An introduction to Numbers Dr Andrew French. You will need to consult your times table and your tables of integer powers.

Slides:

Advertisements

Similar presentations

Thinking Mathematically

Advertisements

Calculating in Other Bases

James Tam Beyond base 10: Non-decimal based number system What exactly is decimal? How do other number systems work (binary, octal and hex) How to convert.

Reading Writing Arithmetic The technologies of writing and number systems.

Agenda Shortcuts converting among numbering systems –Binary to Hex / Hex to Binary –Binary to Octal / Octal to Binary Signed and unsigned binary numbers.

Number Systems. 2 The total number of allowable symbols in a number system is called the radix or base of the system. Decimal Numbers: radix = 10 (symbols:

Introduction to Computing CPSC 203 January 24, 2006 Heejin Lim Chapter 1 Chapter 2 (part of)

Chapter Chapter Goals Know the different types of numbers Describe positional notation.

The Binary Number System

Binary, Decimal, & Hexadecimal Numbers

BASICS OF COMPUTER APPLICATIONS ASB 102. UNIT 1 Introducing computer system  Number system  What is number system?  Types of number system  Their.

2.1 2 Number Systems Foundations of Computer Science  Cengage Learning.

Chapter 1 1 Number Systems. 2 Objectives  Understand why computers use binary (Base-2) numbering.  Understand how to convert Base-2 numbers to Base-

Copyright © Cengage Learning. All rights reserved. 0 Precalculus Review.

Lecture for Week Spring.  Numbers can be represented in many ways. We are familiar with the decimal system since it is most widely used in everyday.

CS105 INTRODUCTION TO COMPUTER CONCEPTS BINARY VALUES & NUMBER SYSTEMS Instructor: Cuong (Charlie) Pham.

3.4/3.5 The Integers and Division/ Primes and Greatest Common Divisors Let each of a and b be integers. We say that a divides b, in symbols a | b, provided.

How Computers Work Dr. John P. Abraham Professor UTPA.

DECIMAL BASE Based on power of 10 In the number 2,468 – from right to left -- the 8 represents the ones, the 6 represents the tens, the 4 represents the.

What time is it? Someone might say “1:30” or “1:28” or “1:27:55” Each is appropriate for a different situation In science we describe a value as having.

Binary Arithmetic & Data representation

Supplemental Chapter Number Bases

ENGINEERS FUTURE To optimize things When we type some letters or words, the computer translates them in numbers as computers can understand only numbers.

Chapter 2 Binary Values and Number Systems. 2 2 Natural Numbers Zero and any number obtained by repeatedly adding one to it. Examples: 100, 0, 45645,

Computer Systems Architecture Copyright © Genetic Computer School 2008 CSA 1- 0 Lesson 1 Number System.

Number Systems Ron Christensen CIS 121.

Binary Values and Number Systems Chapter Goals Distinguish among categories of numbers Describe positional notation Convert numbers in other bases.

Number systems, Operations, and Codes

Introduction to Computing Dr. Nadeem A Khan. Lecture 10.

Number Representation. Representing numbers n Numbers are represented as successive powers of a base, or radix.

Binary Values and Number Systems

CMSC 104, Lecture 051 Binary / Hex Binary and Hex The number systems of Computer Science.

ECE2030 Introduction to Computer Engineering Lecture 2: Number System Prof. Hsien-Hsin Sean Lee School of Electrical and Computer Engineering Georgia Tech.

CPS120: Introduction to Computer Science Computer Math: Converting to Decimal.

Positional Notation 642 in base 10 positional notation is:

Lecture 2 Binary Values and Number Systems. The number 943 is an example of a number written in positional notation. The relative positions of the digits.

CPIT 201 Introduction to Computing

Chapter 2 Number Systems: Decimal, Binary, and Hex.

Dale & Lewis Chapter 2 Binary Numbers and Number Systems.

Visualizing Decimal and Binary

Computer Science and Software Engineering© 2014 Project Lead The Way, Inc. Bits and Bytes.

BASIC OPERATIONS The four basic mathematical operations are: + Addition - - Subtraction × Multiplication ÷ Division.

1 4. Computer Maths and Logic 4.1 Number Systems.

Module #9 – Number Theory 1/5/ Algorithms, The Integers and Matrices.

Topic 14.1 Extended Hexadecimal  Decimal is base 10 and uses 10 digits (0,1,2,3,4,5,6,7,8,9).  Binary is base 2 and uses 2 digits (0,1).  Computers.

Chapter 2 Binary Values and Number Systems Chapter Goals Distinguish among categories of numbers Describe positional notation Convert numbers in.

Number Systems. Topics  The Decimal Number System  The Binary Number System  Converting from Binary to Decimal  Converting from Decimal to Binary.

1 EGR 277 – Digital Logic Syllabus Office Hours No food or drinks in the classrooms Web page (demonstration) Lecture #1 EGR 277 – Digital Logic Reading.

CMSC 1041 Binary / Hex Binary and Hex The number systems of Computer Science.

Binary numbers. Primary memory Memory = where programs and data are stored – Unit = bit “BIT” is a contraction for what two words? Either a 1 or a 0 (because.

CPIT 201 King AbdulAziz University Faculty of Computing & Information Technology Information Technology Department CH 2 Number Systems CPIT 201 Introduction.

Numeral Systems Rubel Biswas.

Number systems Visualizing Decimal and Binary. We count in base 10 because people started by counting on their fingers Base 10 is a number system that.

Dr. Nermin Hamza 1. Materials Book: Digital Design 4 th M. Morris Mano and Michael D. Ciletti 2.

Each digit appearing to the left of the decimal point represents a value between zero and nine times an increasing power of ten. Digits appearing to the.

Lecturer: Santokh Singh

Decimal Numbers.

Chapter 1: Arithmetic & Prealgebra

Introduction to Computing

Integer Real Numbers Character Boolean Memory Address CPU Data Types

CSE 102 Introduction to Computer Engineering

Number Systems Lab session 1 Xuan Guo.

Objective The student will be able to:

2.0 COMPUTER SYSTEM 2.2 Number System and Representation

IT 0213: INTRODUCTION TO COMPUTER ARCHITECTURE

Hexadecimal Binary Made Easier.

Binary / Hex Binary and Hex The number systems of Computer Science.

Chapter 2: Number Systems

Digital Logic Design (CSNB163)

Decimals – Outcomes Represent addition, subtraction, multiplication, and division in ℚ using number lines and decomposition. Perform addition, subtraction,

Presentation transcript:

An introduction to Numbers Dr Andrew French

You will need to consult your times table and your tables of integer powers

You will find it very useful to learn the powers up to 16 3 = 4,096

The DECIMAL system is when numbers are written right to left in powers of ten. Only ten symbols are needed (0,1,2,3,4,5,6,7,8,9) plus a DECIMAL POINT to describe any number, of which there are infinitely many. Not bad eh? In ancient cultures a different symbol is used for each integer, just like the way we say ‘one’, ‘two’, ‘three’ etc. How are numbers ‘best’ written down? Does it matter? So means 1 x x x x x x

The decimal system enables us to perform arithmetic calculations on numbers (i.e. addition, subtraction, multiplication and division) in a straightforward, systematic way. You have been practising it for many years now! Note we can use the decimal system to help us work out multiplications using a small set of memorized results (i.e. your times table) 123 x 456 = = 40, ,088

Use the ‘matrix decimal expansion’ to work out (NO CALCULATOR!) 167 x 394 = 0.15 x 17.2 =

Use the ‘matrix decimal expansion’ to work out (NO CALCULATOR!) 167 x 394 = 0.15 x 17.2 = = 30,000 18, ,798 =

We don’t have to use the decimal system. In fact we can use any (integer!) number of symbols from two upwards. A two symbol (0 or 1) system is BINARY (which is used to store and manipulate numbers by computers) Binary numbers 0, 1 DecimalBinary x x x x x 2 0 = = Note = x x x x x x x x x x x What are the decimal integers (a) 64 (b) 73 in binary?

Binary numbers 0, 1 DecimalBinary x x x x x 2 0 = = Note = x x x x x x x x x x x What are the decimal integers (a) 64 is since 2 6 = 64 (b) 73 is since = 73 in binary? 1 x x x x x x x We don’t have to use the decimal system. In fact we can use any (integer!) number of symbols from two upwards. A two symbol (0 or 1) system is BINARY (which is used to store and manipulate numbers by computers)

Hexadecimal numbers 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F DecimalHexadecimal x x 16 0 = = D2 4 x x x 16 0 = 4 x x = ABCDEF A sixteen symbol system is HEXADECIMAL, which is typically used to describe computer memory addresses. Decimal Hexadecimal or ‘base 16’ What is (a) 31 (b) 117 in hexadecimal?

Hexadecimal numbers 0,1,2,3,4,5,6,7,8,9,A,B,C,D,E,F DecimalHexadecimal x x 16 0 = = D2 4 x x x 16 0 = 4 x x = ABCDEF A sixteen symbol system is HEXADECIMAL, which is typically used to describe computer memory addresses. Decimal Hexadecimal or ‘base 16’ What is (a) 31is 1F since 1 x x 16 0 = 31 (b) 117 is 75 since 7 x x 16 0 = = 117 in hexadecimal?

Other ‘popular’ bases are: 12Duodecimal0,1,2,3,4,5,6,7,8,9,A,B 60SexagesimalUsed by the ancient Babylonians around 3000BC Note this wasn’t a proper ‘place value’ system as there was no zero! cuneiform digits Although it did appear later as