on Mersenne primes? . -
Chapter 7 Expressions and Assignment Statements
Chapter 7 Expressions and Assignment Statements Chapter 7 Topics Introduction Arithmetic Expressions Overloaded Operators Type Conversions Relational and Boolean Expressions Short-Circuit Evaluation Assignment Statements Mixed-Mode Assignment Chapter 7 Expressions and Assignment Statements Introduction Expressions are the fundamental means of specifying computations in a programming language. To understand expression evaluation, need to be familiar with the orders of operator and operand evaluation. Essence of imperative languages is dominant role of assignment statements. Arithmetic Expressions Their evaluation was one of the motivations for the development of the first programming languages. Most of the characteristics of arithmetic expressions in programming languages were inherited from conventions that had evolved in math. Arithmetic expressions consist of operators, operands, parentheses, and function calls. The operators can be unary, or binary. C-based languages include a ternary operator, which has three operands (conditional expression). The purpose of an arithmetic expression is to specify an arithmetic computation. An implementation of such a computation must cause two actions: o Fetching the operands from memory o Executing the arithmetic operations on those operands. Design issues for arithmetic expressions: 1. What are the operator precedence rules? 2. What are the operator associativity rules? 3. What is the order of operand evaluation? 4. Are there restrictions on operand evaluation side effects? 5. Does the language allow user-defined operator overloading? 6. What mode mixing is allowed in expressions? Operator Evaluation Order 1. Precedence The operator precedence rules for expression evaluation define the order in which “adjacent” operators of different precedence levels are evaluated (“adjacent” means they are separated by at most one operand). -
Operators and Expressions
UNIT – 3 OPERATORS AND EXPRESSIONS Lesson Structure 3.0 Objectives 3.1 Introduction 3.2 Arithmetic Operators 3.3 Relational Operators 3.4 Logical Operators 3.5 Assignment Operators 3.6 Increment and Decrement Operators 3.7 Conditional Operator 3.8 Bitwise Operators 3.9 Special Operators 3.10 Arithmetic Expressions 3.11 Evaluation of Expressions 3.12 Precedence of Arithmetic Operators 3.13 Type Conversions in Expressions 3.14 Operator Precedence and Associability 3.15 Mathematical Functions 3.16 Summary 3.17 Questions 3.18 Suggested Readings 3.0 Objectives After going through this unit you will be able to: Define and use different types of operators in Java programming Understand how to evaluate expressions? Understand the operator precedence and type conversion And write mathematical functions. 3.1 Introduction Java supports a rich set of operators. We have already used several of them, such as =, +, –, and *. An operator is a symbol that tells the computer to perform certain mathematical or logical manipulations. Operators are used in programs to manipulate data and variables. They usually form a part of mathematical or logical expressions. Java operators can be classified into a number of related categories as below: 1. Arithmetic operators 2. Relational operators 1 3. Logical operators 4. Assignment operators 5. Increment and decrement operators 6. Conditional operators 7. Bitwise operators 8. Special operators 3.2 Arithmetic Operators Arithmetic operators are used to construct mathematical expressions as in algebra. Java provides all the basic arithmetic operators. They are listed in Tabled 3.1. The operators +, –, *, and / all works the same way as they do in other languages. -
Simple Computer Example Register Structure
Simple Computer Example Register Structure Read pp. 27-85 Simple Computer • To illustrate how a computer operates, let us look at the design of a very simple computer • Specifications 1. Memory words are 16 bits in length 2. 2 12 = 4 K words of memory 3. Memory can be accessed in one clock cycle 4. Single Accumulator for ALU (AC) 5. Registers are fully connected Simple Computer Continued 4K x 16 Memory MAR 12 MDR 16 X PC 12 ALU IR 16 AC Simple Computer Specifications (continued) 6. Control signals • INCPC – causes PC to increment on clock edge - [PC] +1 PC •ACin - causes output of ALU to be stored in AC • GMDR2X – get memory data register to X - [MDR] X • Read (Write) – Read (Write) contents of memory location whose address is in MAR To implement instructions, control unit must break down the instruction into a series of register transfers (just like a complier must break down C program into a series of machine level instructions) Simple Computer (continued) • Typical microinstruction for reading memory State Register Transfer Control Line(s) Next State 1 [[MAR]] MDR Read 2 • Timing State 1 State 2 During State 1, Read set by control unit CLK - Data is read from memory - MDR changes at the Read beginning of State 2 - Read is completed in one clock cycle MDR Simple Computer (continued) • Study: how to write the microinstructions to implement 3 instructions • ADD address • ADD (address) • JMP address ADD address: add using direct addressing 0000 address [AC] + [address] AC ADD (address): add using indirect addressing 0001 address [AC] + [[address]] AC JMP address 0010 address address PC Instruction Format for Simple Computer IR OP 4 AD 12 AD = address - Two phases to implement instructions: 1. -
ARM Instruction Set
4 ARM Instruction Set This chapter describes the ARM instruction set. 4.1 Instruction Set Summary 4-2 4.2 The Condition Field 4-5 4.3 Branch and Exchange (BX) 4-6 4.4 Branch and Branch with Link (B, BL) 4-8 4.5 Data Processing 4-10 4.6 PSR Transfer (MRS, MSR) 4-17 4.7 Multiply and Multiply-Accumulate (MUL, MLA) 4-22 4.8 Multiply Long and Multiply-Accumulate Long (MULL,MLAL) 4-24 4.9 Single Data Transfer (LDR, STR) 4-26 4.10 Halfword and Signed Data Transfer 4-32 4.11 Block Data Transfer (LDM, STM) 4-37 4.12 Single Data Swap (SWP) 4-43 4.13 Software Interrupt (SWI) 4-45 4.14 Coprocessor Data Operations (CDP) 4-47 4.15 Coprocessor Data Transfers (LDC, STC) 4-49 4.16 Coprocessor Register Transfers (MRC, MCR) 4-53 4.17 Undefined Instruction 4-55 4.18 Instruction Set Examples 4-56 ARM7TDMI-S Data Sheet 4-1 ARM DDI 0084D Final - Open Access ARM Instruction Set 4.1 Instruction Set Summary 4.1.1 Format summary The ARM instruction set formats are shown below. 3 3 2 2 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 9876543210 1 0 9 8 7 6 5 4 3 2 1 0 9 8 7 6 5 4 3 2 1 0 Cond 0 0 I Opcode S Rn Rd Operand 2 Data Processing / PSR Transfer Cond 0 0 0 0 0 0 A S Rd Rn Rs 1 0 0 1 Rm Multiply Cond 0 0 0 0 1 U A S RdHi RdLo Rn 1 0 0 1 Rm Multiply Long Cond 0 0 0 1 0 B 0 0 Rn Rd 0 0 0 0 1 0 0 1 Rm Single Data Swap Cond 0 0 0 1 0 0 1 0 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 1 Rn Branch and Exchange Cond 0 0 0 P U 0 W L Rn Rd 0 0 0 0 1 S H 1 Rm Halfword Data Transfer: register offset Cond 0 0 0 P U 1 W L Rn Rd Offset 1 S H 1 Offset Halfword Data Transfer: immediate offset Cond 0 -
MIPS IV Instruction Set
MIPS IV Instruction Set Revision 3.2 September, 1995 Charles Price MIPS Technologies, Inc. All Right Reserved RESTRICTED RIGHTS LEGEND Use, duplication, or disclosure of the technical data contained in this document by the Government is subject to restrictions as set forth in subdivision (c) (1) (ii) of the Rights in Technical Data and Computer Software clause at DFARS 52.227-7013 and / or in similar or successor clauses in the FAR, or in the DOD or NASA FAR Supplement. Unpublished rights reserved under the Copyright Laws of the United States. Contractor / manufacturer is MIPS Technologies, Inc., 2011 N. Shoreline Blvd., Mountain View, CA 94039-7311. R2000, R3000, R6000, R4000, R4400, R4200, R8000, R4300 and R10000 are trademarks of MIPS Technologies, Inc. MIPS and R3000 are registered trademarks of MIPS Technologies, Inc. The information in this document is preliminary and subject to change without notice. MIPS Technologies, Inc. (MTI) reserves the right to change any portion of the product described herein to improve function or design. MTI does not assume liability arising out of the application or use of any product or circuit described herein. Information on MIPS products is available electronically: (a) Through the World Wide Web. Point your WWW client to: http://www.mips.com (b) Through ftp from the internet site “sgigate.sgi.com”. Login as “ftp” or “anonymous” and then cd to the directory “pub/doc”. (c) Through an automated FAX service: Inside the USA toll free: (800) 446-6477 (800-IGO-MIPS) Outside the USA: (415) 688-4321 (call from a FAX machine) MIPS Technologies, Inc. -
Advanced Computer Architecture
Computer Architecture MTIT C 103 MIPS ISA and Processor Compiled By Afaq Alam Khan Introduction The MIPS architecture is one example of a RISC architecture The MIPS architecture is a register architecture. All arithmetic and logical operations involve only registers (or constants that are stored as part of the instructions). The MIPS architecture also includes several simple instructions for loading data from memory into registers and storing data from registers in memory; for this reason, the MIPS architecture is called a load/store architecture Register ◦ MIPS has 32 integer registers ($0, $1, ....... $30, $31) and 32 floating point registers ($f0, $f1, ....... $f30, $f31) ◦ Size of each register is 32 bits The $k0, $K1, $at, and $gp registers are reserved for os, assembler and global data And are not used by the programmer Miscellaneous Registers ◦ $PC: The $pc or program counter register points to the next instruction to be executed and is automatically updated by the CPU after instruction are executed. This register is not typically accessed directly by user programs ◦ $Status: The $status or status register is the processor status register and is updated after each instruction by the CPU. This register is not typically directly accessed by user programs. ◦ $cause: The $cause or exception cause register is used by the CPU in the event of an exception or unexpected interruption in program control flow. Examples of exceptions include division by 0, attempting to access in illegal memory address, or attempting to execute an invalid instruction (e.g., trying to execute a data item instead of code). ◦ $hi / $lo : The $hi and $lo registers are used by some specialized multiply and divide instructions. -
PYTHON BASIC OPERATORS Rialspo Int.Co M/Pytho N/Pytho N Basic O Perato Rs.Htm Copyrig Ht © Tutorialspoint.Com
PYTHON BASIC OPERATORS http://www.tuto rialspo int.co m/pytho n/pytho n_basic_o perato rs.htm Copyrig ht © tutorialspoint.com What is an operator? Simple answer can be g iven using expression 4 + 5 is equal to 9. Here, 4 and 5 are called operands and + is called operator. Python lang uag e supports the following types of operators. Arithmetic Operators Comparison (i.e., Relational) Operators Assig nment Operators Log ical Operators Bitwise Operators Membership Operators Identity Operators Let's have a look on all operators one by one. Python Arithmetic Operators: Assume variable a holds 10 and variable b holds 20, then: [ Show Example ] Operator Description Example + Addition - Adds values on either side of the a + b will g ive 30 operator - Subtraction - Subtracts rig ht hand operand a - b will g ive -10 from left hand operand * Multiplication - Multiplies values on either side a * b will g ive 200 of the operator / Division - Divides left hand operand by rig ht b / a will g ive 2 hand operand % Modulus - Divides left hand operand by rig ht b % a will g ive 0 hand operand and returns remainder ** Exponent - Performs exponential (power) a**b will g ive 10 to the power 20 calculation on operators // Floor Division - The division of operands 9//2 is equal to 4 and 9.0//2.0 is equal to where the result is the quotient in which the 4.0 dig its after the decimal point are removed. Python Comparison Operators: Assume variable a holds 10 and variable b holds 20, then: [ Show Example ] Operator Description Example == Checks if the value of two operands are equal (a == b) is not true. -
The Central Processor Unit
Systems Architecture The Central Processing Unit The Central Processing Unit – p. 1/11 The Computer System Application High-level Language Operating System Assembly Language Machine level Microprogram Digital logic Hardware / Software Interface The Central Processing Unit – p. 2/11 CPU Structure External Memory MAR: Memory MBR: Memory Address Register Buffer Register Address Incrementer R15 / PC R11 R7 R3 R14 / LR R10 R6 R2 R13 / SP R9 R5 R1 R12 R8 R4 R0 User Registers Booth’s Multiplier Barrel IR Shifter Control Unit CPSR 32-Bit ALU The Central Processing Unit – p. 3/11 CPU Registers Internal Registers Condition Flags PC Program Counter C Carry IR Instruction Register Z Zero MAR Memory Address Register N Negative MBR Memory Buffer Register V Overflow CPSR Current Processor Status Register Internal Devices User Registers ALU Arithmetic Logic Unit Rn Register n CU Control Unit n = 0 . 15 M Memory Store SP Stack Pointer MMU Mem Management Unit LR Link Register Note that each CPU has a different set of User Registers The Central Processing Unit – p. 4/11 Current Process Status Register • Holds a number of status flags: N True if result of last operation is Negative Z True if result of last operation was Zero or equal C True if an unsigned borrow (Carry over) occurred Value of last bit shifted V True if a signed borrow (oVerflow) occurred • Current execution mode: User Normal “user” program execution mode System Privileged operating system tasks Some operations can only be preformed in a System mode The Central Processing Unit – p. 5/11 Register Transfer Language NAME Value of register or unit ← Transfer of data MAR ← PC x: Guard, only if x true hcci: MAR ← PC (field) Specific field of unit ALU(C) ← 1 (name), bit (n) or range (n:m) R0 ← MBR(0:7) Rn User Register n R0 ← MBR num Decimal number R0 ← 128 2_num Binary number R1 ← 2_0100 0001 0xnum Hexadecimal number R2 ← 0x40 M(addr) Memory Access (addr) MBR ← M(MAR) IR(field) Specified field of IR CU ← IR(op-code) ALU(field) Specified field of the ALU(C) ← 1 Arithmetic and Logic Unit The Central Processing Unit – p. -
The Interrupt Program Status Register (IPSR) Contains the Exception Type Number of the Current ISR
Lab #4: POLLING & INTERRUPTS CENG 255 - iHaz - 2016 Lab4 Objectives Recognize different kinds of exceptions. Understand the behavior of interrupts. Realize the advantages and disadvantages of interrupts relative to polling. Explain what polling is and write code for it. Explain what an Interrupt Service Routine (ISR) is and write code for it. Must be Done Individually Before the Lab. Pre-Lab4 Questions Describe the major difference between polling 1 and interrupt. 2 Explain what APSR, IPSR and EPSR are. 3 Explain how PRIMASK is used. 4 Explain what an exception vector table is. 5 Explain what PORT Control registers are. Must be Done Individually Before the Lab. Polling vs. Interrupt Describe the major difference between polling and interrupt. Polling Interrupt • In polling, the processor continuously • An interrupt is a signal to the microprocessor polls or tests a given device as to whether from a device that requires attention. Upon it requires attention. The polling is receiving an interrupt signal, the microcontroller carried out by a polling program that interrupts whatever it is doing and serves the shares processing time with the currently device. The program which is associated with the running task. A device indicates it interrupt is called the interrupt service routine requires attention by setting a bit in its (ISR) or interrupt handler. device status register. • When ISR is done, the microprocessor continues • Polling the device usually means reading with its original task as if it had never been its status register every so often until the interrupted. This is achieved by pushing the device's status changes to indicate that it contents of all of its internal registers on the has completed the request. -
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.