Lecture # 5Data 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

Review Programs

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

Review Programs

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

Review Programs

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 RepresentData 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 ten12345 =

5 * 100 + 5*1 +

4 * 101 + 4*10 +

3 * 102 + 3*100 +

2 * 103 + 2*1000 +

1 * 104 1*10,000

Binary Numbers

• Each Digit is a power of two10110 =

0 * 20 (1)+

1 * 21 (2)+

1 * 22 (4)+

0 * 23 (8)+

1 * 24 (16)

= 22

Binary Numbers

• Each Digit is a power of two1011101 =

= 93

1 * 20 (1) +

0 * 21 (2) +

1 * 22 (4) +

1 * 23 (8) +

1 * 24 (16) +

0 * 25 (32) +

1 * 26 (64)

Why Binary?

• Any physical phenomenon that has two states can be used to store a binary number

11010 = 26

Magnetism

+ - + - + +

MagneticMaterial

Read/Write Head1

101011 = 43

Voltage

+5 +5 +50 0 0

100101 = 37

Holes in PaperLight = 1Dark = 0

101010 = 42

PhotoSensor

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– 1010 - is a 4 bit number– 01010100 - 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 numbersIntegers and Floating Point

• Booleans (True, False)

• Characters

• Variables

Integers

• 100

• 100245

• -45

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

• 1.23

• 5623.1232

• -0.00232

Floating point numbers

• Numbers with decimal points

• 1.23 = 0.123e1• 5623.1232 = 0.56231232e4• -0.00232=-0.232e-2

• Stored differently (sign + fraction + exponent)

Information

• Binary numbers

• Integers and Floating PointBooleans (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 false6!=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

Dad32@Abc68 97 100 51 50 64 65 98 99

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

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)

• CharactersVariables

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

Review Programs

Binary Exercise

• Binary devices include:

• The binary number 101101 = 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 101101 = 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

Review Programs

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