The Binary System.

Slides:



Advertisements
Similar presentations
Connecting with Computer Science, 2e
Advertisements

Representing Information as Bit Patterns Lecture 4 CSCI 1405, CSCI 1301 Introduction to Computer Science Fall 2009.
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:
Chapter 1.5 The Binary System CSCI 3. Basic Concepts Behind the Binary System In the decimal system, things are organized into columns – H | T | O – 1.
2.1 2 Number Systems Foundations of Computer Science  Cengage Learning.
Computer Systems Nat 4/5 Computing Science Lesson 1: Binary.
Binary Numbers.
Connecting with Computer Science 2 Objectives Learn why numbering systems are important to understand Refresh your knowledge of powers of numbers Learn.
Partial Sums An Addition Algorithm.
Lecture 5.
Numeral Systems Subjects: Numeral System Positional systems Decimal
Representing text Each of different symbol on the text (alphabet letter) is assigned a unique bit patterns the text is then representing as.
Binary Real Numbers. Introduction Computers must be able to represent real numbers (numbers w/ fractions) Two different ways:  Fixed-point  Floating-point.
Chapter 1 Data Storage(2) Yonsei University 1 st Semester, 2014 Sanghyun Park.
MTH 232 Section 7.1 Decimals and Real Numbers. Objectives 1.Define decimal numbers and represent them using manipulatives; 2.Write decimals in expanded.
2-1 Chapter 2 - Data Representation Principles of Computer Architecture by M. Murdocca and V. Heuring © 1999 M. Murdocca and V. Heuring Chapter Contents.
Computer Architecture
1 Problem Solving using computers Data.. Representation & storage Representation of Numeric data The Binary System.
Binary Fractions. Fractions A radix separates the integer part from the fraction part of a number Columns to the right of the radix have negative.
Lecture 4 Last Lecture –Positional Numbering Systems –Converting Between Bases Today’s Topics –Signed Integer Representation Signed magnitude One’s complement.
Lecture 5. Topics Sec 1.4 Representing Information as Bit Patterns Representing Text Representing Text Representing Numeric Values Representing Numeric.
Computer Arithmetic and the Arithmetic Unit Lesson 2 - Ioan Despi.
NUMBER SYSTEM Decimal System Binary System. We use two digits in this system (0,1) just like the existing system of computers.. And write the number in.
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.
Section 3.1: Number Representation Practice HW (not to hand in) From Barr Text p. 185 # 1-5.
Chapter 1 Data Storage © 2007 Pearson Addison-Wesley. All rights reserved.
Chapter 2 Data Representation.
Chapter 1 Data Storage © 2007 Pearson Addison-Wesley. All rights reserved.
Data Storage © 2007 Pearson Addison-Wesley. All rights reserved.
Introduction To Number Systems Binary System M. AL-Towaileb1.
Converting Fractions and Decimals Objective: Learn to convert fractions and decimals.
Number Representation Lecture Topics How are numeric data items actually stored in computer memory? How much space (memory locations) is.
Computer Systems Nat 4/5 Computing Science Lesson 1: Binary.
COMPUTER SCIENCE Data Representation and Machine Concepts Section 1.5 Instructor: Lin Chen Sept 2013.
Lecture 6 Excess Notation. Excess 8 notation indicates that the value for zero is the bit pattern for 8, that is 1000 Excess 8 notation indicates that.
IT1004: Data Representation and Organization Negative number representation.
Data Storage © 2007 Pearson Addison-Wesley. All rights reserved.
Chapter 1 Data Storage © 2007 Pearson Addison-Wesley. All rights reserved.
ECE DIGITAL LOGIC LECTURE 2: DIGITAL COMPUTER AND NUMBER SYSTEMS Assistant Prof. Fareena Saqib Florida Institute of Technology Fall 2016, 01/14/2016.
More Digital Representation Discrete information is represented in binary (PandA), and “continuous” information is made discrete.
Learning Objectives 3.3.1f - Describe the nature and uses of floating point form 3.3.1h - Convert a real number to floating point form Learn how to normalise.
Chapter 1: Data Storage.
Nat 4/5 Computing Science Lesson 1: Binary
Department of Computer Science Georgia State University
Fundamentals of Computer Science
Computer Science: An Overview Eleventh Edition
Introduction To Computer Science
Binary Positional Notation
Positional Notation A positional or place-value notation is a numeral system in which each position is related to the next by a constant multiplier, called.
Number Systems Lab session 1 Xuan Guo.
Binary Lesson 1 Nybbles.
Binary Lesson 1 Nybbles.
Introduction to IT By: Muhammed s. anwar.
CSCI206 - Computer Organization & Programming
Binary Lesson 1 Nybbles.
Digital Logic Design (CSNB163)
Starter Using the fingers on only one hand, what is the highest number you can count to? Rules: You must start at 1 You must count sequentially (i.e.
Data Representation and Organization
Storing Integers and Fractions
Lecture 4 Number Systems. von Neumann Model Every computer today is based on the von Neumann Model. It is based on 3 ideas: 1.Four subsystems 2.Stored.
Converting Fractions and Decimals
William Stallings Computer Organization and Architecture 10th Edition
Terminating and Repeating Decimals
Converting from Base-n to Base-10
COMS 161 Introduction to Computing
Presentation transcript:

The Binary System

The Binary System Bit Patterns are used to represent information. Text Numeric values Images Sound And others Numeric values: using only the digits 0 and 1

The Binary System rather than the 10 digits 0 through 9 that are used in the more common base 10 notational system.

The Binary System Binary Notation Recall that in the base 10 system, each position in a representation is associated with a quantity. To illustrate, the pattern 375 represents (3 × hundred)+(7 × ten)+(5 × one), which, in more technical notation, is 3 × 102+7 × 101+5 × 100.

The Binary System The traditional decimal system is based on powers of ten. The Binary system is based on powers of two. (1101)2=1 × 23+1 × 22+0 × 21+1 × 20

Figure 1.13 The base ten and binary systems

Figure 1.14 Decoding the binary representation 100101

Figure 1.15 An algorithm for finding the binary representation of a positive integer

Figure 1. 16 Applying the algorithm in Figure 1 Figure 1.16 Applying the algorithm in Figure 1.15 to obtain the binary representation of thirteen

Figure: Converting base 10 representation to binary form 2 78……0 39……1 19……1 9……1 4……0 2……0 1……1 (78)10=(1001110)2

The Binary System Binary Addition To understand the process of adding two integers that are represented in binary, let us first recall the process of adding values that are represented in traditional base 10 notation. 58+17=?

Figure 1.17 The binary addition facts

The Binary System Binary Addition 111010+11011=?

The Binary System Fractions in Binary To extend binary notation to accommodate fractional values, we use a radix point in the same role as the decimal point in decimal notation. That is, the digits to the left of the point represent the integer part, the digits to its right represent the fractional part of the value.

Figure 1.18 Decoding the binary representation 101.101

Figure: Converting base 10 representation to binary form 0.574 × 2 1.148 0.296 0.592 1.184 2 78……0 39……1 19……1 9……1 4……0 2……0 1……1 (78)10=(1001110)2 (0.574)10≈(0.1001001)2

The Binary System Summary binary notation binary addition fractions in binary