Spring 2010

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Spring 2010. Lecture 3 Chapter 1.1 thru 1.5 Wednesday, January 20 th 2010. Our Objectives for this section:. Review the Chapter 1 reading assignment. Learn about the bottom level encoding of data via the binary and hex number systems

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Spring 2010

Lecture 3

Chapter 1.1 thru 1.5

Wednesday, January 20th 2010

Our Objectives for this section:
• Review the Chapter 1 reading assignment.
• Learn about the bottom level encoding of data via the binary and hex number systems
• Learn about the central role of using bit patterns to encode information.
Objectives: (cont’d)
• Develop an understanding of the rudiments of data storage.
• This provides the building blocks to understand the chapters that follow.
• Perform number system conversions
• These conversions will be a part of the midterm exam.
• It’s IMPORTANT to remember!These slides are not a substitute for the reading. They are provided here merely for review of
• what you have read and taken notes on already. You MUST complete the reading assignments, attend class, and take notes. As you re-read, and then revise your notes – you’ll be putting these ideas and concepts into your own words, and you will have made great advances in learning the material.
Intro..
• This chapter presents the rudiments of data storage within digital computers. It introduces the basics of digital circuitry and how a simple flip-flop can be used to store a single bit. It then discusses addressable memory cells and mass storage systems (magnetic disk, compact disks, and magnetic tape).
• Having established this background, the chapter discusses how information (text, numeric values, images, and sound) are encoded as bit patterns. The optional sections delve more deeply into these topics by presenting the problems of overflow errors, truncation errors, error detection and correction techniques, and data compression.
Chapter 1: Data Storage
• 1.1 Bits and Their Storage
• 1.2 Main Memory
• 1.3 Mass Storage
• 1.4 Representing Information as Bit Patterns
• 1.5 The Binary System
Chapter 1: Data Storage(cont’d)
• 1.6 Storing Integers
• 1.7 Storing Fractions
• 1.8 Data Compression
• 1.9 Communications Errors

We will not cover these sections of Chapter 1.

I will post additional optional materials, that you can study if you are interested.

Bits and Bit Patterns
• Bit: Binary Digit (0 or 1)
• Bit Patterns are used to represent information.
• Numbers
• Text characters
• Images
• Sound
• And others
Boolean Operations
• Boolean Operation: An operation that manipulates one or more true/false values
• Specific operations
• AND
• OR
• XOR (exclusive or)
• NOT
Gates
• Gate: A device that computes a Boolean operation
• Often implemented as (small) electronic circuits
• Provide the building blocks from which computers are constructed
• VLSI (Very Large Scale Integration)
Figure 1.2A pictorial representation of AND, OR, XOR, and NOT gates as well as their input and output values
Flip-flops
• Flip-flop: A circuit built from gates that can store one bit.
• One input line is used to set its stored value to 1
• One input line is used to set its stored value to 0
• While both input lines are 0, the most recently stored value is preserved
Abstraction: flip-flop

A simple flip-flop circuit

Another way of

constructing a flip-flop

Abstraction: flip-flop

A simple flip-flop circuit

Another way of

constructing a flip-flop

• Hexadecimal notation: A shorthand notation for long bit patterns
• Divides a pattern into groups of four bits each
• Represents each group by a single symbol
• Example: 10100011 becomes A3
• How? Break the binary number into four bit groups, and convert to Hex. See the chart on the next slide:

1010 0011

A 3

Main Memory Cells
• Cell: A unit of main memory (typically 8 bits which is one byte)
• Most significant bit: (MSB) the bit at the left (high-order) end of the conceptual row of bits in a memory cell
• Least significant bit: (LSB) the bit at the right (low-order) end of the conceptual row of bits in a memory cell
• Address: A “name” that uniquely identifies one cell in the computer’s main memory
• The names are actually numbers.
• These numbers are assigned consecutively starting at zero.
• Numbering the cells in this manner associates an order with the memory cells.
Memory Terminology
• Random Access Memory (RAM): Memory in which individual cells can be easily accessed in any order
• Dynamic Memory (DRAM): RAM composed of volatile memory
Measuring Memory Capacity
• Kilobyte: 210 bytes = 1024 bytes
• Example: 3 KB = 3 times1024 bytes
• Sometimes “kibi” rather than “kilo”
• Megabyte: 220 bytes = 1,048,576 bytes
• Example: 3 MB = 3 times 1,048,576 bytes
• Sometimes “megi” rather than “mega”
• Gigabyte: 230 bytes = 1,073,741,824 bytes
• Example: 3 GB = 3 times 1,073,741,824 bytes
• Sometimes “gigi” rather than “giga”
Mass Storage
• On-line versus off-line
• Typically larger than main memory
• Typically less volatile than main memory
• Typically slower than main memory
Mass Storage Systems
• Magnetic Systems
• Disk
• Tape
• Optical Systems
• CD
• DVD
• Flash Drives
Files
• File: A unit of data stored in mass storage system
• Fields and keyfields
• Physical record versus Logical record
• Buffer: A memory area used for the temporary storage of data (usually as a step in transferring the data)
Representing Text
• Each character (letter, punctuation, etc.) is assigned a unique bit pattern.
• ASCII: Uses patterns of 7-bits to represent most symbols used in written English text
• Unicode: Uses patterns of 16-bits to represent the major symbols used in languages world side
• ISO standard: Uses patterns of 32-bits to represent most symbols used in languages world wide
Representing Numeric Values
• Binary notation: Uses bits to represent a number in base two
• Limitations of computer representations of numeric values
• Overflow – occurs when a value is too big to be represented
• Truncation – occurs when a value cannot be represented accurately
Representing Images
• Bit map techniques
• Pixel: short for “picture element”
• RGB
• Luminance and chrominance
• Vector techniques
• Scalable
• TrueType and PostScript
Representing Sound
• Sampling techniques
• Used for high quality recordings
• Records actual audio
• MIDI
• Musical Instrument Digital Interface
• Used in music synthesizers
• Records “musical score”
The Binary System

The traditional decimal system is based

on powers of ten.

The Binary system is based on powers

of two.

Figure 1.17 An algorithm for finding the binary representation of a positive integer
Converting binary to decimal values.
• Ordered from highest to lowest, the first eight place values of the binary number system are:

27, 26, 25, 24, 23, 22, 21, 20.

• To convert a byte, multiply each digit to its corresponding place value and add all eight products. For example, to convert the binary value of 00011001 into a decimal value:

27, 26, 25, 24, 23, 22, 21, 20.

0 0 0 1 1 0 0 1

=(0 x 27) + (0 x 26) + (0 x 25) + (1 x 24) + (1 x 23) + (0 x 22) +(0 x 21) + (1 x 20)

= 16 + 8 + 1 = 25.

Quick Quiz 1
• In the world of computers, the term____________________ refers to the two state number system with which all information within the computer is represented.
• binary
Quick Quiz 2
• True or False.

A byte consists of four bits and a nibble consists of two bits.

• False
Quick Quiz 3
• ____________________ provide the building blocks from which computers are constructed.

gates

Quick Quiz 4
• A “name” that uniquely identifies one cell in the computer’s main memory is called an ____________________.

Quick Quiz 5

Specify the reason Hexadecimal notation is used: