BinaryAim: Explain binary and binary units

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

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

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

talk to the hands!

BinaryWhat is a denary number?

234

Why Base 10?

BinaryWhat is a binary number?

Binary is the universal

language of computers

1s248163264128

1100110100101010111101010100101110

10101111010101010101001011000101000

10001111100011010001000101001011101

Why Base 2?

BinaryConverting denary to binary

234

1s248163264128

0 0 01

234-128=106

1

106-64=42

1

42-32=10

1 1

10-8=2

BinaryConverting denary to binary - EXERCISE

Convert the following to 8 bit binary:

1634128132

00010000001000101000000010000100

4725511127

00101111111111110000101101111111

BinaryConverting denary to binary – Online Game

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

BinaryAdding binary to binary

Adding 8 bit binary numbers

00101010 + 01101101

10 1 0 1 0 1 0

00

1 0 1 1 0 11 1 1 1 10

10

10

1

THREE RULES!0 + 0 = 00 + 1 = 11 + 1 = 0 (carry 1)

151109

42DEC

BinaryAdding binary to binary

Adding 8 bit binary numbers

10010110 + 10011011

00 0 1 0 1 1 0

11

0 1 1 0 1 110

110

OVERFLOW!ERROROVERFLOW!ERROR

010

11

101 305

155150DEC

BinaryAdding binary to binary - EXERCISE

00010010 + 01000011 =

10000101 + 00111110 =

00101010 + 01101101 = 10010110 + 10001101 =

BinaryAdding binary to binary - EXERCISE

00010010 + 01000011 =

1

0 0 1 0 0 1 0

0

0

0 0 0 0 1 1

10

1

101010

BinaryAdding binary to binary - EXERCISE

1000010 + 00111110 =

0

0 0 0 0 0 1 0

0

1

1 1 1 1 1 0

00

1

11 0

1

0

1

0

1

0

1

BinaryAdding binary to binary - EXERCISE

00101010 + 01101101 =

1

0 1 0 1 0 1 0

0

0

1 0 1 1 0 1

111 10

1

10

1

0

1

BinaryAdding binary to binary - EXERCISE

10010110 + 10001101 =

0

0 0 1 0 1 1 0

1

1

0 0 1 1 0 1

110

1

10 0

1

0

1

01

OVERFLOW!

BinaryTools to Help

BinaryUnits

What is a bit?

A bit can either be a 1 or 0

BinaryUnits

What is a byte?

A byte is 8 bits

BinaryUnits

A nibble is 4 bits

A nibble is half a byte

What is a nibble?

This is a mouseThis is a mouseThis is a mouseThis is a mouseThis This is a mouseThis is a mouseThis is a mouseThis is a mouseThis is a mouse

BinaryUnits

A kilobyte is 1024 bytes

What is a Kilobyte (KB)?

x 1024

Why not 1000?

BinaryUnits

What is a Megabyte (MB)?

A megabyte is 1024 kilobytes

BinaryUnits

What is a Gigabyte (GB)?

A gigabyte is 1024 megabytes

BinaryUnits

What is a Terabyte (TB)?

A terabyte is 1024 gigabytes

BinaryUnits

What is a Petabyte (PB)?

A petabyte is 1024 terabytes

BinaryUnits - EXERCISE

Arrange the following in size order:

BITBYTE

NIBBLE

KILOBYTE

MEGABYTEGIGABYTE

TERABYTEPETABYTE

BinaryAim: Explain binary and binary units

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

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

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

Binary and HexadecimalWeb Resources

LESSON FILEShttp://edmundo.ecis.org/downloads/

CISCO BINARY GAME http://forums.cisco.com/CertCom/game/binary_game_page.htm

BINARY UNITShttp://www.teach-ict.com/gcse_new/computer%20systems/storage_units/miniweb/index.htm