AQA Computer Science A-Level Boolean algebra Advanced Notes
|
|
|
- Annis Ellis
- 5 years ago
- Views:
Transcription
1 Q Computer Science -Level 465 Boolean algebra dvanced Notes
2 Specification: 4651 Using Boolean algebra: Be familiar with the use of Boolean identities and De Morgan s laws to manipulate and simplify Boolean expressions
3 Boolean algebra Just like algebra in Mathematics, Boolean algebra concerns representing values with letters and simplifying expressions Boolean algebra uses the Boolean values TRUE and FLSE which can be represented as 1 and 0 respectively Notation Expression Meaning, B, C, etc n unknown Boolean value being represented by a letter just like x or y in conventional algebra NOT n overline represents the NOT operation being applied to what is below the line B ND B, said dot B where a dot represents the ND (multiplication) operation B + B n alternative notation for ND B Just like in Mathematics, the product of two algebraic values can be represented without any symbol OR B, where an addition symbol represents the OR operation Order of precedence lgebraic operations have an order of precedence, meaning that some operations must be applied before others You may have met BODMS in Mathematics, this is the same idea Operator Brackets NOT ND OR Precedence Highest Lowest For example, the expression B OR NOT C ND would actually be carried out in the order B OR ((NOT C) ND )
4 Boolean identities There are a number of useful identities which can be used to simplify Boolean expressions 0 = 0 B 1 = B C C = C nything ND 0 is always 0 This is because the ND operation represents multiplication nything ND 1 is always the original value This is because the ND operation represents multiplication ny Boolean value ND itself is equivalent to just the value, as the truth table below shows C C C = = 0 D + 0 = D E + 1 = 1 F + F = F ny Boolean value OR 0 is the equivalent of adding 0 to the value, which leaves the value unchanged ny Boolean value OR 1 is the equivalent of adding 1 to the value, which will always result in 1 ny Boolean value OR itself equals the value itself, as the truth table shows F F + F = = 0 G = G ny Boolean value with two lines above has had the NOT operation performed on it twice, meaning the value has not been changed
5 De Morgan s laws Named after British logician ugustus De Morgan, these two laws of Boolean algebra come in incredibly useful when simplifying expressions De Morgan s laws can be remembered by recalling the phrase: break the bar and change the sign Where the bar refers to an overline representing the NOT operation and the sign refers to changing between + ( OR ) and ( ND ) For example, the Boolean expression + B can have De Morgan s law applied to it as follows: Break the bar: + B Change the sign: B + B = B De Morgan s law can also be applied in reverse, by changing the sign and building the bar For example, the Boolean expression C + D can be simplified as follows: Change the sign: C D Build the bar: C D C + D = C D
6 Distributive rules Just like expanding brackets in Mathematics, you can use distributive rules in Boolean algebra as follows: (B + C) = B + C Examples Example 1 Simplify the Boolean expression + B + B Use De Morgan s laws Break the bar and change the sign = + B + Use + = 1 = B + 1 Use + 1 = 1 = 1 Example 2 Simplify the Boolean expression C B + C B C B + C B Take out B as a common factor B ( C + C) Use + = 1 B ( 1) Use + 1 = B
Boolean Algebra A B A AND B = A*B A B A OR B = A+B
Boolean Algebra Algebra is the branch of mathematics that deals with variables. Variables represent unknown values and usually can stand for any real number. Because computers use only 2 numbers as we
Cambridge International AS & A Level Computer Science
Topic Support Guide Cambridge International AS & A Level Computer Science 9608 For examination from 2017 Topic 3.3.2 Boolean algebra Cambridge International Examinations retains the copyright on all its
At this point in our study of digital circuits, we have two methods for representing combinational logic: schematics and truth tables.
HPTER FIVE oolean lgebra 5.1 Need for oolean Expressions t this point in our study of digital circuits, we have two methods for representing combinational logic: schematics and truth tables. 0 0 0 1 0
JAVA OPERATORS GENERAL
JAVA OPERATORS GENERAL Java provides a rich set of operators to manipulate variables. We can divide all the Java operators into the following groups: Arithmetic Operators Relational Operators Bitwise Operators
If Control Construct
If Control Construct A mechanism for deciding whether an action should be taken JPC and JWD 2002 McGraw-Hill, Inc. 1 Boolean Algebra Logical expressions have the one of two values - true or false A rectangle
Introduction to Boolean Algebra
Introduction to Boolean Algebra Boolean algebra which deals with two-valued (true / false or and ) variables and functions find its use in modern digital computers since they too use two-level systems
Logical Operators and switch
Lecture 5 Relational and Equivalence Operators SYS-1S22 / MTH-1A66 Logical Operators and switch Stuart Gibson sg@sys.uea.ac.uk S01.09A 1 Relational Operator Meaning < Less than > Greater than
Introduction to Boolean Algebra
Introduction to Boolean Algebra Boolean algebra which deals with two-valued (true / false or and ) variables and functions find its use in modern digital computers since they too use two-level systems
Bawar Abid Abdalla. Assistant Lecturer Software Engineering Department Koya University
Logic Design First Stage Lecture No.5 Boolean Algebra Bawar Abid Abdalla Assistant Lecturer Software Engineering Department Koya University Boolean Operations Laws of Boolean Algebra Rules of Boolean Algebra
PRG PROGRAMMING ESSENTIALS. Lecture 2 Program flow, Conditionals, Loops
PRG PROGRAMMING ESSENTIALS 1 Lecture 2 Program flow, Conditionals, Loops https://cw.fel.cvut.cz/wiki/courses/be5b33prg/start Michal Reinštein Czech Technical University in Prague, Faculty of Electrical
Boolean Algebra Boolean Algebra
What is the result and type of the following expressions? Int x=2, y=15; float u=2.0, v=15.0; -x x+y x-y x*v y / x x/y y%x x%y u*v u/v v/u u%v x * u (x+y)*u u / (x-x) x++ u++ u = --x u = x -- u *= ++x
F453 Module 7: Programming Techniques. 7.2: Methods for defining syntax
7.2: Methods for defining syntax 2 What this module is about In this module we discuss: explain how functions, procedures and their related variables may be used to develop a program in a structured way,
1.8 Intro to Variables, Algebraic Expressions, and Equations
1.8 Intro to Variables, Algebraic Expressions, and Equations Professor Tim Busken M.S. Applied Mathematics with a Concentration in Dynamical Systems San Diego State University 2011 Southwestern College
LECTURE 2 An Introduction to Boolean Algebra
IST 210: Boot Camp Ritendra Datta LECTURE 2 An Introduction to Boolean Algebra 2.1. Outline of Lecture Fundamentals Negation, Conjunction, and Disjunction Laws of Boolean Algebra Constructing Truth Tables
DIGITAL SYSTEM DESIGN
DIGITAL SYSTEM DESIGN UNIT I: Introduction to Number Systems and Boolean Algebra Digital and Analog Basic Concepts, Some history of Digital Systems-Introduction to number systems, Binary numbers, Number
Stage 7 Checklists Have you reached this Standard?
Stage 7 Checklists Have you reached this Standard? Main Criteria for the whole year. J K L Use positive integer powers and associated real roots Apply the four operations with decimal numbers Write a quantity
SOFTWARE TESTING UNIT-VI Logic Based Testing
OVERVEW OF LOGC BASED TESTNG : NTRODUCTON: The functional requirements of many programs can be specified by decision tables, which provide a useful basis for program and test design. Consistency and completeness
Flow of Control. Flow of control The order in which statements are executed. Transfer of control
1 Programming in C Flow of Control Flow of control The order in which statements are executed Transfer of control When the next statement executed is not the next one in sequence 2 Flow of Control Control
V2 2/4/ Ch Programming in C. Flow of Control. Flow of Control. Flow of control The order in which statements are executed
Programming in C 1 Flow of Control Flow of control The order in which statements are executed Transfer of control When the next statement executed is not the next one in sequence 2 Flow of Control Control
CSC Discrete Math I, Spring Sets
CSC 125 - Discrete Math I, Spring 2017 Sets Sets A set is well-defined, unordered collection of objects The objects in a set are called the elements, or members, of the set A set is said to contain its
GO - OPERATORS. This tutorial will explain the arithmetic, relational, logical, bitwise, assignment and other operators one by one.
http://www.tutorialspoint.com/go/go_operators.htm GO - OPERATORS Copyright tutorialspoint.com An operator is a symbol that tells the compiler to perform specific mathematical or logical manipulations.
BOOLEAN ALGEBRA AND CIRCUITS
UNIT 3 Structure BOOLEAN ALGEBRA AND CIRCUITS Boolean Algebra and 3. Introduction 3. Objectives 3.2 Boolean Algebras 3.3 Logic 3.4 Boolean Functions 3.5 Summary 3.6 Solutions/ Answers 3. INTRODUCTION This
Java provides a rich set of operators to manipulate variables. We can divide all the Java operators into the following groups:
Basic Operators Java provides a rich set of operators to manipulate variables. We can divide all the Java operators into the following groups: Arithmetic Operators Relational Operators Bitwise Operators
Cecil Jones Academy Mathematics Fundamental Map
Fundamentals Year 7 (Core) Knowledge Unit 1 Unit 2 Solve problems involving prime numbers Use highest common factors to solve problems Use lowest common multiples to solve problems Explore powers and roots
2.2 Set Operations. Introduction DEFINITION 1. EXAMPLE 1 The union of the sets {1, 3, 5} and {1, 2, 3} is the set {1, 2, 3, 5}; that is, EXAMPLE 2
2.2 Set Operations 127 2.2 Set Operations Introduction Two, or more, sets can be combined in many different ways. For instance, starting with the set of mathematics majors at your school and the set of
Chapter 3: Operators, Expressions and Type Conversion
101 Chapter 3 Operators, Expressions and Type Conversion Chapter 3: Operators, Expressions and Type Conversion Objectives To use basic arithmetic operators. To use increment and decrement operators. To
To become familiar with array manipulation, searching, and sorting.
ELECTRICAL AND COMPUTER ENGINEERING 06-88-211: COMPUTER AIDED ANALYSIS LABORATORY EXPERIMENT #2: INTRODUCTION TO ARRAYS SID: OBJECTIVE: SECTIONS: Total Mark (out of 20): To become familiar with array manipulation,
Logical statements and. Lecture 1 ICOM 4075
Logical statements and operations Lecture 1 ICOM 4075 What is a statement? By a statementwe understand a sentence that affirms or denies the validity of a property or concept Examples: The color white
Loops and Expression Types
Software and Programming I Loops and Expression Types Roman Kontchakov / Carsten Fuhs Birkbeck, University of London Outline The while, for and do Loops Sections 4.1, 4.3 and 4.4 Variable Scope Section
BITG 1223: Selection Control Structure by: ZARITA (FTMK) LECTURE 4 (Sem 1, 16/17)
BITG 1223: Selection Control Structure by: ZARITA (FTMK) LECTURE 4 (Sem 1, 16/17) 1 Learning Outcomes At the end of this lecture, you should be able to: 1. Explain the concept of selection control structure
Information Science 1
Information Science Boolean Expressions Week College of Information Science and Engineering Ritsumeikan University Topics covered l Terms and concepts from Week 9 l Binary (Boolean) logic History Boolean
2.2 Order of Operations
2.2 Order of Operations Learning Objectives Evaluate algebraic expressions with grouping symbols. Evaluate algebraic expressions with fraction bars. Evaluate algebraic expressions using a graphing calculator.
1.4 MULTIPLYING WHOLE NUMBER EXPRESSIONS
1.4 MULTIPLYING WHOLE NUMBER EXPRESSIONS Understanding Multiplication of Whole Numbers Multiplication of whole numbers can be thought of as repeated addition. For example, suppose that a small parking
[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics
![[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics](/thumbs/82/86066673.jpg "[Ch 6] Set Theory. 1. Basic Concepts and Definitions. 400 lecture note #4. 1) Basics")
400 lecture note #4 [Ch 6] Set Theory 1. Basic Concepts and Definitions 1) Basics Element: ; A is a set consisting of elements x which is in a/another set S such that P(x) is true. Empty set: notated {
CS112 Lecture: Working with Numbers
CS112 Lecture: Working with Numbers Last revised January 30, 2008 Objectives: 1. To introduce arithmetic operators and expressions 2. To expand on accessor methods 3. To expand on variables, declarations
1.1 - Introduction to Sets
1.1 - Introduction to Sets Math 166-502 Blake Boudreaux Department of Mathematics Texas A&M University January 18, 2018 Blake Boudreaux (Texas A&M University) 1.1 - Introduction to Sets January 18, 2018
Multiple-Subscripted Arrays
Arrays in C can have multiple subscripts. A common use of multiple-subscripted arrays (also called multidimensional arrays) is to represent tables of values consisting of information arranged in rows and
Definitions. 03 Logic networks Boolean algebra. Boolean set: B 0,
3. Boolean algebra 3 Logic networks 3. Boolean algebra Definitions Boolean functions Properties Canonical forms Synthesis and minimization alessandro bogliolo isti information science and technology institute
Chapter 1: Review of Number Systems
Introduction to Number Systems This section is a review of the basic mathematical concepts needed prior to learning algebra. According to the NCTM Standards, students need to be able to: Understand numbers,
Unit 1 Algebraic Functions and Graphs
Algebra 2 Unit 1 Algebraic Functions and Graphs Name: Unit 1 Day 1: Function Notation Today we are: Using Function Notation We are successful when: We can Use function notation to evaluate a function This
Starting Boolean Algebra
Boolean Algebra March 2, 27 Diagram for FunChip2 Here is a picture of FunChip2 that we created more or less randomly in class on /25 (used in various Activities): Starting Boolean Algebra Boolean algebra
Building Concepts: Building Expressions
Lesson Overview Algebraic Focus: What does it mean to say two expressions are equivalent? In this lesson students view expressions as objects in their own right and interpret the form and structure of
WEEK 4 OPERATORS, EXPRESSIONS AND STATEMENTS
WEEK 4 OPERATORS, EXPRESSIONS AND STATEMENTS OPERATORS Review: Data values can appear as literals or be stored in variables/constants Data values can be returned by method calls Operators: special symbols
Programming Lecture 3
Programming Lecture 3 Expressions (Chapter 3) Primitive types Aside: Context Free Grammars Constants, variables Identifiers Variable declarations Arithmetic expressions Operator precedence Assignment statements
CITS2401 Computer Analysis & Visualisation
FACULTY OF ENGINEERING, COMPUTING AND MATHEMATICS CITS2401 Computer Analysis & Visualisation SCHOOL OF COMPUTER SCIENCE AND SOFTWARE ENGINEERING Topic 3 Introduction to Matlab Material from MATLAB for
2nd Paragraph should make a point (could be an advantage or disadvantage) and explain the point fully giving an example where necessary.
STUDENT TEACHER WORKING AT GRADE TERM TARGET CLASS YEAR TARGET The long answer questions in this booklet are designed to stretch and challenge you. It is important that you understand how they should be
Chapter 4: Making Decisions
Chapter 4: Making Decisions 4.1 Relational Operators Relational Operators Used to compare numbers to determine relative order Operators: > Greater than < Less than >= Greater than or equal to
Formal Methods of Software Design, Eric Hehner, segment 1 page 1 out of 5
Formal Methods of Software Design, Eric Hehner, segment 1 page 1 out of 5 [talking head] Formal Methods of Software Engineering means the use of mathematics as an aid to writing programs. Before we can
Basic data types. Building blocks of computation
Basic data types Building blocks of computation Goals By the end of this lesson you will be able to: Understand the commonly used basic data types of C++ including Characters Integers Floating-point values
Operators. Java operators are classified into three categories:
Operators Operators are symbols that perform arithmetic and logical operations on operands and provide a meaningful result. Operands are data values (variables or constants) which are involved in operations.
Lecture (04) Boolean Algebra and Logic Gates
Lecture (4) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee ١ Dr. Ahmed ElShafee, ACU : Spring 26, Logic Design Boolean algebra properties basic assumptions and properties: Closure law A set S is
Lecture (04) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee
Lecture (4) Boolean Algebra and Logic Gates By: Dr. Ahmed ElShafee Boolean algebra properties basic assumptions and properties: Closure law A set S is closed with respect to a binary operator, for every
Introduction to Programming, Aug-Dec 2006
Introduction to Programming, Aug-Dec 2006 Lecture 3, Friday 11 Aug 2006 Lists... We can implicitly decompose a list into its head and tail by providing a pattern with two variables to denote the two components
Chapter 4: Making Decisions
Chapter 4: Making Decisions CSE 142 - Computer Programming I 1 4.1 Relational Operators Relational Operators Used to compare numbers to determine relative order Operators: > Greater than < Less than >=
Accuplacer Arithmetic Study Guide
Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole (the number on the bottom) Example: parts
Introduction II. Sets. Terminology III. Definition. Definition. Definition. Example
Sets Slides by Christopher M. ourke Instructor: erthe Y. Choueiry Spring 2006 Computer Science & Engineering 235 Introduction to Discrete Mathematics Sections 1.6 1.7 of Rosen cse235@cse.unl.edu Introduction
Lab copy. Do not remove! Mathematics 152 Spring 1999 Notes on the course calculator. 1. The calculator VC. The web page
Mathematics 152 Spring 1999 Notes on the course calculator 1. The calculator VC The web page http://gamba.math.ubc.ca/coursedoc/math152/docs/ca.html contains a generic version of the calculator VC and
Department of Computer Science
Department of Computer Science Definition An operator is a symbol (+,-,*,/) that directs the computer to perform certain mathematical or logical manipulations and is usually used to manipulate data and
Chapter 2: Using Data
Chapter 2: Using Data TRUE/FALSE 1. A variable can hold more than one value at a time. F PTS: 1 REF: 52 2. The legal integer values are -2 31 through 2 31-1. These are the highest and lowest values that
CS 61C Summer 2012 Discussion 11 State, Timing, and CPU (Solutions)
State Elements State elements provide a means of storing values, and controlling the flow of information in the circuit. The most basic state element (we re concerned with) is a DQ Flip-Flop: D is a single
Introduction to Computer Programming CSCI-UA 2. Review Midterm Exam 1
Review Midterm Exam 1 Review Midterm Exam 1 Exam on Monday, October 7 Data Types and Variables = Data Types and Variables Basic Data Types Integers Floating Point Numbers Strings Data Types and Variables
Desktop Command window
Chapter 1 Matlab Overview EGR1302 Desktop Command window Current Directory window Tb Tabs to toggle between Current Directory & Workspace Windows Command History window 1 Desktop Default appearance Command
CDA 3200 Digital Systems. Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012
CDA 3200 Digital Systems Instructor: Dr. Janusz Zalewski Developed by: Dr. Dahai Guo Spring 2012 Outline Data Representation Binary Codes Why 6-3-1-1 and Excess-3? Basic Operations of Boolean Algebra Examples
Basic Structure of Denotational Definitions
asic Structure of Denotational Definitions This chapter presents the format for denotational definitions. We use the abstract syntax and semantic algebra formats to define the appearance and the meaning
Therefore, after becoming familiar with the Matrix Method, you will be able to solve a system of two linear equations in four different ways.
Grade 9 IGCSE A1: Chapter 9 Matrices and Transformations Materials Needed: Straightedge, Graph Paper Exercise 1: Matrix Operations Matrices are used in Linear Algebra to solve systems of linear equations.
2 Review of Set Theory
2 Review of Set Theory Example 2.1. Let Ω = {1, 2, 3, 4, 5, 6} 2.2. Venn diagram is very useful in set theory. It is often used to portray relationships between sets. Many identities can be read out simply
Prefix/Infix/Postfix Notation
Prefix/Infix/Postfix Notation One commonly writes arithmetic expressions, such as 3 + 4 * (5-2) in infix notation which means that the operator is placed in between the two operands. In this example, the
EC121 Mathematical Techniques A Revision Notes
EC Mathematical Techniques A Revision Notes EC Mathematical Techniques A Revision Notes Mathematical Techniques A begins with two weeks of intensive revision of basic arithmetic and algebra, to the level
Intermediate Algebra. Gregg Waterman Oregon Institute of Technology
Intermediate Algebra Gregg Waterman Oregon Institute of Technology c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license
Switching Circuits & Logic Design
Switching Circuits & Logic Design Jie-Hong Roland Jiang 江介宏 Department of Electrical Engineering National Taiwan University Fall 23 5 Karnaugh Maps K-map Walks and Gray Codes http://asicdigitaldesign.wordpress.com/28/9/26/k-maps-walks-and-gray-codes/
Logic Design: Part 2
Orange Coast College Business Division Computer Science Department CS 6- Computer Architecture Logic Design: Part 2 Where are we? Number systems Decimal Binary (and related Octal and Hexadecimal) Binary
Microsoft Excel 2010
www.jadehorizon.com Microsoft Excel 2010 Sorting and Filtering Sorting and Filtering Microsoft Excel 2010 Table of Contents Table of Contents INTRODUCTION... 3 CONVENTIONS... 3 TABLE DESIGN RULES... 5
Programming Languages Third Edition
Programming Languages Third Edition Chapter 12 Formal Semantics Objectives Become familiar with a sample small language for the purpose of semantic specification Understand operational semantics Understand
Chapter 4: Making Decisions. Copyright 2012 Pearson Education, Inc. Sunday, September 7, 14
Chapter 4: Making Decisions 4.1 Relational Operators Relational Operators Used to compare numbers to determine relative order Operators: > Greater than < Less than >= Greater than or equal to
CSCE 120: Learning To Code
CSCE 120: Learning To Code Manipulating Data I Introduction This module is designed to get you started working with data by understanding and using variables and data types in JavaScript. It will also
DLD VIDYA SAGAR P. potharajuvidyasagar.wordpress.com. Vignana Bharathi Institute of Technology UNIT 1 DLD P VIDYA SAGAR
UNIT I Digital Systems: Binary Numbers, Octal, Hexa Decimal and other base numbers, Number base conversions, complements, signed binary numbers, Floating point number representation, binary codes, error
(Refer Slide Time: 01:12)
Internet Technology Prof. Indranil Sengupta Department of Computer Science and Engineering Indian Institute of Technology, Kharagpur Lecture No #22 PERL Part II We continue with our discussion on the Perl
Algebra of Sets (Mathematics & Logic A)
Algebra of Sets (Mathematics & Logic A) RWK/MRQ October 28, 2002 Note. These notes are adapted (with thanks) from notes given last year by my colleague Dr Martyn Quick. Please feel free to ask me (not
Mathematically Rigorous Software Design Review of mathematical prerequisites
Mathematically Rigorous Software Design 2002 September 27 Part 1: Boolean algebra 1. Define the Boolean functions and, or, not, implication ( ), equivalence ( ) and equals (=) by truth tables. 2. In an
Watkins Mill High School. Algebra 2. Math Challenge
Watkins Mill High School Algebra 2 Math Challenge "This packet will help you prepare for Algebra 2 next fall. It will be collected the first week of school. It will count as a grade in the first marking
4 KARNAUGH MAP MINIMIZATION
4 KARNAUGH MAP MINIMIZATION A Karnaugh map provides a systematic method for simplifying Boolean expressions and, if properly used, will produce the simplest SOP or POS expression possible, known as the
Hello, World and Variables
Hello, World and Variables Hello, World! The most basic program in any language (Python included) is often considered to be the Hello, world! statement. As it s name would suggest, the program simply returns
Propositional Logic. Part I
Part I Propositional Logic 1 Classical Logic and the Material Conditional 1.1 Introduction 1.1.1 The first purpose of this chapter is to review classical propositional logic, including semantic tableaux.
Formulas and Functions
Conventions used in this document: Keyboard keys that must be pressed will be shown as Enter or Ctrl. Controls to be activated with the mouse will be shown as Start button > Settings > System > About.
IT 201 Digital System Design Module II Notes
IT 201 Digital System Design Module II Notes BOOLEAN OPERATIONS AND EXPRESSIONS Variable, complement, and literal are terms used in Boolean algebra. A variable is a symbol used to represent a logical quantity.
Flow Control. So Far: Writing simple statements that get executed one after another.
Flow Control So Far: Writing simple statements that get executed one after another. Flow Control So Far: Writing simple statements that get executed one after another. Flow control allows the programmer
7/25/2016. Example: Addition of Unsigned Bit Patterns. ECE 120: Introduction to Computing. Adding Two Non-Negative Patterns Can Overflow
University of Illinois at Urbana-Champaign Dept. of Electrical and Computer Engineering ECE 120: Introduction to Computing 2 s Complement Overflow and Boolean Logic Example: ddition of Unsigned Bit Patterns
YOLOP Language Reference Manual
YOLOP Language Reference Manual Sasha McIntosh, Jonathan Liu & Lisa Li sam2270, jl3516 and ll2768 1. Introduction YOLOP (Your Octothorpean Language for Optical Processing) is an image manipulation language
Get Free notes at Module-I One s Complement: Complement all the bits.i.e. makes all 1s as 0s and all 0s as 1s Two s Complement: One s complement+1 SIGNED BINARY NUMBERS Positive integers (including zero)
Mathematics Year 9-11 Skills and Knowledge Checklist. Name: Class: Set : Premier Date Year 9 MEG :
Personal targets to help me achieve my grade : AFL Sheet Number 1 : Standard Form, Decimals, Fractions and Percentages Standard Form I can write a number as a product of it s prime factors I can use the
NZ Mathematics Level 1-Yr 9 Curriculum Objectives Addressed Within Numbers Up! Volcanic Panic
4-7 1-11 1 Number Count, order and compare numbers up to 5, then later to 9, and then up to 20. Make sets up to 5 (then 9, then 20). Explore the number system from zero to 99 Rote count from zero to 99
Computational Expression
Computational Expression Conditionals Janyl Jumadinova 10 October, 2018 Janyl Jumadinova Computational Expression 10 October, 2018 1 / 16 Computational Thinking: a problem solving process Decomposition
MAT 090 Brian Killough s Instructor Notes Strayer University
MAT 090 Brian Killough s Instructor Notes Strayer University Success in online courses requires self-motivation and discipline. It is anticipated that students will read the textbook and complete sample
CS112 Lecture: Variables, Expressions, Computation, Constants, Numeric Input-Output
CS112 Lecture: Variables, Expressions, Computation, Constants, Numeric Input-Output Last revised January 12, 2006 Objectives: 1. To introduce arithmetic operators and expressions 2. To introduce variables
Lecture 5: Making Decisions
Lecture 5: Making Decisions Topics 5.1 Relational Operators 5.2 The if Statement 5.3 The if/else Statement 5.4 Logical Operators 5.5 Examples 4-2 3 5.1 Relational Operators Used to compare numbers to determine
List of NEW Maths content
List of NEW Maths content Our brand new Maths content for the new Maths GCSE (9-1) consists of 212 chapters broken up into 37 titles and 4 topic areas (Algebra, Geometry & Measures, Number and Statistics).
A point is pictured by a dot. While a dot must have some size, the point it represents has no size. Points are named by capital letters..
Chapter 1 Points, Lines & Planes s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My guess that you might already be pretty familiar with many
About the Tutorial. Audience. Prerequisites. Copyright & Disclaimer. Compiler Design
i About the Tutorial A compiler translates the codes written in one language to some other language without changing the meaning of the program. It is also expected that a compiler should make the target
CMAT Language - Language Reference Manual COMS 4115
CMAT Language - Language Reference Manual COMS 4115 Language Guru: Michael Berkowitz (meb2235) Project Manager: Frank Cabada (fc2452) System Architect: Marissa Ojeda (mgo2111) Tester: Daniel Rojas (dhr2119)
YEAR 10- Mathematics Term 1 plan
Week YEAR 10- Mathematics Term 1 plan 2016-2017 Course Objectives 1 The number system To understand and use 4 rules and order of operation. To understand and use Recurring decimals. Add subtract multiply