Lecture # 5 Data Representation

Today Questions: From notes/reading/life? Prepare for Quiz # 1 (Multiple Choice) 1.Introduce: How do Computers store data? 2.Explain: Data Types: Binary numbers, Integers, Floating Point, Booleans, Characters, Variables 3.Demo: Do some binary conversions: on board 4.Practice: Do some binary examples: in head, on keyboard 5.Evaluate: We will share and evaluate your conversions 6.Re-practice: Turn the crank on binary as you go to sleep Understand Data Types, Storage ReviewPrograms

Today Questions: From notes/reading/life? Prepare for Quiz # 1 (Multiple Choice) 1.Introduce: How do Computers store data? 2.Explain: Data Types: Binary numbers, Integers, Floating Point, Booleans, Characters, Variables 3.Demo: Do some binary conversions: on board 4.Practice: Do some binary examples: in head, on keyboard 5.Evaluate: We will share and evaluate your conversions 6.Re-practice: Turn the crank on binary as you go to sleep Understand Data Types, Storage ReviewPrograms

Today Questions: From notes/reading/life? Prepare for Quiz # 1 (Multiple Choice) 1.Introduce: How do Computers store data? 2.Explain: Data Types: Binary numbers, Integers, Floating Point, Booleans, Characters, Variables 3.Demo: Do some binary conversions: on board 4.Practice: Do some binary examples: in head, on keyboard 5.Evaluate: We will share and evaluate your conversions 6.Re-practice: Turn the crank on binary as you go to sleep Understand Data Types, Storage ReviewPrograms

Data Representation If we want to compare, sort and organize data, we need to have a way to represent it in a computer – electronically. Even the characters you are now reading, as words, must be able to be represented and encoded electronically and numerically. The following slides will explain how we represent and encode data in a computer, and how we manipulate and reason about it in a computer program.

How to Represent Data in a Computer

Foundations of Computing Information Data Types –Binary numbers –Integers and Floating Point –Booleans (True, False) –Characters –Variables Programs –Expressions –Assignment –Sequences

There are 10 kinds of people in the world – those who understand binary and those who do not.

Information Data Types  Binary numbers Integers and Floating Point Booleans (True, False) Characters Variables

Decimal Numbers Each digit is a power of ten = 5 * *1 + 4 * * * * * * * *10,000

Binary Numbers Each Digit is a power of two = 0 * 2 0 (1)+ 1 * 2 1 (2)+ 1 * 2 2 (4)+ 0 * 2 3 (8)+ 1 * 2 4 (16) = 22

Binary Numbers Each Digit is a power of two = = 93 1 * 2 0 (1) + 0 * 2 1 (2) + 1 * 2 2 (4) + 1 * 2 3 (8) + 1 * 2 4 (16) + 0 * 2 5 (32) + 1 * 2 6 (64)

Why Binary? Any physical phenomenon that has two states can be used to store a binary number 11010= 26

Magnetism Magnetic Material Read/Write Head = 43

Voltage = 37

Holes in Paper Light = 1 Dark = = 42 Photo Sensor Light

Binary Students Male = 0 Female = 1

Why Binary? Any physical phenomenon that has two states can be used to store a binary number Each binary digit is called a BIT – is a 4 bit number – is an 8 bit number An 8 bit number is called a BYTE

Size of a Binary Number How many different numbers can you store in 2 bits? How many can you store in 8 bits? In general, 2 (number of bits) numbers can be stored How many in 10 bits? –1024 = 1K How many in 20 bits? –1,048,576 = 1Meg

Information Binary numbers  Integers and Floating Point Booleans (True, False) Characters Variables

Integers

Size of an Integer How many bits required for the number 17? 5 bits How many bits for the number 1023? 10 bits

Integer Expressions * means multiply / means divide 2*4+3 = 11 2*(4+3) = 14 (7+9)/2 = 8

Floating point numbers Numbers with decimal points

Floating point numbers Numbers with decimal points 1.23 = 0.123e = e =-0.232e-2 Stored differently (sign + fraction + exponent)

Information Binary numbers Integers and Floating Point  Booleans (True, False) Characters Variables

Booleans 1 = true 0 = false

Boolean Expressions (7>3) is true ((2+4)<6) is false –Note Arithmetic Expression in Boolean Expression > Greater than < less than <= less than or equal >= greater than or equal == equal != not equal 7<=6 is false 6!=5 is true

Information Binary numbers Integers and Floating Point Booleans (True, False)  Characters Variables

ASCII Code for Characters Every character is defined to have an 8 bit (1 byte) number What is special about the order of the numbers? Type ‘ g ’ Store 103

ASCII Code for Characters A numeric character is different from its ASCII number

ASCII Code for Characters

What about Chinese, Sanscrit, Hebrew, Cyrillic, etc ??

UNICODE rather than ASCII 2 Bytes per character –Twice as much space –65,536 possible characters (2^16)

Expressions with characters ‘ A ’ + 2 = ‘ C ’ ‘ g ’ - ‘ d ’ = 3 ‘ F ’ + 32 = ‘ f ’ ‘ A ’ < ‘ D ’ is true ‘ % ’ >= ‘ + ’ is false

Information Binary numbers Integers and Floating Point Booleans (True, False) Characters  Variables

Variable A named place to store a value –George = 32 –Size = 17 –Weight = 120

Today Questions: From notes/reading/life? Prepare for Quiz # 1 (Multiple Choice) 1.Introduce: How do Computers store data? 2.Explain: Data Types: Binary numbers, Integers, Floating Point, Booleans, Characters, Variables 3.Demo: Do some binary conversions: on board 4.Practice: Do some binary examples: in head, on keyboard 5.Evaluate: We will share and evaluate your conversions 6.Re-practice: Turn the crank on binary as you go to sleep Understand Data Types, Storage ReviewPrograms

Binary Exercise Binary devices include: The binary number = what in decimal? How many bits are required to store the decimal number 256?

Review Binary devices include: paper and magnetic tape, disks, transistors The binary number = what in decimal? 45 How many bits are required to store the decimal number 256? 9 bits

Today Questions: From notes/reading/life? Prepare for Quiz # 1 (Multiple Choice) 1.Introduce: How do Computers store data? 2.Explain: Data Types: Binary numbers, Integers, Floating Point, Booleans, Characters, Variables 3.Demo: Do some binary conversions: on board 4.Practice: Do some binary examples: in head, on keyboard 5.Evaluate: We will share and evaluate your conversions 6.Re-practice: Turn the crank on binary as you go to sleep Understand Data Types, Storage ReviewPrograms

Programs Computer Programs make use of a these data types to perform a given task Standard arithmetic operations can be applied to manipulate the input data types and output a result