CS125 : Introduction to Computer Science Lecture Notes #5 Boolean Expressions, Simple Conditionals, and Statements C 2005, 2004
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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. -
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 -
THE MEANING of “EQUALS” Charles Darr Take a Look at the Following Mathematics Problem
PROFESSIONAL DEVELOPMENT THE MEANING OF “EQUALS” Charles Darr Take a look at the following mathematics problem. has been explored by mathematics education researchers internationally (Falkner, Levi and Carpenter, 1999; Kieran, 1981, 1992; MacGregor Write the number in the square below that you think and Stacey, 1997; Saenz-Ludlow and Walgamuth, 1998; Stacey and best completes the equation. MacGregor, 1999; Wright, 1999). However, the fact that so many students appear to have this 4 + 5 = + 3 misconception highlights some important considerations that we, as mathematics educators, can learn from and begin to address. How difficult do you consider this equation to be? At what age do you In what follows I look at two of these considerations. I then go on to think a student should be able to complete it correctly? discuss some strategies we can employ in the classroom to help our I recently presented this problem to over 300 Year 7 and 8 students at students gain a richer sense of what the equals sign represents. a large intermediate school. More than half answered it incorrectly.1 Moreover, the vast majority of the students who wrote something other The meaning of “equals” than 6 were inclined to write the missing number as “9”. Firstly, it is worth considering what the equals sign means in a This result is not just an intermediate school phenomenon, however. mathematical sense, and why so many children seem to struggle to Smaller numbers of students in other Years were also tested. In Years 4, develop this understanding. 5 and 6, even larger percentages wrote incorrect responses, while at Years From a mathematical point of view, the equals sign is not a command 9 and 10, more than 20 percent of the students were still not writing a to do something. -
It's the Symbol You Put Before the Answer
It’s the symbol you put before the answer Laura Swithinbank discovers that pupils often ‘see’ things differently “It’s the symbol you put before the answer.” 3. A focus on both representing and solving a problem rather than on merely solving it; ave you ever heard a pupil say this in response to being asked what the equals sign is? Having 4. A focus on both numbers and letters, rather than H heard this on more than one occasion in my on numbers alone (…) school, I carried out a brief investigation with 161 pupils, 5. A refocusing of the meaning of the equals sign. Year 3 to Year 6, in order to find out more about the way (Kieran, 2004:140-141) pupils interpret the equals sign. The response above was common however, what really interested me was the Whilst reflecting on the Kieran summary, some elements variety of other answers I received. Essentially, it was immediately struck a chord with me with regard to my own clear that pupils did not have a consistent understanding school context, particularly the concept of ‘refocusing the of the equals sign across the school. This finding spurred meaning of the equals sign’. The investigation I carried me on to consider how I presented the equals sign to my out clearly echoed points raised by Kieran. For example, pupils, and to deliberate on the following questions: when asked to explain the meaning of the ‘=’ sign, pupils at my school offered a wide range of answers including: • How can we define the equals sign? ‘the symbol you put before the answer’; ‘the total of the • What are the key issues and misconceptions with number’; ‘the amount’; ‘altogether’; ‘makes’; and ‘you regard to the equals sign in primary mathematics? reveal the answer after you’ve done the maths question’. -
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. -
Perl II Operators, Truth, Control Structures, Functions, and Processing the Command Line
Perl II Operators, truth, control structures, functions, and processing the command line Dave Messina v3 2012 1 Math 1 + 2 = 3 # kindergarten x = 1 + 2 # algebra my $x = 1 + 2; # Perl What are the differences between the algebra version and the Perl version? 2 Math my $x = 5; my $y = 2; my $z = $x + $y; 3 Math my $sum = $x + $y; my $difference = $x - $y; my $product = $x * $y; my $quotient = $x / $y; my $remainder = $x % $y; 4 Math my $x = 5; my $y = 2; my $sum = $x + $y; my $product = $x - $y; Variable names are arbitrary. Pick good ones! 5 What are these called? my $sum = $x + $y; my $difference = $x - $y; my $product = $x * $y; my $quotient = $x / $y; my $remainder = $x % $y; 6 Numeric operators Operator Meaning + add 2 numbers - subtract left number from right number * multiply 2 numbers / divide left number from right number % divide left from right and take remainder take left number to the power ** of the right number 7 Numeric comparison operators Operator Meaning < Is left number smaller than right number? > Is left number bigger than right number? <= Is left number smaller or equal to right? >= Is left number bigger or equal to right? == Is left number equal to right number? != Is left number not equal to right number? Why == ? 8 Comparison operators are yes or no questions or, put another way, true or false questions True or false: > Is left number larger than right number? 2 > 1 # true 1 > 3 # false 9 Comparison operators are true or false questions 5 > 3 -1 <= 4 5 == 5 7 != 4 10 What is truth? 0 the number 0 is false "0" -
Unicode Compression: Does Size Really Matter? TR CS-2002-11
Unicode Compression: Does Size Really Matter? TR CS-2002-11 Steve Atkin IBM Globalization Center of Competency International Business Machines Austin, Texas USA 78758 [email protected] Ryan Stansifer Department of Computer Sciences Florida Institute of Technology Melbourne, Florida USA 32901 [email protected] July 2003 Abstract The Unicode standard provides several algorithms, techniques, and strategies for assigning, transmitting, and compressing Unicode characters. These techniques allow Unicode data to be represented in a concise format in several contexts. In this paper we examine several techniques and strategies for compressing Unicode data using the programs gzip and bzip. Unicode compression algorithms known as SCSU and BOCU are also examined. As far as size is concerned, algorithms designed specifically for Unicode may not be necessary. 1 Introduction Characters these days are more than one 8-bit byte. Hence, many are concerned about the space text files use, even in an age of cheap storage. Will storing and transmitting Unicode [18] take a lot more space? In this paper we ask how compression affects Unicode and how Unicode affects compression. 1 Unicode is used to encode natural-language text as opposed to programs or binary data. Just what is natural-language text? The question seems simple, yet there are complications. In the information age we are accustomed to discretization of all kinds: music with, for instance, MP3; and pictures with, for instance, JPG. Also, a vast amount of text is stored and transmitted digitally. Yet discretizing text is not generally considered much of a problem. This may be because the En- glish language, western society, and computer technology all evolved relatively smoothly together. -
Multiplication and Division Instructions
MultiplicationMultiplication andand DivisionDivision InstructionsInstructions • MUL Instruction • IMUL Instruction • DIV Instruction • Signed Integer Division • Implementing Arithmetic Expressions Irvine, Kip R. Assembly Language for Intel-Based Computers, 2003. 1 MULMUL InstructionInstruction • The MUL (unsigned multiply) instruction multiplies an 8-, 16-, or 32-bit operand by either AL, AX, or EAX. • The instruction formats are: MUL r/m8 MUL r/m16 MUL r/m32 Implied operands: Irvine, Kip R. Assembly Language for Intel-Based Computers, 2003. 2 MULMUL ExamplesExamples 100h * 2000h, using 16-bit operands: .data val1 WORD 2000h The Carry flag indicates whether or val2 WORD 100h not the upper half of .code the product contains mov ax,val1 significant digits. mul val2 ; DX:AX = 00200000h, CF=1 12345h * 1000h, using 32-bit operands: mov eax,12345h mov ebx,1000h mul ebx ; EDX:EAX = 0000000012345000h, CF=0 Irvine, Kip R. Assembly Language for Intel-Based Computers, 2003. 3 YourYour turnturn .. .. .. What will be the hexadecimal values of DX, AX, and the Carry flag after the following instructions execute? mov ax,1234h mov bx,100h mul bx DX = 0012h, AX = 3400h, CF = 1 Irvine, Kip R. Assembly Language for Intel-Based Computers, 2003. 4 YourYour turnturn .. .. .. What will be the hexadecimal values of EDX, EAX, and the Carry flag after the following instructions execute? mov eax,00128765h mov ecx,10000h mul ecx EDX = 00000012h, EAX = 87650000h, CF = 1 Irvine, Kip R. Assembly Language for Intel-Based Computers, 2003. 5 IMULIMUL InstructionInstruction • IMUL (signed integer multiply ) multiplies an 8-, 16-, or 32-bit signed operand by either AL, AX, or EAX • Preserves the sign of the product by sign-extending it into the upper half of the destination register Example: multiply 48 * 4, using 8-bit operands: mov al,48 mov bl,4 imul bl ; AX = 00C0h, OF=1 OF=1 because AH is not a sign extension of AL. -
Programming Basics
Readings and References • Reading » Fluency with Information Technology Programming Basics • Chapter 18, Fundamental Concepts Expressed in JavaScript • Other References INFO/CSE 100, Autumn 2004 » Games and Puzzles Fluency in Information Technology • Thomas Jefferson National Accelerator Facility, Office of Science Education http://www.cs.washington.edu/100 • http://education.jlab.org/indexpages/elementgames.html 25-Oct-2004 cse100-11-programming © 2004 University of Washington 1 25-Oct-2004 cse100-11-programming © 2004 University of Washington 2 The Plan Begin with HTML • We will learn JavaScript over the next few Basic HTML is static lectures the contents of the file are displayed as given • JavaScript is used with HTML in Web pages <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" • JavaScript is a contemporary programming language -- "http://www.w3.org/TR/html4/loose.dtd"> we will learn only its basics <html> <head> • You will program in a text editor and run your program <title>Simple A</title> </head> with your browser <body> What is 2.0 + 2.0? </body> </html> JavaScript is a way to make HTML “dynamic” 25-Oct-2004 cse100-11-programming © 2004 University of Washington 3 25-Oct-2004 cse100-11-programming © 2004 University of Washington 4 Add some “dynamic” content JavaScript in an HTML page Scripting languages let us create active pages » implement actions to be taken at run-time when the page is <script> block loaded or in response to user event in <head> <head> <title>Simple B</title> Language we are javascript <head> -
UEB Guidelines for Technical Material
Guidelines for Technical Material Unified English Braille Guidelines for Technical Material This version updated October 2008 ii Last updated October 2008 iii About this Document This document has been produced by the Maths Focus Group, a subgroup of the UEB Rules Committee within the International Council on English Braille (ICEB). At the ICEB General Assembly in April 2008 it was agreed that the document should be released for use internationally, and that feedback should be gathered with a view to a producing a new edition prior to the 2012 General Assembly. The purpose of this document is to give transcribers enough information and examples to produce Maths, Science and Computer notation in Unified English Braille. This document is available in the following file formats: pdf, doc or brf. These files can be sourced through the ICEB representatives on your local Braille Authorities. Please send feedback on this document to ICEB, again through the Braille Authority in your own country. Last updated October 2008 iv Guidelines for Technical Material 1 General Principles..............................................................................................1 1.1 Spacing .......................................................................................................1 1.2 Underlying rules for numbers and letters.....................................................2 1.3 Print Symbols ..............................................................................................3 1.4 Format.........................................................................................................3