Binary

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# Binary - PowerPoint PPT Presentation

Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa. Binary. Objective 2: Add two 8-bit binary integers and explain overflow errors which may occur. Aim: Explain binary and binary units.

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## PowerPoint Slideshow about 'Binary' - kristy

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Presentation Transcript

Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa

### Binary

Objective 2: Add two 8-bit binary integers and explain overflow errors which may occur

Aim: Explain binary and binary units

Objective 3: Define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte

234

### Binary

Why Base 10?

What is a denary number?

talk to the hands!

### Binary

128

64

32

16

8

4

2

1s

Why Base 2?

1100110100101010111101010100101110

What is a binary number?

Binary is the universal language of computers

1010111101010101010100101100010100010001111100011010001000101001011101

### Binary

128

64

32

16

8

4

2

1s

1

1

1

0

1

0

1

0

234

Converting denary to binary

234-128=106

106-64=42

42-32=10

10-8=2

Convert the following to 8 bit binary:

### Binary

16

47

00010000

00101111

34

255

00100010

11111111

Converting denary to binary - EXERCISE

128

11

10000000

00001011

132

127

10000100

01111111

### Binary

Converting denary to binary – Online Game

http://forums.cisco.com/CertCom/game/binary_game_page.htm

THREE RULES!

0 + 0 = 0

0 + 1 = 1

1 + 1 = 0 (carry 1)

### Binary

00101010 + 01101101

DEC

0

0

1

0

1

0

1

0

42

109

0

1

1

0

1

1

0

1

1

0

0

1

0

1

1

1

151

1

1

1

OVERFLOW!

ERROR

OVERFLOW!

ERROR

### Binary

10010110 + 10011011

DEC

1

0

0

1

0

1

1

0

150

155

1

0

0

1

1

0

1

1

1

0

0

1

1

0

0

0

1

305

1

1

1

1

### Binary

00010010 + 01000011 =

10000101 + 00111110 =

Adding binary to binary - EXERCISE

00101010 + 01101101 =

10010110 + 10001101 =

### Binary

00010010 + 01000011 =

0

0

0

1

0

0

1

0

0

1

0

0

0

0

1

1

0

1

Adding binary to binary - EXERCISE

0

1

0

1

0

1

1

### Binary

1000010 + 00111110 =

1

0

0

0

0

0

1

0

0

0

1

1

1

1

1

0

0

1

Adding binary to binary - EXERCISE

1

1

0

0

0

0

0

1

1

1

1

### Binary

00101010+ 01101101 =

0

0

1

0

1

0

1

0

0

1

1

0

1

1

0

1

Adding binary to binary - EXERCISE

1

0

0

1

0

1

1

1

1

1

1

### Binary

10010110+ 10001101 =

1

0

0

1

0

1

1

0

1

0

0

0

1

1

0

1

OVERFLOW!

Adding binary to binary - EXERCISE

0

0

1

0

0

0

1

1

1

1

1

1

Tools to Help

What is a bit?

### Binary

Units

A bit can either be a 1 or 0

What is a byte?

### Binary

Units

A byte is 8 bits

What is a nibble?

### Binary

This is a mouse

This is a mouse

This is a mouse

This is a mouse

This This is a mouse

This is a mouse

This is a mouse

This is a mouse

This is a mouse

Units

A nibble is 4 bits

A nibble is half a byte

What is a Kilobyte (KB)?

### Binary

x 1024

Units

A kilobyte is 1024 bytes

Why not 1000?

What is a Megabyte (MB)?

### Binary

A megabyte is 1024 kilobytes

Units

What is a Gigabyte (GB)?

### Binary

A gigabyte is 1024 megabytes

Units

What is a Terabyte (TB)?

### Binary

A terabyte is 1024 gigabytes

Units

What is a Petabyte (PB)?

### Binary

A petabyte is 1024 terabytes

Units

Arrange the following in size order:

### Binary

MEGABYTE

GIGABYTE

Units - EXERCISE

PETABYTE

TERABYTE

NIBBLE

BIT

KILOBYTE

BYTE

Objective 1: Convert positive denary whole numbers (0-255) into 8-bit binary numbers and vice versa

### Binary

Objective 2: Add two 8-bit binary integers and explain overflow errors which may occur

Aim: Explain binary and binary units

Objective 3: Define the terms bit, nibble, byte, kilobyte, megabyte, gigabyte, terabyte