Binary

1
Binary

• Converting to and from decimal

2
Decimal

• We normally use the decimal (denary) system, also
  called base 10
• There are 10 different symbols (digits)
• 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
• To count higher than nine we re-use the symbols
  by putting them in columns
• The value of a symbol depends on its position

3
Decimal positions
Eight thousand two hundred and fifty three
4
Binary

• Computers use the binary system, also called base
  2
• There are two different symbols (digits)
• 0, 1
• To count higher than one we re-use the symbols by
  putting them in columns
• The value of a symbol depends on its position

5
Binary positions
One eight, one four, no twos and one unit That
makes thirteen
6
Counting in binary and decimal
7
Why do computers use binary?

• Computer components that store or handle data are
  often two-state devices
• This is like a switch that can be on or off
• A memory unit could exist in two voltage states,
  high or low
• A voltage on a cable could be high or low
• A light could be on or off
• Two states can be coded by binary 0 and 1

8
Why am I learning about binary?

• In your Cisco course, you will learn about IP
  addresses and how to split up a network into
  subnets
• You need to work out subnet addresses and
  workstation addresses
• For this you need to use binary

9
Bytes or octets

• We often handle binary digits (bits) in groups of
  eight
• Sometimes these groups are called bytes
• Sometimes they are called octets
• We shall often be calling them octets
• Examples of octets
• 00101101
• 10110010

10
Convert binary to decimal
Convert 11001010 binary to decimal Write in the
binary digits under their values
11
Convert binary to decimal
Convert 11001010 binary to decimal Write in the
binary digits under their values Next write in
the value for each binary 1 digit
12
Convert binary to decimal
Convert 11001010 binary to decimal Write in the
binary digits under their values Next write in
the value for each binary 1 digit Add up the
values 128 64 8 2 202
13
One for you to try

• Convert 10010101 from binary (base 2) to decimal
  (base 10)

14
Answer

• Convert 10010101 from binary (base 2) to decimal
  (base 10)

128 16 4 1 149
15
Convert 185 decimal to binary
Convert 185 decimal to binary Can you take 128
from 185? Yes. Put 1 under 128 What is left?
185-128 57
16
Convert 185 decimal to binary
We have 57 left Can you take 64 from 57? No. Put
0 under 64 What is left? Still 57
17
Convert 185 decimal to binary
We have 57 left Can you take 32 from 57? Yes. Put
1 under 32 What is left? 57 32 25
18
Convert 185 decimal to binary
We have 25 left Can you take 16 from 25? Yes. Put
1 under 16 What is left? 25 16 9
19
Convert 185 decimal to binary
We have 9 left Can you take 8 from 9? Yes. Put 1
under 8 What is left? 9 8 1
20
Convert 185 decimal to binary
Wwe have 1 left Can you take 4 from 1? No. Put 0
under 4 What is left? Still 1
21
Convert 185 decimal to binary
We have 1 left Can you take 2 from 1? No. Put 0
under 2 What is left? Still 1
22
Convert 185 decimal to binary
We have 1 left Can you take 1 from 1? Yes. Put 1
under 1 What is left? Nothing. Finished.
23
Convert 185 decimal to binary
185 decimal is 10111001 binary
24
Convert decimal to binary
Check write in the values of the 1 digits and
add them up 128 32 16 8 1 185 Thats
the number we started with. Its correct.
25
One for you to try

• Convert 248 from decimal to binary
• Check your answer

26
Answer

• Convert 248 from decimal to binary
• Check your answer

128 64 32 16 8 248 So 11111000 is
correct.
27

• End